TSTP Solution File: SWW246+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW246+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:22:25 EDT 2023
% Result : Theorem 23.61s 6.72s
% Output : Refutation 25.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1325
% Syntax : Number of formulae : 2526 ( 495 unt; 126 typ; 0 def)
% Number of atoms : 6360 (2373 equ; 0 cnn)
% Maximal formula atoms : 17 ( 2 avg)
% Number of connectives : 42198 ( 558 ~; 145 |; 502 &;37680 @)
% ( 196 <=>;3117 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 185 ( 185 >; 0 *; 0 +; 0 <<)
% Number of symbols : 128 ( 126 usr; 9 con; 0-5 aty)
% Number of variables : 6073 ( 0 ^;6033 !; 40 ?;6073 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_Groups_Ozero__class_Ozero_type,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
thf(t_a_type,type,
t_a: $i ).
thf(tc_Nat_Onat_type,type,
tc_Nat_Onat: $i ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_Groups_Oplus__class_Oplus_type,type,
c_Groups_Oplus__class_Oplus: $i > $i ).
thf(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize_type,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize: $i > $i > $i ).
thf(c_Groups_Oone__class_Oone_type,type,
c_Groups_Oone__class_Oone: $i > $i ).
thf(tc_Polynomial_Opoly_type,type,
tc_Polynomial_Opoly: $i > $i ).
thf(c_Polynomial_Opoly_type,type,
c_Polynomial_Opoly: $i > $i > $i ).
thf(c_Groups_Otimes__class_Otimes_type,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
thf(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: $i > $i ).
thf(c_Polynomial_OpCons_type,type,
c_Polynomial_OpCons: $i > $i ).
thf(class_Rings_Oidom_type,type,
class_Rings_Oidom: $i > $o ).
thf(class_Groups_Omonoid__add_type,type,
class_Groups_Omonoid__add: $i > $o ).
thf(class_Fields_Ofield_type,type,
class_Fields_Ofield: $i > $o ).
thf(c_Polynomial_Opdivmod__rel_type,type,
c_Polynomial_Opdivmod__rel: $i > $i > $i > $i > $i > $o ).
thf(c_Divides_Odiv__class_Omod_type,type,
c_Divides_Odiv__class_Omod: $i > $i > $i > $i ).
thf(class_Divides_Osemiring__div_type,type,
class_Divides_Osemiring__div: $i > $o ).
thf(c_Divides_Odiv__class_Odiv_type,type,
c_Divides_Odiv__class_Odiv: $i > $i > $i > $i ).
thf(tc_Int_Oint_type,type,
tc_Int_Oint: $i ).
thf(class_Fields_Ofield__inverse__zero_type,type,
class_Fields_Ofield__inverse__zero: $i > $o ).
thf(c_Groups_Ouminus__class_Ouminus_type,type,
c_Groups_Ouminus__class_Ouminus: $i > $i ).
thf(c_Rings_Oinverse__class_Odivide_type,type,
c_Rings_Oinverse__class_Odivide: $i > $i ).
thf(class_Orderings_Opreorder_type,type,
class_Orderings_Opreorder: $i > $o ).
thf(c_Orderings_Oord__class_Oless_type,type,
c_Orderings_Oord__class_Oless: $i > $i > $i > $o ).
thf(class_Rings_Osemiring__0_type,type,
class_Rings_Osemiring__0: $i > $o ).
thf(class_Rings_Olinordered__semidom_type,type,
class_Rings_Olinordered__semidom: $i > $o ).
thf(c_Nat_Osemiring__1__class_Oof__nat_type,type,
c_Nat_Osemiring__1__class_Oof__nat: $i > $i > $i ).
thf(class_Rings_Ocomm__semiring__1_type,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(c_Rings_Odvd__class_Odvd_type,type,
c_Rings_Odvd__class_Odvd: $i > $i ).
thf(class_RealVector_Oreal__normed__field_type,type,
class_RealVector_Oreal__normed__field: $i > $o ).
thf(c_Deriv_Oderiv_type,type,
c_Deriv_Oderiv: $i > $i > $i > $i > $o ).
thf(c_Groups_Ominus__class_Ominus_type,type,
c_Groups_Ominus__class_Ominus: $i > $i ).
thf(class_Groups_Ozero_type,type,
class_Groups_Ozero: $i > $o ).
thf(c_Polynomial_Odegree_type,type,
c_Polynomial_Odegree: $i > $i > $i ).
thf(c_Polynomial_Omonom_type,type,
c_Polynomial_Omonom: $i > $i > $i > $i ).
thf(class_Rings_Oring__no__zero__divisors_type,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
thf(class_Rings_Ocomm__semiring_type,type,
class_Rings_Ocomm__semiring: $i > $o ).
thf(c_Polynomial_Ocoeff_type,type,
c_Polynomial_Ocoeff: $i > $i > $i ).
thf(class_Orderings_Oord_type,type,
class_Orderings_Oord: $i > $o ).
thf(tc_HOL_Obool_type,type,
tc_HOL_Obool: $i ).
thf(class_Groups_Ouminus_type,type,
class_Groups_Ouminus: $i > $o ).
thf(class_Rings_Osemiring__1_type,type,
class_Rings_Osemiring__1: $i > $o ).
thf(c_Nat_Osemiring__1__class_Oof__nat__aux_type,type,
c_Nat_Osemiring__1__class_Oof__nat__aux: $i > $i > $i > $i > $i ).
thf(c_Nat_OSuc_type,type,
c_Nat_OSuc: $i ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(class_Groups_Oab__semigroup__add_type,type,
class_Groups_Oab__semigroup__add: $i > $o ).
thf(c_Polynomial_Opoly__gcd_type,type,
c_Polynomial_Opoly__gcd: $i > $i > $i > $i ).
thf(c_Polynomial_Osmult_type,type,
c_Polynomial_Osmult: $i > $i ).
thf(c_Rings_Oinverse__class_Oinverse_type,type,
c_Rings_Oinverse__class_Oinverse: $i > $i ).
thf(c_Orderings_Oord__class_Oless__eq_type,type,
c_Orderings_Oord__class_Oless__eq: $i > $i > $i > $o ).
thf(class_Groups_Ominus_type,type,
class_Groups_Ominus: $i > $o ).
thf(tc_fun_type,type,
tc_fun: $i > $i > $i ).
thf(class_Rings_Omult__zero_type,type,
class_Rings_Omult__zero: $i > $o ).
thf(class_Rings_Ocomm__semiring__0_type,type,
class_Rings_Ocomm__semiring__0: $i > $o ).
thf(class_Divides_Oring__div_type,type,
class_Divides_Oring__div: $i > $o ).
thf(class_Rings_Ocomm__ring_type,type,
class_Rings_Ocomm__ring: $i > $o ).
thf(class_Power_Opower_type,type,
class_Power_Opower: $i > $o ).
thf(class_Rings_Olinordered__ring_type,type,
class_Rings_Olinordered__ring: $i > $o ).
thf(c_Polynomial_OAbs__poly_type,type,
c_Polynomial_OAbs__poly: $i > $i > $i ).
thf(class_Nat_Osemiring__char__0_type,type,
class_Nat_Osemiring__char__0: $i > $o ).
thf(class_Groups_Oab__group__add_type,type,
class_Groups_Oab__group__add: $i > $o ).
thf(class_Groups_Ocancel__semigroup__add_type,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
thf(class_Groups_Ocancel__comm__monoid__add_type,type,
class_Groups_Ocancel__comm__monoid__add: $i > $o ).
thf(class_Groups_Oab__semigroup__mult_type,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
thf(class_Groups_Ocomm__monoid__add_type,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
thf(class_Groups_Olinordered__ab__group__add_type,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
thf(class_Rings_Odivision__ring_type,type,
class_Rings_Odivision__ring: $i > $o ).
thf(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(class_Groups_Omonoid__mult_type,type,
class_Groups_Omonoid__mult: $i > $o ).
thf(class_Groups_Ocancel__ab__semigroup__add_type,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
thf(class_Rings_Ocomm__ring__1_type,type,
class_Rings_Ocomm__ring__1: $i > $o ).
thf(class_Groups_Oordered__ab__group__add_type,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
thf(class_Groups_Ogroup__add_type,type,
class_Groups_Ogroup__add: $i > $o ).
thf(c_COMBB_type,type,
c_COMBB: $i > $i > $i > $i ).
thf(c_Orderings_Oorder_Ostrict__mono_type,type,
c_Orderings_Oorder_Ostrict__mono: $i > $i > $i > $i > $o ).
thf(c_COMBS_type,type,
c_COMBS: $i > $i > $i > $i ).
thf(c_fconj_type,type,
c_fconj: $i ).
thf(c_fNot_type,type,
c_fNot: $i ).
thf(c_COMBC_type,type,
c_COMBC: $i > $i > $i > $i > $i ).
thf(c_Orderings_Oorder_Omono_type,type,
c_Orderings_Oorder_Omono: $i > $i > $i > $i > $o ).
thf(class_Rings_Oring_type,type,
class_Rings_Oring: $i > $o ).
thf(class_Rings_Olinordered__idom_type,type,
class_Rings_Olinordered__idom: $i > $o ).
thf(class_Rings_Oring__1__no__zero__divisors_type,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
thf(class_Rings_Odvd_type,type,
class_Rings_Odvd: $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_Rings_Osemiring_type,type,
class_Rings_Osemiring: $i > $o ).
thf(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_type,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
thf(class_Rings_Ozero__neq__one_type,type,
class_Rings_Ozero__neq__one: $i > $o ).
thf(class_Groups_Ocomm__monoid__mult_type,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
thf(class_Groups_Oordered__ab__semigroup__add__imp__le_type,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
thf(class_Groups_Oone_type,type,
class_Groups_Oone: $i > $o ).
thf(class_Rings_Olinordered__semiring__strict_type,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
thf(class_Rings_Ono__zero__divisors_type,type,
class_Rings_Ono__zero__divisors: $i > $o ).
thf(c_If_type,type,
c_If: $i > $i ).
thf(c_fequal_type,type,
c_fequal: $i > $i ).
thf(class_Rings_Oordered__ring_type,type,
class_Rings_Oordered__ring: $i > $o ).
thf(class_Lattices_Oboolean__algebra_type,type,
class_Lattices_Oboolean__algebra: $i > $o ).
thf(c_Polynomial_Opos__poly_type,type,
c_Polynomial_Opos__poly: $i > $i > $o ).
thf(class_Rings_Oring__1_type,type,
class_Rings_Oring__1: $i > $o ).
thf(class_Rings_Olinordered__comm__semiring__strict_type,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
thf(class_Int_Oring__char__0_type,type,
class_Int_Oring__char__0: $i > $o ).
thf(class_Orderings_Owellorder_type,type,
class_Orderings_Owellorder: $i > $o ).
thf(c_Orderings_Oord__class_OLeast_type,type,
c_Orderings_Oord__class_OLeast: $i > $i > $i ).
thf(class_Rings_Olinordered__ring__strict_type,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
thf(class_Rings_Odivision__ring__inverse__zero_type,type,
class_Rings_Odivision__ring__inverse__zero: $i > $o ).
thf(class_Groups_Oordered__cancel__ab__semigroup__add_type,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
thf(class_Groups_Oordered__comm__monoid__add_type,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
thf(class_RealVector_Oreal__normed__algebra_type,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
thf(c_Polynomial_Osynthetic__div_type,type,
c_Polynomial_Osynthetic__div: $i > $i > $i > $i ).
thf(class_Fields_Olinordered__field_type,type,
class_Fields_Olinordered__field: $i > $o ).
thf(c_Nat_Onat_Onat__case_type,type,
c_Nat_Onat_Onat__case: $i > $i > $i > $i ).
thf(c_COMBI_type,type,
c_COMBI: $i > $i ).
thf(class_Fields_Olinordered__field__inverse__zero_type,type,
class_Fields_Olinordered__field__inverse__zero: $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_Polynomial_Opcompose_type,type,
c_Polynomial_Opcompose: $i > $i > $i > $i ).
thf(c_Polynomial_Opoly__rec_type,type,
c_Polynomial_Opoly__rec: $i > $i > $i > $i > $i > $i ).
thf(c_COMBK_type,type,
c_COMBK: $i > $i > $i ).
thf(v_p_type,type,
v_p: $i ).
thf(c_Polynomial_Oorder_type,type,
c_Polynomial_Oorder: $i > $i > $i > $i ).
thf(class_Lattices_Oab__semigroup__idem__mult_type,type,
class_Lattices_Oab__semigroup__idem__mult: $i > $o ).
thf(c_Transcendental_Odiffs_type,type,
c_Transcendental_Odiffs: $i > $i > $i > $i ).
thf(c_Groups_Osgn__class_Osgn_type,type,
c_Groups_Osgn__class_Osgn: $i > $i > $i ).
thf(class_RealVector_Oreal__field_type,type,
class_RealVector_Oreal__field: $i > $o ).
thf(80,axiom,
! [A: $i,B: $i] :
( ( class_Divides_Osemiring__div @ B )
=> ( ( c_Divides_Odiv__class_Omod @ B @ A @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__self) ).
thf(1411,plain,
! [A: $i,B: $i] :
( ( class_Divides_Osemiring__div @ B )
=> ( ( c_Divides_Odiv__class_Omod @ B @ A @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(1184,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ A ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__commute) ).
thf(5116,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).
thf(1188,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__power__inverse) ).
thf(5136,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188]) ).
thf(328,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ A ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ E ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ E ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ E ) @ C ) ) ) )
=> ( ( ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) ) )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ D @ C ) @ ( c_Polynomial_Odegree @ D @ C ) )
= ( c_Groups_Ozero__class_Ozero @ D ) ) )
& ( ~ ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) ) )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ D @ C ) @ ( c_Polynomial_Odegree @ D @ C ) )
= ( c_Groups_Oone__class_Oone @ D ) ) ) )
=> ( ( c_Polynomial_Opoly__gcd @ D @ B @ A )
= C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__unique) ).
thf(2072,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ A ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ E ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ E ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ E ) @ C ) ) ) )
=> ( ( ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) ) )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ D @ C ) @ ( c_Polynomial_Odegree @ D @ C ) )
= ( c_Groups_Ozero__class_Ozero @ D ) ) )
& ( ~ ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) ) )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ D @ C ) @ ( c_Polynomial_Odegree @ D @ C ) )
= ( c_Groups_Oone__class_Oone @ D ) ) ) )
=> ( ( c_Polynomial_Opoly__gcd @ D @ B @ A )
= C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(824,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_RealVector_Oreal__normed__field @ F )
=> ( ( c_Deriv_Oderiv @ F @ E @ D @ C )
=> ( ( c_Deriv_Oderiv @ F @ B @ D @ A )
=> ( c_Deriv_Oderiv @ F @ ( hAPP @ ( hAPP @ ( c_COMBS @ F @ F @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ ( tc_fun @ F @ F ) @ F ) @ ( c_Groups_Otimes__class_Otimes @ F ) ) @ E ) ) @ B ) @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( hAPP @ E @ D ) ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ C ) @ ( hAPP @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__mult_H) ).
thf(3798,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_RealVector_Oreal__normed__field @ F )
=> ( ( c_Deriv_Oderiv @ F @ E @ D @ C )
=> ( ( c_Deriv_Oderiv @ F @ B @ D @ A )
=> ( c_Deriv_Oderiv @ F @ ( hAPP @ ( hAPP @ ( c_COMBS @ F @ F @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ ( tc_fun @ F @ F ) @ F ) @ ( c_Groups_Otimes__class_Otimes @ F ) ) @ E ) ) @ B ) @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( hAPP @ E @ D ) ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ C ) @ ( hAPP @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(784,axiom,
class_Divides_Osemiring__div @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Divides_Osemiring__div) ).
thf(3666,plain,
class_Divides_Osemiring__div @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(562,axiom,
class_Orderings_Oorder @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
thf(2876,plain,
class_Orderings_Oorder @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(796,axiom,
( ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__1) ).
thf(3698,plain,
( ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(438,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__field @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide_Ozero) ).
thf(2463,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__field @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(466,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( 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(2544,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( 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)],[466]) ).
thf(857,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( 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(3927,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(1080,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(4728,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)],[1080]) ).
thf(241,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Owellorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Orderings_Oord__class_OLeast @ C @ A ) )
=> ~ ( hBOOL @ ( hAPP @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__Least) ).
thf(1818,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Owellorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Orderings_Oord__class_OLeast @ C @ A ) )
=> ~ ( hBOOL @ ( hAPP @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(375,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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__pos) ).
thf(2250,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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(1039,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel__disj) ).
thf(4560,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ) )
& ( ( ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( 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)],[1039]) ).
thf(1001,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(4447,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)],[1001]) ).
thf(870,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(3962,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)],[870]) ).
thf(1176,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ B )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ B ) @ A ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ B ) @ A ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__self__if) ).
thf(5088,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ B )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ B ) @ A ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ B ) @ A ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176]) ).
thf(63,axiom,
class_Groups_Ocomm__monoid__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).
thf(1369,plain,
class_Groups_Ocomm__monoid__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(568,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__eq__divide) ).
thf(2889,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(1041,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( ( hAPP @ ( 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(4571,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( ( hAPP @ ( 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)],[1041]) ).
thf(1002,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 ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) ).
thf(4450,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 ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(400,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Orderings_Opreorder @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Opreorder) ).
thf(2341,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Orderings_Opreorder @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(336,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( 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(2109,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( 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)],[336]) ).
thf(341,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(2131,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)],[341]) ).
thf(715,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(3399,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)],[715]) ).
thf(378,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ ( hAPP @ ( 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(2263,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ ( hAPP @ ( 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)],[378]) ).
thf(858,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(3930,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)],[858]) ).
thf(761,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 ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__less__one) ).
thf(3581,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 ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(1110,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(4852,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)],[1110]) ).
thf(840,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).
thf(3863,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(252,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( class_Fields_Ofield @ G )
=> ( ( c_Polynomial_Opdivmod__rel @ G @ F @ E @ D @ C )
=> ( ( c_Polynomial_Opdivmod__rel @ G @ F @ E @ B @ A )
=> ( D = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__unique__div) ).
thf(1850,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( class_Fields_Ofield @ G )
=> ( ( c_Polynomial_Opdivmod__rel @ G @ F @ E @ D @ C )
=> ( ( c_Polynomial_Opdivmod__rel @ G @ F @ E @ B @ A )
=> ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(471,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) @ ( hAPP @ 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(2559,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(732,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ C ) @ B )
= A )
<=> ( ( ( B
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) )
& ( ( B
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__eq__eq) ).
thf(3449,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ C ) @ B )
= A )
=> ( ( ( B
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) )
& ( ( B
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) )
& ( ( ( ( B
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) )
& ( ( B
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ C ) @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(888,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(4015,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)],[888]) ).
thf(288,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__bin__lemma) ).
thf(1950,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(136,axiom,
! [A: $i,B: $i] :
( ( class_Divides_Osemiring__div @ B )
=> ( ( c_Divides_Odiv__class_Odiv @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__by__0) ).
thf(1549,plain,
! [A: $i,B: $i] :
( ( class_Divides_Osemiring__div @ B )
=> ( ( c_Divides_Odiv__class_Odiv @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(278,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Divides_Odiv__class_Odiv @ D @ B @ C ) ) @ A )
= ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__div__mult) ).
thf(1924,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Divides_Odiv__class_Odiv @ D @ B @ C ) ) @ A )
= ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(334,axiom,
! [A: $i,B: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( hAPP @ c_Nat_OSuc @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__antisym) ).
thf(2104,plain,
! [A: $i,B: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( hAPP @ c_Nat_OSuc @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(694,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 ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ 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(3317,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 ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ 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 ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(971,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( c_Groups_Ozero__class_Ozero @ B )
= ( hAPP @ ( hAPP @ ( 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(4339,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( ( c_Groups_Ozero__class_Ozero @ B )
= ( hAPP @ ( hAPP @ ( 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 )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(262,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(1882,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)],[262]) ).
thf(488,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Divides_Osemiring__div @ F )
=> ( ( ( c_Divides_Odiv__class_Omod @ F @ E @ D )
= ( c_Divides_Odiv__class_Omod @ F @ C @ D ) )
=> ( ( ( c_Divides_Odiv__class_Omod @ F @ B @ D )
= ( c_Divides_Odiv__class_Omod @ F @ A @ D ) )
=> ( ( c_Divides_Odiv__class_Omod @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ B ) @ D )
= ( c_Divides_Odiv__class_Omod @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ C ) @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__cong) ).
thf(2622,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Divides_Osemiring__div @ F )
=> ( ( ( c_Divides_Odiv__class_Omod @ F @ E @ D )
= ( c_Divides_Odiv__class_Omod @ F @ C @ D ) )
=> ( ( ( c_Divides_Odiv__class_Omod @ F @ B @ D )
= ( c_Divides_Odiv__class_Omod @ F @ A @ D ) )
=> ( ( c_Divides_Odiv__class_Omod @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ B ) @ D )
= ( c_Divides_Odiv__class_Omod @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ C ) @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ominus @ E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ E ) ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__apply) ).
thf(1522,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ominus @ E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ E ) ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(852,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(3912,plain,
class_Groups_Ocancel__ab__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(414,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( hAPP @ c_Nat_OSuc @ A ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ? [C: $i] :
( ( B
= ( hAPP @ 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(2380,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( hAPP @ c_Nat_OSuc @ A ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ? [C: $i] :
( ( B
= ( hAPP @ 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
= ( hAPP @ c_Nat_OSuc @ C ) )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A ) ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(554,axiom,
( ( class_Rings_Oidom @ t_a )
=> ~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant @ t_a @ t_a @ ( c_Polynomial_Opoly @ t_a @ v_p ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_assms) ).
thf(2854,plain,
( ( class_Rings_Oidom @ t_a )
=> ~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant @ t_a @ t_a @ ( c_Polynomial_Opoly @ t_a @ v_p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(1052,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_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ A ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__power__div__base) ).
thf(4623,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_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ A ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zminus2) ).
thf(1305,plain,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(1047,axiom,
class_Rings_Ocomm__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).
thf(4592,plain,
class_Rings_Ocomm__semiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).
thf(109,axiom,
class_Groups_Ominus @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ominus) ).
thf(1486,plain,
class_Groups_Ominus @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(407,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__ring @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__diff__left) ).
thf(2363,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__ring @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(254,axiom,
class_Rings_Olinordered__ring__strict @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).
thf(1855,plain,
class_Rings_Olinordered__ring__strict @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(450,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( 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(2495,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( 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)],[450]) ).
thf(673,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oab__group__add @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ B ) ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__poly__code_I2_J) ).
thf(3230,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oab__group__add @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ B ) ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(1170,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ C @ B ) ) @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( 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_mod__mult__distrib) ).
thf(5069,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ C @ B ) ) @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( 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)],[1170]) ).
thf(416,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Orderings_Oord @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oord) ).
thf(2395,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Orderings_Oord @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(93,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ B ) @ ( c_Polynomial_Odegree @ C @ A ) )
=> ( ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ C ) @ B @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__poly__less) ).
thf(1443,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ B ) @ ( c_Polynomial_Odegree @ C @ A ) )
=> ( ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ C ) @ B @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(532,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(2776,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)],[532]) ).
thf(235,axiom,
class_Divides_Oring__div @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Oring__div) ).
thf(1808,plain,
class_Divides_Oring__div @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(496,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__field @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide_Oadd) ).
thf(2659,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__field @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(588,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) )
<=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ! [D: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ D ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split) ).
thf(2953,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ! [D: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ D ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ! [D: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ D ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) )
=> ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(75,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Groups_Ocancel__comm__monoid__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Ocancel__comm__monoid__add) ).
thf(1401,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Groups_Ocancel__comm__monoid__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) ) @ ( c_Polynomial_Opoly__gcd @ C @ B @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__dvd1) ).
thf(1422,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) ) @ ( c_Polynomial_Opoly__gcd @ C @ B @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(586,axiom,
! [A: $i,B: $i] :
( ( class_Divides_Osemiring__div @ B )
=> ( ( c_Divides_Odiv__class_Omod @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__by__1) ).
thf(2947,plain,
! [A: $i,B: $i] :
( ( class_Divides_Osemiring__div @ B )
=> ( ( c_Divides_Odiv__class_Omod @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(143,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__ab__group__add @ E )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
<=> ( c_Orderings_Oord__class_Oless @ E @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__less) ).
thf(1569,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__ab__group__add @ E )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ B ) @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( c_Orderings_Oord__class_Oless @ E @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ E @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(284,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__field @ E )
=> ( ( c_Deriv_Oderiv @ E @ D @ C @ B )
=> ( ( B = A )
=> ( c_Deriv_Oderiv @ E @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Deriv_Olemma__DERIV__subst) ).
thf(1939,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__field @ E )
=> ( ( c_Deriv_Oderiv @ E @ D @ C @ B )
=> ( ( B = A )
=> ( c_Deriv_Oderiv @ E @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(500,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_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) @ C ) ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zmult2__eq) ).
thf(2671,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_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) @ C ) ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(133,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Ozero__neq__one @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Ozero__neq__one) ).
thf(1544,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Ozero__neq__one @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(1050,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(4603,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)],[1050]) ).
thf(606,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ 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_Odiff__right) ).
thf(3012,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ 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)],[606]) ).
thf(184,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Divides_Oring__div @ F )
=> ( ( ( c_Divides_Odiv__class_Omod @ F @ E @ D )
= ( c_Divides_Odiv__class_Omod @ F @ C @ D ) )
=> ( ( ( c_Divides_Odiv__class_Omod @ F @ B @ D )
= ( c_Divides_Odiv__class_Omod @ F @ A @ D ) )
=> ( ( c_Divides_Odiv__class_Omod @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ F ) @ E ) @ B ) @ D )
= ( c_Divides_Odiv__class_Omod @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ F ) @ C ) @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__diff__cong) ).
thf(1671,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Divides_Oring__div @ F )
=> ( ( ( c_Divides_Odiv__class_Omod @ F @ E @ D )
= ( c_Divides_Odiv__class_Omod @ F @ C @ D ) )
=> ( ( ( c_Divides_Odiv__class_Omod @ F @ B @ D )
= ( c_Divides_Odiv__class_Omod @ F @ A @ D ) )
=> ( ( c_Divides_Odiv__class_Omod @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ F ) @ E ) @ B ) @ D )
= ( c_Divides_Odiv__class_Omod @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ F ) @ C ) @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(905,axiom,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
= ( hAPP @ ( hAPP @ ( 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(4090,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
= ( hAPP @ ( hAPP @ ( 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)],[905]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Oring__div @ C )
=> ( ( c_Divides_Odiv__class_Omod @ C @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ C @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ ( c_Divides_Odiv__class_Omod @ C @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__minus__eq) ).
thf(1310,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Oring__div @ C )
=> ( ( c_Divides_Odiv__class_Omod @ C @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ C @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ ( c_Divides_Odiv__class_Omod @ C @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(519,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 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ C ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B ) ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ A ) )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ C ) @ B ) @ A ) ) ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Deriv_Oinverse__diff__inverse) ).
thf(2740,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 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ C ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B ) ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ A ) )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ C ) @ B ) @ A ) ) ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(305,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ 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_zero__less__int__conv) ).
thf(1999,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ 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_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__field @ E )
=> ( ( c_Deriv_Oderiv @ E @ D @ C @ B )
=> ( ( c_Deriv_Oderiv @ E @ D @ C @ A )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__unique) ).
thf(1233,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__field @ E )
=> ( ( c_Deriv_Oderiv @ E @ D @ C @ B )
=> ( ( c_Deriv_Oderiv @ E @ D @ C @ A )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(944,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(4247,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)],[944]) ).
thf(692,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(3313,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Oidom @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(997,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__cancel2) ).
thf(4435,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(1145,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(4980,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)],[1145]) ).
thf(1090,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ C )
=> ( ( B
= ( hAPP @ ( hAPP @ ( 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(4762,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ C )
=> ( ( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).
thf(686,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( ( ( B
= ( hAPP @ 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
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__is__add) ).
thf(3276,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( ( B
= ( hAPP @ 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
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) )
& ( ( ( ( B
= ( hAPP @ 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
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
=> ( ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(197,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Oring__div @ D )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ C ) @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ ( c_Divides_Odiv__class_Omod @ D @ C @ A ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__diff__left__eq) ).
thf(1705,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Oring__div @ D )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ C ) @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ ( c_Divides_Odiv__class_Omod @ D @ C @ A ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(608,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oab__group__add @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ E ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__pCons) ).
thf(3017,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oab__group__add @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ E ) ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(228,axiom,
! [A: $i,B: $i] :
( ( class_Divides_Osemiring__div @ B )
=> ( ( c_Divides_Odiv__class_Omod @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__0) ).
thf(1788,plain,
! [A: $i,B: $i] :
( ( class_Divides_Osemiring__div @ B )
=> ( ( c_Divides_Odiv__class_Omod @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(88,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Ofield @ B )
=> ( ( c_Polynomial_Opoly__gcd @ B @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
= ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ B ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ B @ A ) @ ( c_Polynomial_Odegree @ B @ A ) ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd_Osimps_I1_J) ).
thf(1426,plain,
! [A: $i,B: $i] :
( ( class_Fields_Ofield @ B )
=> ( ( c_Polynomial_Opoly__gcd @ B @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
= ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ B ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ B @ A ) @ ( c_Polynomial_Odegree @ B @ A ) ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(748,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__commute) ).
thf(3530,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(986,axiom,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ c_fNot @ A ) )
| ~ ( hBOOL @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__1) ).
thf(4403,plain,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ c_fNot @ A ) )
| ~ ( hBOOL @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(729,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(3439,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)],[729]) ).
thf(619,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(3049,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)],[619]) ).
thf(809,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult1__eq) ).
thf(3745,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(1082,axiom,
class_Power_Opower @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Power_Opower) ).
thf(4739,plain,
class_Power_Opower @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).
thf(603,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Divides_Odiv__class_Omod @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__mult1) ).
thf(3004,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Divides_Odiv__class_Omod @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(316,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__zero__left) ).
thf(2035,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(1108,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(4839,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)],[1108]) ).
thf(1060,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ B ) @ A )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__eq__0) ).
thf(4647,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ B ) @ A )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).
thf(643,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring @ C )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ C @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) ) @ B ) ) @ A )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ ( hAPP @ ( c_Polynomial_Opoly @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__minus) ).
thf(3135,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring @ C )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ C @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) ) @ B ) ) @ A )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ ( hAPP @ ( c_Polynomial_Opoly @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(864,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( c_Divides_Odiv__class_Omod @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ B )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self1__is__0) ).
thf(3942,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( c_Divides_Odiv__class_Omod @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ B )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(890,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(4026,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)],[890]) ).
thf(617,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) )
= ( hAPP @ ( 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(3044,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(211,axiom,
class_Groups_Ouminus @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ouminus) ).
thf(1735,plain,
class_Groups_Ouminus @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(910,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(4110,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)],[910]) ).
thf(1027,axiom,
! [A: $i] :
( ( class_Groups_Oab__group__add @ A )
=> ( ( hAPP @ ( 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(4528,plain,
! [A: $i] :
( ( class_Groups_Oab__group__add @ A )
=> ( ( hAPP @ ( 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)],[1027]) ).
thf(434,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( c_Divides_Odiv__class_Omod @ 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_Divides_Odiv__class_Omod @ D @ C @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__mult2) ).
thf(2448,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( c_Divides_Odiv__class_Omod @ 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_Divides_Odiv__class_Omod @ D @ C @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(583,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ ( c_Polynomial_Opoly__gcd @ C @ B @ A ) ) @ ( c_Polynomial_Odegree @ C @ ( c_Polynomial_Opoly__gcd @ C @ B @ A ) ) )
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( ~ ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ ( c_Polynomial_Opoly__gcd @ C @ B @ A ) ) @ ( c_Polynomial_Odegree @ C @ ( c_Polynomial_Opoly__gcd @ C @ B @ A ) ) )
= ( c_Groups_Oone__class_Oone @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__monic) ).
thf(2933,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ ( c_Polynomial_Opoly__gcd @ C @ B @ A ) ) @ ( c_Polynomial_Odegree @ C @ ( c_Polynomial_Opoly__gcd @ C @ B @ A ) ) )
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( ~ ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ ( c_Polynomial_Opoly__gcd @ C @ B @ A ) ) @ ( c_Polynomial_Odegree @ C @ ( c_Polynomial_Opoly__gcd @ C @ B @ A ) ) )
= ( c_Groups_Oone__class_Oone @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(1061,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(4650,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)],[1061]) ).
thf(353,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( hAPP @ ( hAPP @ ( 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(2168,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( ( hAPP @ ( hAPP @ ( 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 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( B = A )
<=> ! [D: $i] :
( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ B ) @ D )
= ( hAPP @ ( c_Polynomial_Ocoeff @ C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_expand__poly__eq) ).
thf(1260,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( ( B = A )
=> ! [D: $i] :
( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ B ) @ D )
= ( hAPP @ ( c_Polynomial_Ocoeff @ C @ A ) @ D ) ) )
& ( ! [D: $i] :
( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ B ) @ D )
= ( hAPP @ ( c_Polynomial_Ocoeff @ C @ A ) @ D ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(680,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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(3253,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( 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)],[680]) ).
thf(301,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ouminus @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ D ) ) @ B ) @ A )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ D ) @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__Compl__def) ).
thf(1988,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ouminus @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ D ) ) @ B ) @ A )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ D ) @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(719,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(3414,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)],[719]) ).
thf(52,axiom,
class_Nat_Osemiring__char__0 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Nat_Osemiring__char__0) ).
thf(1342,plain,
class_Nat_Osemiring__char__0 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(1195,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) )
<=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ C @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ! [D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ E @ A )
=> ( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ D ) ) @ E ) )
=> ( hBOOL @ ( hAPP @ C @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mod) ).
thf(5161,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ C @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ! [D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ E @ A )
=> ( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ D ) ) @ E ) )
=> ( hBOOL @ ( hAPP @ C @ E ) ) ) ) ) ) )
& ( ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ C @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ! [D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ E @ A )
=> ( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ D ) ) @ E ) )
=> ( hBOOL @ ( hAPP @ C @ E ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195]) ).
thf(117,axiom,
! [A: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__self) ).
thf(1507,plain,
! [A: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield__inverse__zero @ C )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__divide__right) ).
thf(1222,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield__inverse__zero @ C )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(406,axiom,
! [A: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__1) ).
thf(2360,plain,
! [A: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(675,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ C )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__eq__imp) ).
thf(3236,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ C )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(778,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(3634,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)],[778]) ).
thf(1018,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_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__diff) ).
thf(4496,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_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(629,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(3088,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)],[629]) ).
thf(276,axiom,
class_Power_Opower @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Power_Opower) ).
thf(1921,plain,
class_Power_Opower @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(566,axiom,
class_Groups_Omonoid__mult @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).
thf(2886,plain,
class_Groups_Omonoid__mult @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(105,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
| ( B = A )
| ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
thf(1475,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
| ( B = A )
| ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(418,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(2400,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)],[418]) ).
thf(461,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( hAPP @ ( hAPP @ ( 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(2531,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( hAPP @ ( hAPP @ ( 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)],[461]) ).
thf(791,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 ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__gt1) ).
thf(3688,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 ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(264,axiom,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zmod) ).
thf(1887,plain,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(815,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(3766,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)],[815]) ).
thf(429,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ B ) )
=> ( ( ( c_Divides_Odiv__class_Odiv @ D @ B @ C )
= A )
<=> ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__div__eq__mult) ).
thf(2432,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ B ) )
=> ( ( ( ( c_Divides_Odiv__class_Odiv @ D @ B @ C )
= A )
=> ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) )
& ( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) )
=> ( ( c_Divides_Odiv__class_Odiv @ D @ B @ C )
= A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Polynomial_Odegree @ C @ ( c_Polynomial_Omonom @ C @ B @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__monom__eq) ).
thf(1243,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Polynomial_Odegree @ C @ ( c_Polynomial_Omonom @ C @ B @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(854,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).
thf(3915,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(225,axiom,
class_Rings_Oidom @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).
thf(1782,plain,
class_Rings_Oidom @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(744,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ 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_zdiff__zmult__distrib2) ).
thf(3513,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ 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)],[744]) ).
thf(1197,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__left__mono) ).
thf(5195,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197]) ).
thf(690,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ C ) @ A ) @ ( c_Polynomial_Osynthetic__div @ C @ B @ A ) ) )
= ( hAPP @ ( hAPP @ ( 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(3308,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ C ) @ A ) @ ( c_Polynomial_Osynthetic__div @ C @ B @ A ) ) )
= ( hAPP @ ( hAPP @ ( 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)],[690]) ).
thf(282,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Groups_Ocomm__monoid__mult @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Ocomm__monoid__mult) ).
thf(1935,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Groups_Ocomm__monoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(827,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__le__trans) ).
thf(3809,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(62,axiom,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) )
= ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zminus2) ).
thf(1366,plain,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) )
= ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(1066,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ozero @ E )
=> ( ( ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ E ) @ B ) @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__eq__iff) ).
thf(4665,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ozero @ E )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ E ) @ B ) @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ E ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).
thf(966,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Owellorder @ C )
=> ( ( hBOOL @ ( hAPP @ B @ A ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Orderings_Oord__class_OLeast @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_LeastI) ).
thf(4322,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Owellorder @ C )
=> ( ( hBOOL @ ( hAPP @ B @ A ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Orderings_Oord__class_OLeast @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(199,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Groups_Ominus @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Ominus) ).
thf(1709,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Groups_Ominus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(398,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( ( hAPP @ ( hAPP @ ( 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(2328,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(1084,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( 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(4743,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
| ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).
thf(1115,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( c_Polynomial_Opcompose @ D @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ D ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) ) @ ( hAPP @ ( hAPP @ ( 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(4866,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( c_Polynomial_Opcompose @ D @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ D ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) ) @ ( hAPP @ ( hAPP @ ( 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)],[1115]) ).
thf(300,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Oring__div @ D )
=> ( ( ( c_Divides_Odiv__class_Omod @ D @ C @ B )
= ( c_Divides_Odiv__class_Omod @ D @ A @ B ) )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ D ) @ C ) @ B )
= ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__minus__cong) ).
thf(1985,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Oring__div @ D )
=> ( ( ( c_Divides_Odiv__class_Omod @ D @ C @ B )
= ( c_Divides_Odiv__class_Omod @ D @ A @ B ) )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ D ) @ C ) @ B )
= ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(901,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ C @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( 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(4070,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ C @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(367,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 ) @ ( hAPP @ ( hAPP @ ( 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(2217,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 ) @ ( hAPP @ ( hAPP @ ( 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)],[367]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ominus @ E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ E ) ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__diff__def) ).
thf(1323,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ominus @ E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ E ) ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( ( c_Polynomial_Odegree @ C @ ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ C @ B @ A ) )
= ( c_Polynomial_Odegree @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__offset__poly) ).
thf(1511,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( ( c_Polynomial_Odegree @ C @ ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ C @ B @ A ) )
= ( c_Polynomial_Odegree @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(504,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ ( c_Divides_Odiv__class_Omod @ D @ B @ A ) ) @ A )
= ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__simps_I2_J) ).
thf(2682,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ ( c_Divides_Odiv__class_Omod @ D @ B @ A ) ) @ A )
= ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(247,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negative__zle) ).
thf(1832,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(439,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(2466,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)],[439]) ).
thf(838,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( hAPP @ ( 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(3855,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ B ) @ A )
= A )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ B ) @ A )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(942,axiom,
class_Rings_Ozero__neq__one @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).
thf(4243,plain,
class_Rings_Ozero__neq__one @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(847,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( hAPP @ 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(3891,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( hAPP @ 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 @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(1057,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(4637,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)],[1057]) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__trans) ).
thf(1409,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(730,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Divides_Odiv__class_Omod @ D @ C @ A ) ) @ ( c_Divides_Odiv__class_Omod @ D @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__eq) ).
thf(3442,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Divides_Odiv__class_Omod @ D @ C @ A ) ) @ ( c_Divides_Odiv__class_Omod @ D @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(682,axiom,
! [A: $i,B: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( hAPP @ c_Nat_OSuc @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).
thf(3263,plain,
! [A: $i,B: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( hAPP @ c_Nat_OSuc @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( c_Polynomial_Opoly__gcd @ C @ A @ B )
= ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ C ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ C @ A ) @ ( c_Polynomial_Odegree @ C @ A ) ) ) ) @ A ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( c_Polynomial_Opoly__gcd @ C @ A @ B )
= ( c_Polynomial_Opoly__gcd @ C @ B @ ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ C ) @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__code) ).
thf(1287,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( c_Polynomial_Opoly__gcd @ C @ A @ B )
= ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ C ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ C @ A ) @ ( c_Polynomial_Odegree @ C @ A ) ) ) ) @ A ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( c_Polynomial_Opoly__gcd @ C @ A @ B )
= ( c_Polynomial_Opoly__gcd @ C @ B @ ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ C ) @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(1034,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__ab__semigroup__add @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__imp__eq) ).
thf(4546,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__ab__semigroup__add @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(508,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__int__left) ).
thf(2698,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(221,axiom,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zdiv__equality_H) ).
thf(1760,plain,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__refl) ).
thf(1298,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(270,axiom,
! [A: $i] :
( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zero) ).
thf(1907,plain,
! [A: $i] :
( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(452,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__add__strict) ).
thf(2501,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__dvd__conv_I2_J) ).
thf(1313,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(954,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield__inverse__zero @ C )
=> ( ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B ) ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__mult__distrib) ).
thf(4275,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield__inverse__zero @ C )
=> ( ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B ) ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(1187,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ B )
=> ( ( ( hAPP @ ( 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(5130,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ B )
=> ( ( ( ( hAPP @ ( 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 ) )
=> ( ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1187]) ).
thf(358,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(2185,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)],[358]) ).
thf(145,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Groups_Ocomm__monoid__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Ocomm__monoid__add) ).
thf(1577,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Groups_Ocomm__monoid__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(277,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(1922,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ 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_order__less__not__sym) ).
thf(1379,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ 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)],[68]) ).
thf(120,axiom,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zminus__zminus) ).
thf(1514,plain,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(158,axiom,
! [A: $i,B: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__int__zless__negative) ).
thf(1609,plain,
! [A: $i,B: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(458,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(2520,plain,
! [A: $i] :
( ( class_Rings_Ocomm__ring @ A )
=> ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(834,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( 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(3835,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( 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)],[834]) ).
thf(390,axiom,
! [A: $i,B: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__inverse) ).
thf(2301,plain,
! [A: $i,B: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(597,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( 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(2989,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( 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)],[597]) ).
thf(251,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( c_Polynomial_Opoly__gcd @ C @ B @ A )
= ( c_Polynomial_Opoly__gcd @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd_Ocommute) ).
thf(1847,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( c_Polynomial_Opoly__gcd @ C @ B @ A )
= ( c_Polynomial_Opoly__gcd @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(975,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(4353,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)],[975]) ).
thf(1095,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__field @ C )
=> ( c_Deriv_Oderiv @ C @ ( hAPP @ ( c_COMBK @ C @ C ) @ B ) @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__const) ).
thf(4788,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__field @ C )
=> ( c_Deriv_Oderiv @ C @ ( hAPP @ ( c_COMBK @ C @ C ) @ B ) @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).
thf(196,axiom,
class_Orderings_Oorder @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).
thf(1704,plain,
class_Orderings_Oorder @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(265,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ ( tc_Polynomial_Opoly @ C ) @ B @ A )
<=> ( c_Polynomial_Opos__poly @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ C ) ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__poly__def) ).
thf(1890,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ ( tc_Polynomial_Opoly @ C ) @ B @ A )
=> ( c_Polynomial_Opos__poly @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ C ) ) @ A ) @ B ) ) )
& ( ( c_Polynomial_Opos__poly @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ C ) ) @ A ) @ B ) )
=> ( c_Orderings_Oord__class_Oless @ ( tc_Polynomial_Opoly @ C ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(930,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) )
=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).
thf(4179,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(529,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( hAPP @ ( 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(2767,plain,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( hAPP @ ( 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)],[529]) ).
thf(215,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(1741,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)],[215]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__divide__distrib) ).
thf(1398,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(1164,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( ( ( c_Polynomial_Osynthetic__div @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
<=> ( ( c_Polynomial_Odegree @ C @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__eq__0__iff) ).
thf(5052,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( ( ( ( c_Polynomial_Osynthetic__div @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( c_Polynomial_Odegree @ C @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( ( c_Polynomial_Odegree @ C @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Polynomial_Osynthetic__div @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164]) ).
thf(734,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( ( hAPP @ ( hAPP @ ( 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(3470,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( ( ( hAPP @ ( hAPP @ ( 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 ) ) )
=> ( ( hAPP @ ( hAPP @ ( 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)],[734]) ).
thf(849,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( 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(3902,plain,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( 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)],[849]) ).
thf(142,axiom,
class_Groups_Ozero @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).
thf(1568,plain,
class_Groups_Ozero @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(658,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ D ) @ B @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ A ) )
= ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ D ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__smult__right) ).
thf(3180,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ D ) @ B @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ A ) )
= ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ D ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(1009,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Divides_Odiv__class_Odiv @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ A ) @ B ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( c_Divides_Odiv__class_Odiv @ C @ A @ B ) ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__add__self2) ).
thf(4471,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Divides_Odiv__class_Odiv @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ A ) @ B ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( c_Divides_Odiv__class_Odiv @ C @ A @ B ) ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(1097,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(4793,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)],[1097]) ).
thf(1154,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( 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(5020,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( 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)],[1154]) ).
thf(842,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1 @ C )
=> ( ( c_Transcendental_Odiffs @ C @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ ( hAPP @ c_Nat_OSuc @ A ) ) ) @ ( hAPP @ B @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diffs__def) ).
thf(3866,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1 @ C )
=> ( ( c_Transcendental_Odiffs @ C @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ ( hAPP @ c_Nat_OSuc @ A ) ) ) @ ( hAPP @ B @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(963,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) )
<=> ~ ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
& ~ ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
| ? [D: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ D ) )
& ~ ( hBOOL @ ( hAPP @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split__asm) ).
thf(4302,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ~ ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
& ~ ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
| ? [D: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ D ) )
& ~ ( hBOOL @ ( hAPP @ C @ D ) ) ) ) )
& ( ~ ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
& ~ ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
| ? [D: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ D ) )
& ~ ( hBOOL @ ( hAPP @ C @ D ) ) ) )
=> ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(1023,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).
thf(4514,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(946,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ C ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) ) @ A ) )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__minus__right) ).
thf(4253,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ C ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) ) @ A ) )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(1141,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_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(4967,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_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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).
thf(988,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(4411,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)],[988]) ).
thf(695,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( c_Polynomial_Odegree @ B @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__pCons__0) ).
thf(3322,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( c_Polynomial_Odegree @ B @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(985,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(4396,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)],[985]) ).
thf(726,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(3431,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)],[726]) ).
thf(36,axiom,
class_Groups_Ominus @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ominus) ).
thf(1302,plain,
class_Groups_Ominus @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(1045,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__cancel) ).
thf(4583,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(1126,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zmult1__eq) ).
thf(4903,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).
thf(651,axiom,
! [A: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ A )
=> ( ( hAPP @ ( 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(3163,plain,
! [A: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ A )
=> ( ( hAPP @ ( 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)],[651]) ).
thf(435,axiom,
! [A: $i,B: $i] :
( ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
<=> ? [C: $i] :
( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__eq__0__iff) ).
thf(2451,plain,
! [A: $i,B: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ? [C: $i] :
( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) ) )
& ( ? [C: $i] :
( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(564,axiom,
! [A: $i,B: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less1) ).
thf(2880,plain,
! [A: $i,B: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(922,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1 @ C )
=> ( ( c_Transcendental_Odiffs @ C @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ C @ tc_Nat_Onat ) @ ( c_Groups_Ouminus__class_Ouminus @ C ) ) @ B ) @ A )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ ( c_Transcendental_Odiffs @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diffs__minus) ).
thf(4147,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1 @ C )
=> ( ( c_Transcendental_Odiffs @ C @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ C @ tc_Nat_Onat ) @ ( c_Groups_Ouminus__class_Ouminus @ C ) ) @ B ) @ A )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ ( c_Transcendental_Odiffs @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(1102,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_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) )
= ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zmult2__eq) ).
thf(4815,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_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) )
= ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).
thf(245,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( 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(1828,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( 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)],[245]) ).
thf(1158,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self3) ).
thf(5032,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).
thf(1193,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_RealVector_Oreal__normed__field @ F )
=> ( ( c_Deriv_Oderiv @ F @ E @ ( hAPP @ D @ C ) @ B )
=> ( ( c_Deriv_Oderiv @ F @ D @ C @ A )
=> ( c_Deriv_Oderiv @ F @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ F @ F ) @ E ) @ D ) @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__chain2) ).
thf(5156,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_RealVector_Oreal__normed__field @ F )
=> ( ( c_Deriv_Oderiv @ F @ E @ ( hAPP @ D @ C ) @ B )
=> ( ( c_Deriv_Oderiv @ F @ D @ C @ A )
=> ( c_Deriv_Oderiv @ F @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ F @ F ) @ E ) @ D ) @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193]) ).
thf(377,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(2254,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)],[377]) ).
thf(187,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__field @ E )
=> ( ( c_Deriv_Oderiv @ E @ D @ C @ B )
=> ( ( B = A )
=> ( c_Deriv_Oderiv @ E @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__cong) ).
thf(1677,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__field @ E )
=> ( ( c_Deriv_Oderiv @ E @ D @ C @ B )
=> ( ( B = A )
=> ( c_Deriv_Oderiv @ E @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(292,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__dvd__cancel) ).
thf(1960,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(647,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__left__mono__neg) ).
thf(3152,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(29,axiom,
class_Groups_Oab__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).
thf(1283,plain,
class_Groups_Oab__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(1100,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Ofield @ E )
=> ( ( D
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ E ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ E ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ A ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__frac__eq) ).
thf(4810,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Ofield @ E )
=> ( ( D
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ E ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ E ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ A ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).
thf(996,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( ( c_Polynomial_Odegree @ C @ ( c_Polynomial_Osynthetic__div @ C @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( c_Polynomial_Odegree @ C @ B ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__synthetic__div) ).
thf(4432,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( ( c_Polynomial_Odegree @ C @ ( c_Polynomial_Osynthetic__div @ C @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( c_Polynomial_Odegree @ C @ B ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(308,axiom,
class_Lattices_Oboolean__algebra @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Oboolean__algebra) ).
thf(2007,plain,
class_Lattices_Oboolean__algebra @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(587,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pow__divides__pow__int) ).
thf(2950,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(1072,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A ) ) @ ( c_Groups_Oone__class_Oone @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__squared__diff__one__factored) ).
thf(4696,plain,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A ) ) @ ( c_Groups_Oone__class_Oone @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
thf(82,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__zdiffD) ).
thf(1415,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(889,axiom,
! [A: $i,B: $i] :
( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ B )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( 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_power__eq__if) ).
thf(4018,plain,
! [A: $i,B: $i] :
( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ B )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( 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)],[889]) ).
thf(1151,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__imp__le) ).
thf(5013,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).
thf(1112,axiom,
! [A: $i] :
( ( class_Groups_Ogroup__add @ A )
=> ( ( hAPP @ ( 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(4857,plain,
! [A: $i] :
( ( class_Groups_Ogroup__add @ A )
=> ( ( hAPP @ ( 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)],[1112]) ).
thf(65,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Rings_Osemiring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring__1) ).
thf(1373,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Rings_Osemiring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(600,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) ) @ ( c_Polynomial_Omonom @ C @ B @ A ) )
= ( c_Polynomial_Omonom @ C @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__monom) ).
thf(2996,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) ) @ ( c_Polynomial_Omonom @ C @ B @ A ) )
= ( c_Polynomial_Omonom @ C @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(801,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(3724,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)],[801]) ).
thf(272,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 @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__mod__bound) ).
thf(1911,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 @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(1049,axiom,
! [A: $i,B: $i] :
( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zdiv__equality) ).
thf(4600,plain,
! [A: $i,B: $i] :
( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).
thf(688,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(3295,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)],[688]) ).
thf(534,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ E )
=> ( ( ( hAPP @ ( hAPP @ ( 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 ) )
= ( hAPP @ ( hAPP @ ( 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(2782,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ E )
=> ( ( ( ( hAPP @ ( hAPP @ ( 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 ) )
= ( hAPP @ ( hAPP @ ( 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 ) )
=> ( ( hAPP @ ( hAPP @ ( 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 ) )
= ( hAPP @ ( hAPP @ ( 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)],[534]) ).
thf(570,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(2893,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)],[570]) ).
thf(165,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(1632,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)],[165]) ).
thf(961,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ B ) @ A ) )
| ( hBOOL @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__2) ).
thf(4297,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ B ) @ A ) )
| ( hBOOL @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(440,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Osemiring__1 @ C )
=> ( ( c_Nat_Osemiring__1__class_Oof__nat__aux @ C @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__aux_Osimps_I1_J) ).
thf(2469,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Osemiring__1 @ C )
=> ( ( c_Nat_Osemiring__1__class_Oof__nat__aux @ C @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(786,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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__offset__poly) ).
thf(3670,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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(883,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(4001,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)],[883]) ).
thf(747,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oab__group__add @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ ( hAPP @ ( 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(3527,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oab__group__add @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ B ) @ A ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(877,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(3983,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)],[877]) ).
thf(147,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Groups_Ouminus @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Ouminus) ).
thf(1581,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Groups_Ouminus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(1070,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_RealVector_Oreal__field @ F )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ C ) @ B ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ F ) @ D ) @ B ) ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ F ) @ E ) @ C ) ) @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__mult__lemma) ).
thf(4686,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_RealVector_Oreal__field @ F )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ C ) @ B ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ F ) @ D ) @ B ) ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ F ) @ E ) @ C ) ) @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).
thf(1166,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(5059,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)],[1166]) ).
thf(623,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(3068,plain,
! [A: $i] :
( ( class_Groups_Oab__group__add @ A )
=> ( class_Groups_Ouminus @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(7,axiom,
! [A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
& ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DIVISION__BY__ZERO) ).
thf(1215,plain,
! [A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
& ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(722,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(3421,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)],[722]) ).
thf(799,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( 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(3712,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( 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)],[799]) ).
thf(445,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( 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_mod__mult__distrib2) ).
thf(2483,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( 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)],[445]) ).
thf(426,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__field @ B )
=> ( c_Deriv_Oderiv @ B @ ( c_COMBI @ B ) @ A @ ( c_Groups_Oone__class_Oone @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__ident) ).
thf(2424,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__field @ B )
=> ( c_Deriv_Oderiv @ B @ ( c_COMBI @ B ) @ A @ ( c_Groups_Oone__class_Oone @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(649,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ F @ E @ D @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBC__1) ).
thf(3157,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ F @ E @ D @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(56,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(1351,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ouminus @ B )
=> ( class_Groups_Ouminus @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(677,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ C ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__frac__num) ).
thf(3243,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ C ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__zmod__imp__zdvd) ).
thf(1405,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(154,axiom,
! [A: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zero) ).
thf(1600,plain,
! [A: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(1054,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__inverse) ).
thf(4628,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).
thf(513,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ 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_Odiff) ).
thf(2718,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ 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)],[513]) ).
thf(193,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__ring__1 @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__diff) ).
thf(1696,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__ring__1 @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(527,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(2762,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)],[527]) ).
thf(878,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) )
= ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__int) ).
thf(3986,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) )
= ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(324,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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(2058,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( 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)],[324]) ).
thf(546,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(2833,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)],[546]) ).
thf(661,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__mult__cancel) ).
thf(3189,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(385,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ C )
=> ( ( ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B )
= ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__eq__iff__eq) ).
thf(2281,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ C )
=> ( ( ( ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B )
= ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B )
= ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(230,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__field @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide_Odiff) ).
thf(1796,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__field @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(616,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( c_Polynomial_Opdivmod__rel @ D @ C @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) @ B @ A )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__by__0__iff) ).
thf(3036,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( ( c_Polynomial_Opdivmod__rel @ D @ C @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) @ B @ A )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) )
& ( A = C ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) )
& ( A = C ) )
=> ( c_Polynomial_Opdivmod__rel @ D @ C @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(124,axiom,
class_Orderings_Oord @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).
thf(1526,plain,
class_Orderings_Oord @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(788,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(3676,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)],[788]) ).
thf(90,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Oring__div @ D )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ C ) @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ C ) @ ( c_Divides_Odiv__class_Omod @ D @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__diff__right__eq) ).
thf(1433,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Oring__div @ D )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ C ) @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ C ) @ ( c_Divides_Odiv__class_Omod @ D @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(1074,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 ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) ).
thf(4701,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 ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(285,axiom,
class_Rings_Oring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring) ).
thf(1943,plain,
class_Rings_Oring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(1,conjecture,
? [A: $i,B: $i] :
( ( B
!= ( c_Groups_Ozero__class_Ozero @ t_a ) )
& ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ? [C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ t_a @ C ) ) @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ t_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) )
& ! [D: $i] :
( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ t_a ) @ ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ ( c_Groups_Ozero__class_Ozero @ t_a ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ t_a ) @ D ) @ A ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ t_a ) @ B ) @ C ) ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ? [A: $i,B: $i] :
( ( B
!= ( c_Groups_Ozero__class_Ozero @ t_a ) )
& ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ? [C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ t_a @ C ) ) @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ t_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) )
& ! [D: $i] :
( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ t_a ) @ ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ ( c_Groups_Ozero__class_Ozero @ t_a ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ t_a ) @ D ) @ A ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ t_a ) @ B ) @ C ) ) @ D ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(1201,plain,
~ ? [A: $i,B: $i] :
( ( B
!= ( c_Groups_Ozero__class_Ozero @ t_a ) )
& ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ? [C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ t_a @ C ) ) @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ t_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) )
& ! [D: $i] :
( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ t_a ) @ ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ ( c_Groups_Ozero__class_Ozero @ t_a ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ t_a ) @ D ) @ A ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ t_a ) @ B ) @ C ) ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(668,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(3211,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)],[668]) ).
thf(415,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ ( hAPP @ ( 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(2392,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ B ) @ A ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(349,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__0 @ E )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ E ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ E ) @ C ) @ B ) )
= ( hAPP @ ( hAPP @ ( 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(2154,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__0 @ E )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ E ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ E ) @ C ) @ B ) )
= ( hAPP @ ( hAPP @ ( 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)],[349]) ).
thf(850,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Ofield__inverse__zero @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ 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_times__divide__times__eq) ).
thf(3906,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Ofield__inverse__zero @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ 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)],[850]) ).
thf(296,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_RealVector_Oreal__normed__field @ F )
=> ( ( c_Deriv_Oderiv @ F @ E @ D @ C )
=> ( ( c_Deriv_Oderiv @ F @ B @ D @ A )
=> ( c_Deriv_Oderiv @ F @ ( hAPP @ ( hAPP @ ( c_COMBS @ F @ F @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ ( tc_fun @ F @ F ) @ F ) @ ( c_Groups_Oplus__class_Oplus @ F ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ F @ F ) @ ( c_Groups_Ouminus__class_Ouminus @ F ) ) @ B ) ) @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ F ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__add__minus) ).
thf(1975,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_RealVector_Oreal__normed__field @ F )
=> ( ( c_Deriv_Oderiv @ F @ E @ D @ C )
=> ( ( c_Deriv_Oderiv @ F @ B @ D @ A )
=> ( c_Deriv_Oderiv @ F @ ( hAPP @ ( hAPP @ ( c_COMBS @ F @ F @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ ( tc_fun @ F @ F ) @ F ) @ ( c_Groups_Oplus__class_Oplus @ F ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ F @ F ) @ ( c_Groups_Ouminus__class_Ouminus @ F ) ) @ B ) ) @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ F ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(743,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( 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(3510,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( 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)],[743]) ).
thf(141,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(1564,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)],[141]) ).
thf(175,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oorder_Ostrict__mono @ tc_Nat_Onat @ D @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) ) @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ tc_Nat_Onat ) @ c_fNot ) ) @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ C @ B ) @ ( hAPP @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ostrict__monoD) ).
thf(1651,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oorder_Ostrict__mono @ tc_Nat_Onat @ D @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) ) @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ tc_Nat_Onat ) @ c_fNot ) ) @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ C @ B ) @ ( hAPP @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(632,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) ) @ B ) ) @ A )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__minus) ).
thf(3097,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) ) @ B ) ) @ A )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Ofield @ E )
=> ( ( c_Polynomial_Opdivmod__rel @ E @ D @ C @ B @ A )
=> ( ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ E ) @ D @ C )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__poly__eq) ).
thf(1206,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Ofield @ E )
=> ( ( c_Polynomial_Opdivmod__rel @ E @ D @ C @ B @ A )
=> ( ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ E ) @ D @ C )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1087,axiom,
class_Rings_Osemiring @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).
thf(4753,plain,
class_Rings_Osemiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).
thf(1046,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(4589,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)],[1046]) ).
thf(757,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__poly__code_I2_J) ).
thf(3567,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(1028,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel) ).
thf(4531,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(660,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(3186,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)],[660]) ).
thf(371,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ A ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__minus__divide__right) ).
thf(2232,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ A ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(212,axiom,
class_Orderings_Olinorder @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).
thf(1736,plain,
class_Orderings_Olinorder @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(898,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 @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ A ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__inverse__less) ).
thf(4059,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 @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ A ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(823,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( 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(3795,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( 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)],[823]) ).
thf(1123,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(4893,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)],[1123]) ).
thf(576,axiom,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__Suc__eq__Suc__mod) ).
thf(2910,plain,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(653,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( 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(3169,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( 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)],[653]) ).
thf(1012,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).
thf(4480,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(494,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Oboolean__algebra @ C )
=> ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__eq__compl__iff) ).
thf(2646,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Oboolean__algebra @ C )
=> ( ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
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(5142,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(1038,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__1) ).
thf(4557,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(103,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Oring @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Oring) ).
thf(1470,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Oring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(198,axiom,
class_Rings_Oring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).
thf(1708,plain,
class_Rings_Oring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(330,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__less) ).
thf(2093,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(226,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ B ) )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( c_Divides_Odiv__class_Omod @ D @ A @ B ) @ C )
= ( c_Divides_Odiv__class_Omod @ D @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mod__cancel) ).
thf(1783,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ B ) )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( c_Divides_Odiv__class_Omod @ D @ A @ B ) @ C )
= ( c_Divides_Odiv__class_Omod @ D @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(903,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
=> ( ( c_Groups_Osgn__class_Osgn @ ( tc_Polynomial_Opoly @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ ( tc_Polynomial_Opoly @ B ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ ( tc_Polynomial_Opoly @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ ( tc_Polynomial_Opoly @ B ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ ( tc_Polynomial_Opoly @ B ) @ A )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ B ) ) @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__poly__def) ).
thf(4076,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
=> ( ( c_Groups_Osgn__class_Osgn @ ( tc_Polynomial_Opoly @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ ( tc_Polynomial_Opoly @ B ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ ( tc_Polynomial_Opoly @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ ( tc_Polynomial_Opoly @ B ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ ( tc_Polynomial_Opoly @ B ) @ A )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ B ) ) @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(531,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__cancel) ).
thf(2773,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(167,axiom,
class_Rings_Ozero__neq__one @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).
thf(1636,plain,
class_Rings_Ozero__neq__one @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(207,axiom,
class_Rings_Ocomm__semiring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).
thf(1730,plain,
class_Rings_Ocomm__semiring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(789,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__diff__conv) ).
thf(3679,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) @ B ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(267,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( c_Divides_Odiv__class_Odiv @ D @ B @ C ) ) @ A )
= ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__power) ).
thf(1900,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( c_Divides_Odiv__class_Odiv @ D @ B @ C ) ) @ A )
= ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(1078,axiom,
! [A: $i,B: $i] :
( ( B = A )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oeq__iff) ).
thf(4712,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).
thf(465,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__simps_I3_J) ).
thf(2541,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(480,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( 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(2596,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( 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)],[480]) ).
thf(218,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( class_Fields_Ofield @ G )
=> ( ( c_Polynomial_Opdivmod__rel @ G @ F @ E @ D @ C )
=> ( ( E
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ G ) ) )
=> ( ( B
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ G ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ G @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ G ) @ A ) @ C ) ) @ ( c_Polynomial_Odegree @ G @ E ) ) ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ G @ E ) @ ( c_Polynomial_Odegree @ G @ E ) ) ) )
=> ( c_Polynomial_Opdivmod__rel @ G @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ G ) @ A ) @ F ) @ E @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ G ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ G ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ G ) @ B ) @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__pCons) ).
thf(1751,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( class_Fields_Ofield @ G )
=> ( ( c_Polynomial_Opdivmod__rel @ G @ F @ E @ D @ C )
=> ( ( E
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ G ) ) )
=> ( ( B
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ G ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ G @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ G ) @ A ) @ C ) ) @ ( c_Polynomial_Odegree @ G @ E ) ) ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ G @ E ) @ ( c_Polynomial_Odegree @ G @ E ) ) ) )
=> ( c_Polynomial_Opdivmod__rel @ G @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ G ) @ A ) @ F ) @ E @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ G ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ G ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ G ) @ B ) @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(181,axiom,
class_Groups_Omonoid__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).
thf(1666,plain,
class_Groups_Omonoid__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(110,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ C ) @ B ) @ A ) )
=> ( ( c_Divides_Odiv__class_Omod @ C @ A @ B )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__imp__mod__0) ).
thf(1487,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ C ) @ B ) @ A ) )
=> ( ( c_Divides_Odiv__class_Omod @ C @ A @ B )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(770,axiom,
class_Groups_Ocomm__monoid__mult @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
thf(3610,plain,
class_Groups_Ocomm__monoid__mult @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(879,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oord__eq__le__trans) ).
thf(3989,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(1094,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__diff__minus) ).
thf(4785,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).
thf(310,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(2015,plain,
class_Groups_Oordered__comm__monoid__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(894,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).
thf(4044,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(26,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) @ ( hAPP @ c_Nat_OSuc @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__Suc) ).
thf(1274,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) @ ( hAPP @ c_Nat_OSuc @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(431,axiom,
! [A: $i] :
( ~ ~ ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ c_fNot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__2) ).
thf(2441,plain,
! [A: $i] :
( ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ c_fNot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(1163,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( c_Divides_Odiv__class_Odiv @ C @ A @ B ) ) ) @ ( c_Divides_Odiv__class_Omod @ C @ A @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__div__equality2) ).
thf(5049,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( c_Divides_Odiv__class_Odiv @ C @ A @ B ) ) ) @ ( c_Divides_Odiv__class_Omod @ C @ A @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).
thf(805,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) ) @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self4) ).
thf(3735,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) ) @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Limits_Ominus__diff__minus) ).
thf(1343,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(540,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(2805,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)],[540]) ).
thf(1131,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
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_square__eq__iff) ).
thf(4920,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
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) ) )
& ( ( ( B = A )
| ( B
= ( hAPP @ ( 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)],[1131]) ).
thf(58,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(1355,plain,
class_Groups_Ocancel__comm__monoid__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(18,axiom,
class_Rings_Ocomm__semiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).
thf(1255,plain,
class_Rings_Ocomm__semiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(981,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( c_Divides_Odiv__class_Omod @ D @ C @ A ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__left__eq) ).
thf(4375,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( c_Divides_Odiv__class_Omod @ D @ C @ A ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(1161,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(5044,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)],[1161]) ).
thf(342,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ 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(2133,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(808,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Ofield @ B )
=> ( ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__class_Onormalizing__field__rules_I2_J) ).
thf(3742,plain,
! [A: $i,B: $i] :
( ( class_Fields_Ofield @ B )
=> ( ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(589,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(2969,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)],[589]) ).
thf(674,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Divides_Odiv__class_Omod @ D @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__right__eq) ).
thf(3233,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Divides_Odiv__class_Omod @ D @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(707,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(3371,plain,
! [A: $i] :
( ( class_Groups_Ozero @ A )
=> ( class_Groups_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(648,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(3154,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)],[648]) ).
thf(1017,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ A )
= ( hAPP @ ( 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(4493,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ A )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(1175,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(5085,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)],[1175]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmod__right) ).
thf(1370,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(829,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 ) )
=> ( ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__unique) ).
thf(3816,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 ) )
=> ( ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(162,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__iff__equal) ).
thf(1619,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(315,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( 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(2032,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( 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)],[315]) ).
thf(1104,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( 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(4821,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).
thf(595,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__right__mono__neg) ).
thf(2986,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(422,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__antisym) ).
thf(2414,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(679,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add) ).
thf(3250,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(926,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( 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(4160,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(1065,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C )
= A )
=> ( B
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__imp) ).
thf(4661,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C )
= A )
=> ( B
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).
thf(460,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__add @ D )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ D @ C ) @ A ) ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ D @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__add) ).
thf(2528,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__add @ D )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ D @ C ) @ A ) ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ D @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(866,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 @ ( hAPP @ ( hAPP @ ( 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(3948,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(896,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__add @ D )
=> ( ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__monom) ).
thf(4053,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__add @ D )
=> ( ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(294,axiom,
class_Rings_Osemiring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__1) ).
thf(1968,plain,
class_Rings_Osemiring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(33,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 @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__div__less__self) ).
thf(1296,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 @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(190,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).
thf(1687,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ( ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B )
=> ( A = B ) )
& ( ( A = B )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(968,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(4327,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)],[968]) ).
thf(356,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ ( hAPP @ ( 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(2179,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(752,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ 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(3546,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ 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)],[752]) ).
thf(1183,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Osemiring__1 @ C )
=> ( ( c_Nat_Osemiring__1__class_Oof__nat @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ B ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__add) ).
thf(5113,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Osemiring__1 @ C )
=> ( ( c_Nat_Osemiring__1__class_Oof__nat @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ B ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183]) ).
thf(802,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(3727,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Orderings_Oorder @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(731,axiom,
! [A: $i] :
( A
!= ( hAPP @ c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
thf(3445,plain,
! [A: $i] :
( A
!= ( hAPP @ c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(652,axiom,
! [A: $i] :
( ( class_Groups_Ozero @ A )
=> ( ( hAPP @ ( hAPP @ ( 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(3166,plain,
! [A: $i] :
( ( class_Groups_Ozero @ A )
=> ( ( hAPP @ ( hAPP @ ( 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)],[652]) ).
thf(433,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__0) ).
thf(2445,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( 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)],[433]) ).
thf(956,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(4280,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)],[956]) ).
thf(561,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__group__add @ D )
=> ( ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__monom) ).
thf(2873,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__group__add @ D )
=> ( ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(876,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ D @ C ) @ B ) @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBK__1) ).
thf(3980,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ D @ C ) @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(249,axiom,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__if) ).
thf(1837,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(683,axiom,
class_Rings_Osemiring__0 @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).
thf(3269,plain,
class_Rings_Osemiring__0 @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(1109,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ E @ D @ C ) @ B ) @ ( hAPP @ 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(4849,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ E @ D @ C ) @ B ) @ ( hAPP @ 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)],[1109]) ).
thf(61,axiom,
class_Rings_Olinordered__semidom @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).
thf(1365,plain,
class_Rings_Olinordered__semidom @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(490,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( B = A )
<=> ( ( hAPP @ ( hAPP @ ( 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(2628,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(933,axiom,
class_Groups_Ocomm__monoid__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
thf(4192,plain,
class_Groups_Ocomm__monoid__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(138,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( hAPP @ ( 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(1555,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(543,axiom,
( ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0) ).
thf(2826,plain,
( ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(925,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( 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(4155,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( 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)],[925]) ).
thf(1148,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__cancel1) ).
thf(4994,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).
thf(1089,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Divides_Osemiring__div @ E )
=> ( ( D
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ E ) @ D ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ E ) @ C ) @ A ) )
=> ( ( ( c_Divides_Odiv__class_Odiv @ E @ B @ D )
= ( c_Divides_Odiv__class_Odiv @ E @ A @ C ) )
<=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__div__div__eq__mult) ).
thf(4757,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Divides_Osemiring__div @ E )
=> ( ( D
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ E ) @ D ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ E ) @ C ) @ A ) )
=> ( ( ( ( c_Divides_Odiv__class_Odiv @ E @ B @ D )
= ( c_Divides_Odiv__class_Odiv @ E @ A @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ A ) ) )
& ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ A ) )
=> ( ( c_Divides_Odiv__class_Odiv @ E @ B @ D )
= ( c_Divides_Odiv__class_Odiv @ E @ A @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).
thf(622,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Osemiring__1 @ C )
=> ( ( c_Nat_Osemiring__1__class_Oof__nat @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__power) ).
thf(3065,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Osemiring__1 @ C )
=> ( ( c_Nat_Osemiring__1__class_Oof__nat @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(699,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ ( c_Divides_Odiv__class_Omod @ D @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__right__eq) ).
thf(3349,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ ( c_Divides_Odiv__class_Omod @ D @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(362,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__pCons) ).
thf(2200,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(485,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__less__div__pos) ).
thf(2609,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(991,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(4417,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)],[991]) ).
thf(1083,axiom,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
= ( hAPP @ ( hAPP @ ( 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(4740,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
= ( hAPP @ ( hAPP @ ( 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)],[1083]) ).
thf(364,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ B ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__minus) ).
thf(2211,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ B ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(78,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(1407,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)],[78]) ).
thf(467,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__commute) ).
thf(2547,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(449,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( 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(2492,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(72,axiom,
! [A: $i,B: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__geq) ).
thf(1392,plain,
! [A: $i,B: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(785,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ C ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__minus__eq__add) ).
thf(3667,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ C ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(780,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( A
= ( hAPP @ 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(3647,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( A
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(337,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(2112,plain,
class_Rings_Olinordered__comm__semiring__strict @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(614,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__imp__not__less) ).
thf(3033,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(717,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B )
= ( hAPP @ ( 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(3408,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B )
= ( hAPP @ ( 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)],[717]) ).
thf(271,axiom,
class_Groups_Ocancel__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).
thf(1910,plain,
class_Groups_Ocancel__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(151,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ A ) )
=> ( ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( c_Divides_Odiv__class_Odiv @ D @ B @ C ) ) @ ( c_Divides_Odiv__class_Odiv @ D @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__add) ).
thf(1592,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ A ) )
=> ( ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( c_Divides_Odiv__class_Odiv @ D @ B @ C ) ) @ ( c_Divides_Odiv__class_Odiv @ D @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(299,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ 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_order__less__asym) ).
thf(1983,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ 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)],[299]) ).
thf(538,axiom,
class_Orderings_Opreorder @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
thf(2801,plain,
class_Orderings_Opreorder @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Divides_Osemiring__div @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ E ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ E ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Divides_Odiv__class_Odiv @ E @ C @ D ) ) @ ( c_Divides_Odiv__class_Odiv @ E @ A @ B ) )
= ( c_Divides_Odiv__class_Odiv @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__div__if__dvd) ).
thf(1375,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Divides_Osemiring__div @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ E ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ E ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Divides_Odiv__class_Odiv @ E @ C @ D ) ) @ ( c_Divides_Odiv__class_Odiv @ E @ A @ B ) )
= ( c_Divides_Odiv__class_Odiv @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(710,axiom,
! [A: $i] :
( ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__Suc) ).
thf(3381,plain,
! [A: $i] :
( ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(1026,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( c_Polynomial_Opoly__gcd @ C @ B @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) ) @ A ) )
= ( c_Polynomial_Opoly__gcd @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__minus__right) ).
thf(4525,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( c_Polynomial_Opoly__gcd @ C @ B @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) ) @ A ) )
= ( c_Polynomial_Opoly__gcd @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).
thf(634,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono1) ).
thf(3102,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(380,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__asym) ).
thf(2268,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(872,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(3968,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)],[872]) ).
thf(915,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ A )
= ( hAPP @ ( 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(4123,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ A )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(451,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
thf(2498,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(851,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Oboolean__algebra @ B )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ B ) @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__compl) ).
thf(3909,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Oboolean__algebra @ B )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ B ) @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(820,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
<=> ? [B: $i] :
( A
= ( hAPP @ c_Nat_OSuc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
thf(3782,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ? [B: $i] :
( A
= ( hAPP @ c_Nat_OSuc @ B ) ) )
& ( ? [B: $i] :
( A
= ( hAPP @ 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)],[820]) ).
thf(773,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Ofield @ E )
=> ( ( D
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ E ) @ B ) @ D )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ E ) @ A ) @ C ) )
<=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ A ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__eq__eq) ).
thf(3615,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Ofield @ E )
=> ( ( D
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ E ) @ B ) @ D )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ E ) @ A ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ A ) @ D ) ) )
& ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ A ) @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ E ) @ B ) @ D )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ E ) @ A ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(132,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( c_Divides_Odiv__class_Odiv @ C @ ( c_Divides_Odiv__class_Omod @ C @ B @ A ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__div__trivial) ).
thf(1541,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( c_Divides_Odiv__class_Odiv @ C @ ( c_Divides_Odiv__class_Omod @ C @ B @ A ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(737,axiom,
! [A: $i,B: $i] :
( ( B != A )
| ( hBOOL @ ( hAPP @ ( c_fequal @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__2) ).
thf(3482,plain,
! [A: $i,B: $i] :
( ( B != A )
| ( hBOOL @ ( hAPP @ ( c_fequal @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(1191,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(5145,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)],[1191]) ).
thf(129,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Oring__div @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ C ) @ B ) @ A ) )
=> ( ( c_Divides_Odiv__class_Odiv @ C @ A @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ ( c_Divides_Odiv__class_Odiv @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__div__neg) ).
thf(1534,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Oring__div @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ C ) @ B ) @ A ) )
=> ( ( c_Divides_Odiv__class_Odiv @ C @ A @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ ( c_Divides_Odiv__class_Odiv @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(505,axiom,
! [A: $i,B: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) )
= A )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( ( hAPP @ c_Nat_OSuc @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) )
!= A )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__Suc) ).
thf(2685,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) )
= A )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( ( hAPP @ c_Nat_OSuc @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) )
!= A )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(1142,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ C ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__two__diff) ).
thf(4974,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ C ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).
thf(233,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ ( c_Divides_Odiv__class_Omod @ D @ B @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mod__imp__dvd) ).
thf(1804,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ ( c_Divides_Odiv__class_Omod @ D @ B @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(549,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B ) @ ( hAPP @ ( 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(2841,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B ) @ ( hAPP @ ( 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)],[549]) ).
thf(47,axiom,
class_Rings_Olinordered__ring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).
thf(1328,plain,
class_Rings_Olinordered__ring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(512,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
<=> ( ( B = A )
| ( B
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__two__disj) ).
thf(2709,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
=> ( ( B = A )
| ( B
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) ) )
& ( ( ( B = A )
| ( B
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(10,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Osemiring__0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Osemiring__0) ).
thf(1227,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Osemiring__0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(670,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(3218,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)],[670]) ).
thf(1033,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(4544,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)],[1033]) ).
thf(255,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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(1856,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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)],[255]) ).
thf(995,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ B ) @ A ) )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ B ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__minus__eq) ).
thf(4429,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ B ) @ A ) )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ B ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(506,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( 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(2692,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( 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)],[506]) ).
thf(149,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Osemiring @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Osemiring) ).
thf(1587,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Osemiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(781,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(3650,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)],[781]) ).
thf(887,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) )
<=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).
thf(4012,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ D @ C @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(219,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
thf(1755,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(863,axiom,
class_Rings_Oidom @ t_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_0) ).
thf(3941,plain,
class_Rings_Oidom @ t_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(621,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ole__neq__trans) ).
thf(3060,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(656,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(3176,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)],[656]) ).
thf(1125,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__smult__iff) ).
thf(4898,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).
thf(959,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( 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(4291,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( 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)],[959]) ).
thf(537,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(2798,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)],[537]) ).
thf(48,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Omult__zero @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Omult__zero) ).
thf(1329,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Omult__zero @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(178,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__field @ E )
=> ( ( c_Deriv_Oderiv @ E @ D @ C @ B )
=> ( c_Deriv_Oderiv @ E @ ( hAPP @ ( c_COMBC @ E @ E @ E @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ E @ E ) @ E ) @ ( c_Rings_Oinverse__class_Odivide @ E ) ) @ D ) ) @ A ) @ C @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ E ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__cdivide) ).
thf(1659,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__field @ E )
=> ( ( c_Deriv_Oderiv @ E @ D @ C @ B )
=> ( c_Deriv_Oderiv @ E @ ( hAPP @ ( c_COMBC @ E @ E @ E @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ E @ E ) @ E ) @ ( c_Rings_Oinverse__class_Odivide @ E ) ) @ D ) ) @ A ) @ C @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ E ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(397,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 ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( 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(2323,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 ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( 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)],[397]) ).
thf(1146,axiom,
! [A: $i,B: $i] :
( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= A ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__if) ).
thf(4983,plain,
! [A: $i,B: $i] :
( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= A ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).
thf(472,axiom,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ A )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__self) ).
thf(2561,plain,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ A )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(765,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 ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( 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(3596,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 ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( 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)],[765]) ).
thf(424,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(2419,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(1133,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] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( 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(4938,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] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ D ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
& ( hBOOL @ ( hAPP @ B @ D ) ) ) )
& ( ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( 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)],[1133]) ).
thf(81,axiom,
class_Groups_Omonoid__mult @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).
thf(1414,plain,
class_Groups_Omonoid__mult @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(283,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(1937,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__semidom @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(395,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( 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(2317,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( 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)],[395]) ).
thf(691,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__pos__pos) ).
thf(3311,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(563,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( 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(2877,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( 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)],[563]) ).
thf(1172,axiom,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
thf(5075,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).
thf(1113,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(4860,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)],[1113]) ).
thf(1180,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ 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(5107,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ 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)],[1180]) ).
thf(545,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(2830,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)],[545]) ).
thf(630,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc1) ).
thf(3094,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(99,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__field @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ A )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide_Ominus) ).
thf(1461,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__field @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ A )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(994,axiom,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
thf(4425,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(87,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( hAPP @ c_Nat_OSuc @ B ) ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negative__zless) ).
thf(1424,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( hAPP @ c_Nat_OSuc @ B ) ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(393,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(2312,plain,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(605,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(3010,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)],[605]) ).
thf(1086,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) ) @ B ) @ A )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) ) @ ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ C ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__mod__minus__left) ).
thf(4750,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) ) @ B ) @ A )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) ) @ ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ C ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).
thf(725,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
= ( c_Divides_Odiv__class_Odiv @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__mult1) ).
thf(3428,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
= ( c_Divides_Odiv__class_Odiv @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(237,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ ( c_Divides_Odiv__class_Omod @ D @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mod) ).
thf(1810,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ ( c_Divides_Odiv__class_Omod @ D @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(229,axiom,
! [A: $i,B: $i] :
( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ B ) )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) ) ) )
& ( ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B )
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zminus2__eq__if) ).
thf(1791,plain,
! [A: $i,B: $i] :
( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ B ) )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) ) ) )
& ( ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B )
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(663,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oantisym) ).
thf(3194,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(403,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oab__group__add @ B )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ B ) ) @ A )
= ( c_Polynomial_OAbs__poly @ B @ ( hAPP @ ( hAPP @ ( c_COMBB @ B @ B @ tc_Nat_Onat ) @ ( c_Groups_Ouminus__class_Ouminus @ B ) ) @ ( c_Polynomial_Ocoeff @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__poly__def) ).
thf(2349,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oab__group__add @ B )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ B ) ) @ A )
= ( c_Polynomial_OAbs__poly @ B @ ( hAPP @ ( hAPP @ ( c_COMBB @ B @ B @ tc_Nat_Onat ) @ ( c_Groups_Ouminus__class_Ouminus @ B ) ) @ ( c_Polynomial_Ocoeff @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(317,axiom,
( ( hAPP @ ( 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(2038,plain,
( ( hAPP @ ( 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)],[317]) ).
thf(94,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) @ A )
<=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__less__iff) ).
thf(1446,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) @ B ) )
& ( ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(779,axiom,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).
thf(3643,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(999,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(4444,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)],[999]) ).
thf(159,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ A ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ C @ A ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zadd1__eq) ).
thf(1612,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ A ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ C @ A ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(592,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 @ ( hAPP @ ( 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(2978,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 @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(441,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ E @ D ) @ C ) @ B ) @ A )
= ( hAPP @ C @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBB__1) ).
thf(2472,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ E @ D ) @ C ) @ B ) @ A )
= ( hAPP @ C @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(860,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(3935,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Rings_Odvd @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(84,axiom,
class_Rings_Ocomm__ring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).
thf(1419,plain,
class_Rings_Ocomm__ring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(244,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__int__def) ).
thf(1825,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(771,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(3611,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)],[771]) ).
thf(738,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ C @ B ) ) @ A ) @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zmod) ).
thf(3486,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ C @ B ) ) @ A ) @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(640,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ E ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pCons) ).
thf(3126,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ E ) ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(391,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oring @ F )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) ) @ A ) )
<=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ F ) @ E ) @ B ) ) @ D ) ) @ C )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__add__iff1) ).
thf(2304,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oring @ F )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ F ) @ E ) @ B ) ) @ D ) ) @ C )
= A ) )
& ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ F ) @ E ) @ B ) ) @ D ) ) @ C )
= A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) ) @ C )
= ( hAPP @ ( hAPP @ ( 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)],[391]) ).
thf(447,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(2487,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)],[447]) ).
thf(183,axiom,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) )
= ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Otransfer__int__nat__functions_I2_J) ).
thf(1668,plain,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) )
= ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(307,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(2006,plain,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(973,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ A )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__minus__left) ).
thf(4347,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ A )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(1136,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B ) @ ( hAPP @ ( 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(4953,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B ) @ ( hAPP @ ( 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)],[1136]) ).
thf(106,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__field @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ D ) @ C ) ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ D ) @ B ) ) ) @ A )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ C ) @ B ) ) @ A ) ) ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ D ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__inverse__lemma) ).
thf(1478,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__field @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ D ) @ C ) ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ D ) @ B ) ) ) @ A )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ C ) @ B ) ) @ A ) ) ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ D ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(983,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ E )
=> ( ( ( D != C )
& ( B != A ) )
<=> ( ( hAPP @ ( hAPP @ ( 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 ) )
!= ( hAPP @ ( hAPP @ ( 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(4384,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ E )
=> ( ( ( ( D != C )
& ( B != A ) )
=> ( ( hAPP @ ( hAPP @ ( 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 ) )
!= ( hAPP @ ( hAPP @ ( 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 ) ) ) )
& ( ( ( hAPP @ ( hAPP @ ( 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 ) )
!= ( hAPP @ ( hAPP @ ( 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)],[983]) ).
thf(126,axiom,
class_Orderings_Opreorder @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
thf(1530,plain,
class_Orderings_Opreorder @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(131,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__smult) ).
thf(1539,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(97,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ B ) @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__minus) ).
thf(1456,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ B ) @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(1022,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
=> ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
=> ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ B @ A )
= ( hAPP @ c_Nat_OSuc @ ( c_Polynomial_Odegree @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psize__def) ).
thf(4508,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
=> ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
=> ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ B @ A )
= ( hAPP @ c_Nat_OSuc @ ( c_Polynomial_Odegree @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(22,axiom,
class_Orderings_Oord @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
thf(1266,plain,
class_Orderings_Oord @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__left) ).
thf(1231,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ B ) @ ( c_Polynomial_Odegree @ C @ B ) )
= ( hAPP @ ( c_Polynomial_Ocoeff @ C @ A ) @ ( c_Polynomial_Odegree @ C @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) ) @ A ) @ B ) )
=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__dvd__antisym) ).
thf(1552,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ B ) @ ( c_Polynomial_Odegree @ C @ B ) )
= ( hAPP @ ( c_Polynomial_Ocoeff @ C @ A ) @ ( c_Polynomial_Odegree @ C @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) ) @ A ) @ B ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(553,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(2851,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)],[553]) ).
thf(405,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pow__divides__eq__nat) ).
thf(2355,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( 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)],[405]) ).
thf(1013,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( 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(4482,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( 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)],[1013]) ).
thf(281,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ? [B: $i] :
( A
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( hAPP @ c_Nat_OSuc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negD) ).
thf(1932,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ? [B: $i] :
( A
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( hAPP @ c_Nat_OSuc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(943,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oab__group__add @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) @ A )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__poly__code_I1_J) ).
thf(4244,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oab__group__add @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) @ A )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(713,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( ( C
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ D ) ) )
& ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
= ( c_Divides_Odiv__class_Odiv @ D @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__mult1__if) ).
thf(3390,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( ( C
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ D ) ) )
& ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
= ( c_Divides_Odiv__class_Odiv @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(830,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) @ B )
= ( c_Divides_Odiv__class_Omod @ D @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self2) ).
thf(3819,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) @ B )
= ( c_Divides_Odiv__class_Omod @ D @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(940,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ ( c_Groups_Oone__class_Oone @ C ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) @ ( hAPP @ c_Nat_OSuc @ ( c_Polynomial_Oorder @ C @ A @ B ) ) ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__2) ).
thf(4237,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ ( c_Groups_Oone__class_Oone @ C ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) @ ( hAPP @ c_Nat_OSuc @ ( c_Polynomial_Oorder @ C @ A @ B ) ) ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(474,axiom,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
thf(2566,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(231,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield__inverse__zero @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__divide__divide) ).
thf(1799,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield__inverse__zero @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(861,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 ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( 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(3937,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 ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( 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)],[861]) ).
thf(287,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__diff__eq) ).
thf(1947,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(914,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ B @ A ) )
=> ( ~ ( hBOOL @ ( hAPP @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( c_Orderings_Oord__class_OLeast @ tc_Nat_Onat @ B )
= ( hAPP @ c_Nat_OSuc @ ( c_Orderings_Oord__class_OLeast @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ tc_HOL_Obool @ tc_Nat_Onat ) @ B ) @ c_Nat_OSuc ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Least__Suc) ).
thf(4120,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ B @ A ) )
=> ( ~ ( hBOOL @ ( hAPP @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( c_Orderings_Oord__class_OLeast @ tc_Nat_Onat @ B )
= ( hAPP @ c_Nat_OSuc @ ( c_Orderings_Oord__class_OLeast @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ tc_HOL_Obool @ tc_Nat_Onat ) @ B ) @ c_Nat_OSuc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(776,axiom,
! [A: $i] :
( ( class_Fields_Ofield__inverse__zero @ A )
=> ( ( hAPP @ ( 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(3628,plain,
! [A: $i] :
( ( class_Fields_Ofield__inverse__zero @ A )
=> ( ( hAPP @ ( 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)],[776]) ).
thf(260,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( 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(1874,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( 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)],[260]) ).
thf(638,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(3115,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)],[638]) ).
thf(814,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( ( hAPP @ ( 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(3760,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( ( ( hAPP @ ( 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 ) )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( B = A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__less__eq__trans) ).
thf(1429,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( B = A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(557,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring @ C )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( 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(2862,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring @ C )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( 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)],[557]) ).
thf(919,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(4135,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)],[919]) ).
thf(793,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Osemiring__1 @ B )
=> ( ( c_Nat_Osemiring__1__class_Oof__nat @ B @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__Suc) ).
thf(3692,plain,
! [A: $i,B: $i] :
( ( class_Rings_Osemiring__1 @ B )
=> ( ( c_Nat_Osemiring__1__class_Oof__nat @ B @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B )
= ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__relations_I1_J) ).
thf(1246,plain,
! [A: $i,B: $i] :
( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B )
= ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B )
= ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(924,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(4152,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)],[924]) ).
thf(203,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__zmod) ).
thf(1720,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(637,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( ( c_Groups_Ozero__class_Ozero @ B )
= ( hAPP @ ( 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(3109,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( ( ( c_Groups_Ozero__class_Ozero @ B )
= ( hAPP @ ( 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 )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(1071,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oord__eq__less__trans) ).
thf(4689,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).
thf(382,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( hAPP @ ( 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(2272,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( hAPP @ ( 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)],[382]) ).
thf(990,axiom,
class_Orderings_Olinorder @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
thf(4416,plain,
class_Orderings_Olinorder @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(627,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__semidom @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ 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_of__nat__0__less__iff) ).
thf(3083,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__semidom @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ 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 @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(937,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(4223,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)],[937]) ).
thf(164,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__int) ).
thf(1627,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ 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_Int_Oint @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(123,axiom,
class_Groups_Ogroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).
thf(1525,plain,
class_Groups_Ogroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(927,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Rings_Ocomm__ring @ D )
& ( class_Rings_Odvd @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ B ) )
=> ! [E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ E ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ F ) @ B ) ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__period_I3_J) ).
thf(4163,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Rings_Ocomm__ring @ D )
& ( class_Rings_Odvd @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ B ) )
=> ! [E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ E ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ F ) @ B ) ) ) @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ F ) @ B ) ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ E ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(1030,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( c_Polynomial_Opoly__gcd @ C @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) ) @ B ) @ A )
= ( c_Polynomial_Opoly__gcd @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__minus__left) ).
thf(4535,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( c_Polynomial_Opoly__gcd @ C @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) ) @ B ) @ A )
= ( c_Polynomial_Opoly__gcd @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(1192,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ ( c_Divides_Odiv__class_Odiv @ D @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self2) ).
thf(5153,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ ( c_Divides_Odiv__class_Odiv @ D @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1192]) ).
thf(363,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 ) @ ( hAPP @ ( hAPP @ ( 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(2203,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 ) @ ( hAPP @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( 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)],[363]) ).
thf(958,axiom,
! [A: $i,B: $i] :
( ( class_Divides_Osemiring__div @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Divides_Odiv__class_Odiv @ B @ A @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__self) ).
thf(4288,plain,
! [A: $i,B: $i] :
( ( class_Divides_Osemiring__div @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Divides_Odiv__class_Odiv @ B @ A @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(1093,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__left) ).
thf(4782,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).
thf(192,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(1695,plain,
class_Rings_Olinordered__comm__semiring__strict @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(565,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ B ) @ A ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__self) ).
thf(2883,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ B ) @ A ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(882,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add1) ).
thf(3999,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(742,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(3508,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Ono__zero__divisors @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(836,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0) ).
thf(3841,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(497,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel1) ).
thf(2662,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( 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)],[497]) ).
thf(304,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield__inverse__zero @ C )
=> ( ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__divide) ).
thf(1996,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield__inverse__zero @ C )
=> ( ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(209,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Groups_Omonoid__mult @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Omonoid__mult) ).
thf(1732,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Groups_Omonoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(491,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ozero @ D )
=> ( ( ( C = B )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ D @ ( c_Polynomial_Omonom @ D @ A @ C ) ) @ B )
= A ) )
& ( ( C != B )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ D @ ( c_Polynomial_Omonom @ D @ A @ C ) ) @ B )
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__monom) ).
thf(2634,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ozero @ D )
=> ( ( ( C = B )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ D @ ( c_Polynomial_Omonom @ D @ A @ C ) ) @ B )
= A ) )
& ( ( C != B )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ D @ ( c_Polynomial_Omonom @ D @ A @ C ) ) @ B )
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(522,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
thf(2749,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(302,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Oring__div @ D )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ C ) @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ ( c_Divides_Odiv__class_Omod @ D @ C @ A ) ) @ ( c_Divides_Odiv__class_Omod @ D @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__diff__eq) ).
thf(1991,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Oring__div @ D )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ C ) @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ ( c_Divides_Odiv__class_Omod @ D @ C @ A ) ) @ ( c_Divides_Odiv__class_Omod @ D @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(43,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Ocomm__ring @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Ocomm__ring) ).
thf(1318,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Ocomm__ring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(239,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(1814,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)],[239]) ).
thf(1059,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__cancel) ).
thf(4644,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).
thf(671,axiom,
! [A: $i,B: $i] :
( ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__mult) ).
thf(3225,plain,
! [A: $i,B: $i] :
( ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(319,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(2043,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)],[319]) ).
thf(1121,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(4889,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)],[1121]) ).
thf(659,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ ( c_Divides_Odiv__class_Odiv @ D @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self1) ).
thf(3183,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ ( c_Divides_Odiv__class_Odiv @ D @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(323,axiom,
class_Groups_Ocancel__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
thf(2057,plain,
class_Groups_Ocancel__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(201,axiom,
class_Groups_Oone @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oone) ).
thf(1712,plain,
class_Groups_Oone @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(764,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( 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(3592,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(101,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( ( c_Orderings_Oorder_Ostrict__mono @ tc_Nat_Onat @ B @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) ) @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ tc_Nat_Onat ) @ c_fNot ) ) @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ A )
=> ( c_Orderings_Oorder_Omono @ tc_Nat_Onat @ B @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ostrict__mono__mono) ).
thf(1466,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( ( c_Orderings_Oorder_Ostrict__mono @ tc_Nat_Onat @ B @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) ) @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ tc_Nat_Onat ) @ c_fNot ) ) @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ A )
=> ( c_Orderings_Oorder_Omono @ tc_Nat_Onat @ B @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(419,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oorder__refl) ).
thf(2402,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(1127,axiom,
! [A: $i,B: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( hAPP @ c_Nat_OSuc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq) ).
thf(4906,plain,
! [A: $i,B: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( hAPP @ c_Nat_OSuc @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( hAPP @ c_Nat_OSuc @ B ) )
=> ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).
thf(578,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(2915,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)],[578]) ).
thf(536,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( 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(2793,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(180,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( c_Polynomial_Omonom @ C @ B @ A )
= ( c_Polynomial_OAbs__poly @ C @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ C @ C @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ C @ ( tc_fun @ C @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ C @ ( tc_fun @ C @ C ) ) @ tc_Nat_Onat ) @ ( c_If @ C ) ) @ ( c_fequal @ A ) ) ) @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monom__def) ).
thf(1663,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( c_Polynomial_Omonom @ C @ B @ A )
= ( c_Polynomial_OAbs__poly @ C @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ C @ C @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ C @ ( tc_fun @ C @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ C @ ( tc_fun @ C @ C ) ) @ tc_Nat_Onat ) @ ( c_If @ C ) ) @ ( c_fequal @ A ) ) ) @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__relations_I4_J) ).
thf(1278,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(517,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
= ( hAPP @ ( 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(2729,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
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) )
& ( ( ( A
= ( c_Groups_Oone__class_Oone @ B ) )
| ( A
= ( hAPP @ ( 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)],[517]) ).
thf(782,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) @ A )
= ( c_Divides_Odiv__class_Omod @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self1) ).
thf(3660,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) @ A )
= ( c_Divides_Odiv__class_Omod @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(502,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(2677,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)],[502]) ).
thf(769,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__add__left) ).
thf(3607,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(740,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
<=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( B
= ( hAPP @ 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(3491,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( B
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
& ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( B
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(984,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(4393,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)],[984]) ).
thf(482,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(2602,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)],[482]) ).
thf(952,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( c_Divides_Odiv__class_Omod @ D @ C @ B ) ) @ A ) @ B )
= ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__simps_I1_J) ).
thf(4269,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( c_Divides_Odiv__class_Omod @ D @ C @ B ) ) @ A ) @ B )
= ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(372,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(2235,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)],[372]) ).
thf(347,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( ( c_Polynomial_Opoly__gcd @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__zero__iff) ).
thf(2144,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( ( ( c_Polynomial_Opoly__gcd @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) )
=> ( ( c_Polynomial_Opoly__gcd @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(206,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
<=> ( 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_neg__imp__zdiv__neg__iff) ).
thf(1727,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( 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 @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(118,axiom,
class_Rings_Odvd @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Odvd) ).
thf(1510,plain,
class_Rings_Odvd @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(1117,axiom,
! [A: $i] :
( ( ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__eq__0__conv) ).
thf(4872,plain,
! [A: $i] :
( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).
thf(574,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(2904,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)],[574]) ).
thf(194,axiom,
class_Int_Oring__char__0 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).
thf(1698,plain,
class_Int_Oring__char__0 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(291,axiom,
class_Rings_Ocomm__ring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring) ).
thf(1959,plain,
class_Rings_Ocomm__ring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(470,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( 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(2556,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(702,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__semidom @ B )
=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( hAPP @ ( hAPP @ ( 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(3358,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__semidom @ B )
=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(383,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( hAPP @ ( 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(2275,plain,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( hAPP @ ( 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 ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(475,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__mono2) ).
thf(2570,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(947,axiom,
class_Groups_Oone @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
thf(4256,plain,
class_Groups_Oone @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(998,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(4438,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)],[998]) ).
thf(584,axiom,
! [A: $i] :
( ( class_Groups_Ozero @ A )
=> ( ( c_Polynomial_Odegree @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__0) ).
thf(2941,plain,
! [A: $i] :
( ( class_Groups_Ozero @ A )
=> ( ( c_Polynomial_Odegree @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(135,axiom,
class_Groups_Ocomm__monoid__mult @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).
thf(1548,plain,
class_Groups_Ocomm__monoid__mult @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(279,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Ocomm__ring__1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Ocomm__ring__1) ).
thf(1927,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Ocomm__ring__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(806,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(3738,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)],[806]) ).
thf(709,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(3375,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)],[709]) ).
thf(152,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ ( c_Divides_Odiv__class_Odiv @ D @ B @ C ) )
= ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__swap) ).
thf(1595,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ ( c_Divides_Odiv__class_Odiv @ D @ B @ C ) )
= ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(835,axiom,
( ( class_Rings_Oidom @ t_a )
=> ~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant @ t_a @ t_a @ ( c_Polynomial_Opoly @ t_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__C0_C) ).
thf(3839,plain,
( ( class_Rings_Oidom @ t_a )
=> ~ ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant @ t_a @ t_a @ ( c_Polynomial_Opoly @ t_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(1020,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(4503,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)],[1020]) ).
thf(1043,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ ( c_Groups_Oone__class_Oone @ C ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) @ A ) ) @ A )
= ( c_Groups_Oone__class_Oone @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__linear__power) ).
thf(4577,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ ( c_Groups_Oone__class_Oone @ C ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) @ A ) ) @ A )
= ( c_Groups_Oone__class_Oone @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).
thf(714,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(3396,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)],[714]) ).
thf(412,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( class_Fields_Ofield @ H )
=> ( ( c_Polynomial_Opdivmod__rel @ H @ G @ F @ E @ D )
=> ( ( c_Polynomial_Opdivmod__rel @ H @ E @ C @ B @ A )
=> ( c_Polynomial_Opdivmod__rel @ H @ G @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ H ) ) @ F ) @ C ) @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ H ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ H ) ) @ F ) @ A ) ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__mult) ).
thf(2376,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( class_Fields_Ofield @ H )
=> ( ( c_Polynomial_Opdivmod__rel @ H @ G @ F @ E @ D )
=> ( ( c_Polynomial_Opdivmod__rel @ H @ E @ C @ B @ A )
=> ( c_Polynomial_Opdivmod__rel @ H @ G @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ H ) ) @ F ) @ C ) @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ H ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ H ) ) @ F ) @ A ) ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(1003,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ 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_Odiff__left) ).
thf(4453,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ 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)],[1003]) ).
thf(921,axiom,
! [A: $i,B: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less2) ).
thf(4144,plain,
! [A: $i,B: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(712,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Ofield @ E )
=> ( ( D
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ E ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ E ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ A ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__frac__eq) ).
thf(3387,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Ofield @ E )
=> ( ( D
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ E ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ E ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ A ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(274,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ E ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ E ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( 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(1916,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ E ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ E ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( 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)],[274]) ).
thf(263,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ C ) ) @ B ) @ A )
= ( c_Polynomial_OAbs__poly @ C @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ C @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ C @ C ) @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ C ) ) @ ( c_Polynomial_Ocoeff @ C @ B ) ) ) @ ( c_Polynomial_Ocoeff @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__poly__def) ).
thf(1884,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ C ) ) @ B ) @ A )
= ( c_Polynomial_OAbs__poly @ C @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ C @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ C @ C ) @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ C ) ) @ ( c_Polynomial_Ocoeff @ C @ B ) ) ) @ ( c_Polynomial_Ocoeff @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(746,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( ( hAPP @ ( hAPP @ ( 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(3519,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( ( ( hAPP @ ( hAPP @ ( 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 ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(628,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__not__sym) ).
thf(3086,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(598,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ C ) @ A )
<=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__divide__less__eq) ).
thf(2991,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ B ) )
& ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(768,axiom,
! [A: $i] :
( ( class_Groups_Ozero @ A )
=> ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) )
= ( c_Polynomial_OAbs__poly @ A @ ( hAPP @ ( c_COMBK @ A @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__poly__def) ).
thf(3604,plain,
! [A: $i] :
( ( class_Groups_Ozero @ A )
=> ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) )
= ( c_Polynomial_OAbs__poly @ A @ ( hAPP @ ( c_COMBK @ A @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(669,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( 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 ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ ( c_Groups_Oone__class_Oone @ C ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) @ ( hAPP @ c_Nat_OSuc @ ( c_Polynomial_Oorder @ C @ A @ B ) ) ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order) ).
thf(3213,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( 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 ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ ( c_Groups_Oone__class_Oone @ C ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) @ ( hAPP @ c_Nat_OSuc @ ( c_Polynomial_Oorder @ C @ A @ B ) ) ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(750,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__Suc) ).
thf(3536,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(1134,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( hAPP @ 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(4943,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( hAPP @ 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 @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).
thf(624,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__commute) ).
thf(3070,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(516,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 ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__inverse) ).
thf(2727,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 ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(320,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(2048,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)],[320]) ).
thf(556,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( hAPP @ ( hAPP @ ( 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(2859,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( hAPP @ ( hAPP @ ( 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)],[556]) ).
thf(160,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( c_Polynomial_Opdivmod__rel @ C @ B @ A @ ( c_Divides_Odiv__class_Odiv @ ( tc_Polynomial_Opoly @ C ) @ B @ A ) @ ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ C ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel) ).
thf(1615,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( c_Polynomial_Opdivmod__rel @ C @ B @ A @ ( c_Divides_Odiv__class_Odiv @ ( tc_Polynomial_Opoly @ C ) @ B @ A ) @ ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ C ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( class_Fields_Ofield @ G )
=> ( ( c_Polynomial_Opdivmod__rel @ G @ F @ E @ D @ C )
=> ( ( c_Polynomial_Opdivmod__rel @ G @ F @ E @ B @ A )
=> ( C = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__unique__mod) ).
thf(1389,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( class_Fields_Ofield @ G )
=> ( ( c_Polynomial_Opdivmod__rel @ G @ F @ E @ D @ C )
=> ( ( c_Polynomial_Opdivmod__rel @ G @ F @ E @ B @ A )
=> ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(535,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(2791,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)],[535]) ).
thf(676,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__field @ D )
=> ( ( c_Deriv_Oderiv @ D @ C @ B @ A )
=> ( ( ( hAPP @ C @ B )
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Deriv_Oderiv @ D @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ D @ D ) @ ( c_Rings_Oinverse__class_Oinverse @ D ) ) @ C ) @ B @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ D ) @ ( hAPP @ C @ B ) ) ) @ A ) ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ D ) @ ( hAPP @ C @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__inverse_H) ).
thf(3240,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__field @ D )
=> ( ( c_Deriv_Oderiv @ D @ C @ B @ A )
=> ( ( ( hAPP @ C @ B )
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Deriv_Oderiv @ D @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ D @ D ) @ ( c_Rings_Oinverse__class_Oinverse @ D ) ) @ C ) @ B @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ D ) @ ( hAPP @ C @ B ) ) ) @ A ) ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ D ) @ ( hAPP @ C @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(1168,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_RealVector_Oreal__normed__field @ F )
=> ( ( c_Deriv_Oderiv @ F @ E @ D @ C )
=> ( ( c_Deriv_Oderiv @ F @ B @ D @ A )
=> ( c_Deriv_Oderiv @ F @ ( hAPP @ ( hAPP @ ( c_COMBS @ F @ F @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ ( tc_fun @ F @ F ) @ F ) @ ( c_Groups_Otimes__class_Otimes @ F ) ) @ E ) ) @ B ) @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ C ) @ ( hAPP @ B @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ A ) @ ( hAPP @ E @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__mult) ).
thf(5065,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_RealVector_Oreal__normed__field @ F )
=> ( ( c_Deriv_Oderiv @ F @ E @ D @ C )
=> ( ( c_Deriv_Oderiv @ F @ B @ D @ A )
=> ( c_Deriv_Oderiv @ F @ ( hAPP @ ( hAPP @ ( c_COMBS @ F @ F @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ ( tc_fun @ F @ F ) @ F ) @ ( c_Groups_Otimes__class_Otimes @ F ) ) @ E ) ) @ B ) @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ C ) @ ( hAPP @ B @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ A ) @ ( hAPP @ E @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).
thf(552,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( 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(2849,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( 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)],[552]) ).
thf(359,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__eq__diff__pred) ).
thf(2188,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(1169,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ 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(5067,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ 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)],[1169]) ).
thf(280,axiom,
! [A: $i,B: $i] :
( ( class_Divides_Osemiring__div @ B )
=> ( ( c_Divides_Odiv__class_Omod @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__by__0) ).
thf(1929,plain,
! [A: $i,B: $i] :
( ( class_Divides_Osemiring__div @ B )
=> ( ( c_Divides_Odiv__class_Omod @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(865,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( hAPP @ ( 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(3945,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( hAPP @ ( 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 ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(501,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__pred) ).
thf(2674,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(311,axiom,
! [A: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zminus) ).
thf(2016,plain,
! [A: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(456,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__add__right) ).
thf(2514,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(892,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc) ).
thf(4032,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(1077,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( 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(4709,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).
thf(1007,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( 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(4465,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(848,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(3900,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)],[848]) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__dvd) ).
thf(1403,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(1178,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(5097,plain,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178]) ).
thf(507,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Nat_Onat_Onat__case @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__case__0) ).
thf(2695,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Nat_Onat_Onat__case @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(19,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Groups_Ozero @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Ozero) ).
thf(1256,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Groups_Ozero @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1021,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Oring @ E )
=> ( ( hAPP @ ( hAPP @ ( 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 ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ C ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ D ) @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__diff__mult) ).
thf(4505,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Oring @ E )
=> ( ( hAPP @ ( hAPP @ ( 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 ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ C ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ D ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(766,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(3599,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)],[766]) ).
thf(1014,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__inverse__eq) ).
thf(4485,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(1144,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(4978,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)],[1144]) ).
thf(811,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) )
= ( c_Divides_Odiv__class_Odiv @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__mult2) ).
thf(3751,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) )
= ( c_Divides_Odiv__class_Odiv @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(388,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) @ ( hAPP @ 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(2293,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) @ ( hAPP @ 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 @ ( hAPP @ c_Nat_OSuc @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(911,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add2) ).
thf(4112,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(797,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oantisym__conv) ).
thf(3700,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(833,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(3832,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)],[833]) ).
thf(1111,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__ring @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ D ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__diff__right) ).
thf(4854,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__ring @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ D ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).
thf(720,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).
thf(3416,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__field @ D )
=> ( ( c_Deriv_Oderiv @ D @ C @ B @ A )
=> ( c_Deriv_Oderiv @ D @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ D @ D ) @ ( c_Groups_Ouminus__class_Ouminus @ D ) ) @ C ) @ B @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__minus) ).
thf(1464,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__field @ D )
=> ( ( c_Deriv_Oderiv @ D @ C @ B @ A )
=> ( c_Deriv_Oderiv @ D @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ D @ D ) @ ( c_Groups_Ouminus__class_Ouminus @ D ) ) @ C ) @ B @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
<=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ B )
| ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
thf(1356,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ B )
| ( B = A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ C @ A @ B )
| ( B = A ) )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(186,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(1675,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)],[186]) ).
thf(227,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_RealVector_Oreal__normed__field @ F )
=> ( ( c_Deriv_Oderiv @ F @ E @ D @ C )
=> ( ( c_Deriv_Oderiv @ F @ B @ D @ A )
=> ( c_Deriv_Oderiv @ F @ ( hAPP @ ( hAPP @ ( c_COMBS @ F @ F @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ ( tc_fun @ F @ F ) @ F ) @ ( c_Groups_Oplus__class_Oplus @ F ) ) @ E ) ) @ B ) @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__add) ).
thf(1786,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_RealVector_Oreal__normed__field @ F )
=> ( ( c_Deriv_Oderiv @ F @ E @ D @ C )
=> ( ( c_Deriv_Oderiv @ F @ B @ D @ A )
=> ( c_Deriv_Oderiv @ F @ ( hAPP @ ( hAPP @ ( c_COMBS @ F @ F @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ ( tc_fun @ F @ F ) @ F ) @ ( c_Groups_Oplus__class_Oplus @ F ) ) @ E ) ) @ B ) @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(610,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(3023,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)],[610]) ).
thf(314,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(2029,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)],[314]) ).
thf(907,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(4096,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)],[907]) ).
thf(1098,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( c_Polynomial_Ocoeff @ C @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ B ) @ A ) )
= ( c_Nat_Onat_Onat__case @ C @ B @ ( c_Polynomial_Ocoeff @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__pCons) ).
thf(4796,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( c_Polynomial_Ocoeff @ C @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ B ) @ A ) )
= ( c_Nat_Onat_Onat__case @ C @ B @ ( c_Polynomial_Ocoeff @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ( B != A )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__cases) ).
thf(1271,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ( B != A )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(794,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__mono) ).
thf(3695,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(698,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( C
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ A ) )
<=> ( ( ( A
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A )
= B ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__eq) ).
thf(3330,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( ( C
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ A ) )
=> ( ( ( A
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A )
= B ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) )
& ( ( ( ( A
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A )
= B ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) )
=> ( C
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(518,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(2738,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)],[518]) ).
thf(929,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Polynomial_Opos__poly @ C @ ( hAPP @ ( hAPP @ ( 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(4171,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( ( c_Polynomial_Opos__poly @ C @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(783,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) ) @ A )
= ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__int) ).
thf(3663,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) ) @ A )
= ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(166,axiom,
class_Divides_Osemiring__div @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Osemiring__div) ).
thf(1635,plain,
class_Divides_Osemiring__div @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(602,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(3002,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)],[602]) ).
thf(526,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oordered__ring @ F )
=> ( ( c_Orderings_Oord__class_Oless @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ F @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ F ) @ B ) @ E ) ) @ D ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__iff2) ).
thf(2759,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oordered__ring @ F )
=> ( ( ( c_Orderings_Oord__class_Oless @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ F @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ F ) @ B ) @ E ) ) @ D ) ) @ A ) ) )
& ( ( c_Orderings_Oord__class_Oless @ F @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ F ) @ B ) @ E ) ) @ D ) ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) ) @ C ) @ ( hAPP @ ( hAPP @ ( 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)],[526]) ).
thf(728,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( c_Polynomial_Odegree @ C @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ A ) @ B ) )
= ( hAPP @ c_Nat_OSuc @ ( c_Polynomial_Odegree @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__pCons__eq) ).
thf(3436,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( c_Polynomial_Odegree @ C @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ A ) @ B ) )
= ( hAPP @ c_Nat_OSuc @ ( c_Polynomial_Odegree @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(20,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 )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__not__zless) ).
thf(1258,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 )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(1194,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ B ) @ A ) )
| ( hBOOL @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__3) ).
thf(5158,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ B ) @ A ) )
| ( hBOOL @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194]) ).
thf(1120,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__field @ E )
=> ( ( c_Deriv_Oderiv @ E @ D @ C @ B )
=> ( c_Deriv_Oderiv @ E @ ( hAPP @ ( c_COMBC @ E @ tc_Nat_Onat @ E @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ tc_Nat_Onat @ E ) @ E ) @ ( c_Power_Opower__class_Opower @ E ) ) @ D ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ E @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ E ) @ ( hAPP @ D @ C ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__power__Suc) ).
thf(4887,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__field @ E )
=> ( ( c_Deriv_Oderiv @ E @ D @ C @ B )
=> ( c_Deriv_Oderiv @ E @ ( hAPP @ ( c_COMBC @ E @ tc_Nat_Onat @ E @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ tc_Nat_Onat @ E ) @ E ) @ ( c_Power_Opower__class_Opower @ E ) ) @ D ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ E @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ E ) @ ( hAPP @ D @ C ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).
thf(701,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Osemiring__1 @ B )
=> ( ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A )
= ( c_Nat_Osemiring__1__class_Oof__nat__aux @ B @ ( hAPP @ ( c_COMBC @ B @ B @ B @ ( c_Groups_Oplus__class_Oplus @ B ) ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__1__class_Oof__nat__code) ).
thf(3355,plain,
! [A: $i,B: $i] :
( ( class_Rings_Osemiring__1 @ B )
=> ( ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A )
= ( c_Nat_Osemiring__1__class_Oof__nat__aux @ B @ ( hAPP @ ( c_COMBC @ B @ B @ B @ ( c_Groups_Oplus__class_Oplus @ B ) ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(402,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Divides_Odiv__class_Omod @ D @ C @ B ) ) @ A ) @ B )
= ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__simps_I4_J) ).
thf(2346,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Divides_Odiv__class_Omod @ D @ C @ B ) ) @ A ) @ B )
= ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(1096,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__divide__eq__iff) ).
thf(4790,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).
thf(1075,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ D ) ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__lemma) ).
thf(4704,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ D ) ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).
thf(1132,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( hAPP @ ( hAPP @ ( 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(4929,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( ( hAPP @ ( hAPP @ ( 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 ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).
thf(370,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Polynomial_Odegree @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ ( c_Groups_Oone__class_Oone @ C ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__linear__power) ).
thf(2229,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Polynomial_Odegree @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ ( c_Groups_Oone__class_Oone @ C ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(365,axiom,
class_Groups_Ominus @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).
thf(2214,plain,
class_Groups_Ominus @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(1105,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ C ) @ A )
<=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__divide__less__eq) ).
thf(4828,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) )
& ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
thf(721,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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(3419,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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)],[721]) ).
thf(204,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Fields_Ofield @ F )
=> ( ( E
!= ( c_Groups_Ozero__class_Ozero @ F ) )
=> ( ( c_Polynomial_Opdivmod__rel @ F @ D @ C @ B @ A )
=> ( c_Polynomial_Opdivmod__rel @ F @ D @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ F ) @ E ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ F ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ F ) @ E ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__smult__right) ).
thf(1722,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Fields_Ofield @ F )
=> ( ( E
!= ( c_Groups_Ozero__class_Ozero @ F ) )
=> ( ( c_Polynomial_Opdivmod__rel @ F @ D @ C @ B @ A )
=> ( c_Polynomial_Opdivmod__rel @ F @ D @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ F ) @ E ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ F ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ F ) @ E ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(339,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__le) ).
thf(2116,plain,
! [A: $i,B: $i] :
( ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ( B != A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ( B != A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(1138,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( c_Polynomial_Odegree @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ C ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Polynomial_Odegree @ C @ B ) ) @ ( c_Polynomial_Odegree @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__mult__eq) ).
thf(4958,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( c_Polynomial_Odegree @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ C ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Polynomial_Odegree @ C @ B ) ) @ ( c_Polynomial_Odegree @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).
thf(711,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(3384,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)],[711]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( class_Divides_Osemiring__div @ B )
=> ( ( c_Divides_Odiv__class_Odiv @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__0) ).
thf(1209,plain,
! [A: $i,B: $i] :
( ( class_Divides_Osemiring__div @ B )
=> ( ( c_Divides_Odiv__class_Odiv @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(514,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( 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(2721,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(700,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( 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(3352,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(881,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ D ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ D ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__smult__left) ).
thf(3996,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ D ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ D ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(777,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 @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ F ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ C @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_If @ E ) @ ( hAPP @ ( 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(3631,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 @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ F ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ C @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_If @ E ) @ ( hAPP @ ( 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)],[777]) ).
thf(464,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Divides_Odiv__class_Odiv @ D @ C @ B ) ) @ B ) ) @ ( c_Divides_Odiv__class_Omod @ D @ C @ B ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mod__equality) ).
thf(2538,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Divides_Odiv__class_Odiv @ D @ C @ B ) ) @ B ) ) @ ( c_Divides_Odiv__class_Omod @ D @ C @ B ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(253,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__diff__nat) ).
thf(1853,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(443,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( c_Polynomial_Omonom @ B @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( hAPP @ ( hAPP @ ( 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(2478,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( c_Polynomial_Omonom @ B @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(979,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ C ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__trans) ).
thf(4369,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ C ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(144,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ C ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( c_Divides_Odiv__class_Odiv @ C @ A @ B ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__div__cancel) ).
thf(1574,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ C ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( c_Divides_Odiv__class_Odiv @ C @ A @ B ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(234,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Groups_Oab__semigroup__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Oab__semigroup__add) ).
thf(1806,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Groups_Oab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(1129,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(4914,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)],[1129]) ).
thf(1073,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SucI) ).
thf(4699,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).
thf(684,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__divide__eq__iff) ).
thf(3270,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(150,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ C ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Divides_Odiv__class_Odiv @ C @ A @ B ) ) @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__div__mult__self) ).
thf(1589,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ C ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Divides_Odiv__class_Odiv @ C @ A @ B ) ) @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(804,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__left) ).
thf(3732,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(113,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(1492,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)],[113]) ).
thf(155,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__right) ).
thf(1603,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(636,axiom,
! [A: $i] :
( ( class_Fields_Ofield @ A )
=> ( ( c_Polynomial_Opoly__gcd @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__0__0) ).
thf(3106,plain,
! [A: $i] :
( ( class_Fields_Ofield @ A )
=> ( ( c_Polynomial_Opoly__gcd @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(733,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ~ ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__1) ).
thf(3468,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ~ ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(664,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( c_Divides_Odiv__class_Omod @ D @ C @ A ) ) @ ( c_Divides_Odiv__class_Omod @ D @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__eq) ).
thf(3197,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( c_Divides_Odiv__class_Omod @ D @ C @ A ) ) @ ( c_Divides_Odiv__class_Omod @ D @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(902,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(4073,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)],[902]) ).
thf(555,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Nat_Onat_Onat__case @ D @ C @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__case__Suc) ).
thf(2856,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Nat_Onat_Onat__case @ D @ C @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(539,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ B ) ) @ A )
= ( hAPP @ ( 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(2802,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ B ) ) @ A )
= ( hAPP @ ( 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)],[539]) ).
thf(644,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( B
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ C ) )
<=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__eq__divide__eq) ).
thf(3138,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( B
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C )
= A ) )
& ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C )
= A )
=> ( B
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(413,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).
thf(2378,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(571,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Divides_Odiv__class_Omod @ D @ C @ A ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__left__eq) ).
thf(2896,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Divides_Odiv__class_Omod @ D @ C @ A ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(1011,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Ofield @ B )
=> ( ( c_Polynomial_Opoly__gcd @ B @ A @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) )
= ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__1__right) ).
thf(4477,plain,
! [A: $i,B: $i] :
( ( class_Fields_Ofield @ B )
=> ( ( c_Polynomial_Opoly__gcd @ B @ A @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) )
= ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(909,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(4107,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)],[909]) ).
thf(295,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Nat_Osemiring__char__0 @ C )
=> ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ C @ B )
= ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__eq__iff) ).
thf(1969,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Nat_Osemiring__char__0 @ C )
=> ( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ C @ B )
= ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Nat_Osemiring__1__class_Oof__nat @ C @ B )
= ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(650,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) )
= ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J) ).
thf(3160,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) )
= ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(182,axiom,
class_Rings_Oordered__ring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).
thf(1667,plain,
class_Rings_Oordered__ring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(357,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( c_Divides_Odiv__class_Omod @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self2__is__0) ).
thf(2182,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( c_Divides_Odiv__class_Omod @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(1159,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(5035,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)],[1159]) ).
thf(1032,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).
thf(4541,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).
thf(759,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( hAPP @ ( hAPP @ ( 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(3572,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(525,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(2757,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)],[525]) ).
thf(257,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oab__group__add @ E )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ B ) @ A ) )
=> ( ( D = C )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__eq) ).
thf(1862,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oab__group__add @ E )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ B ) @ A ) )
=> ( ( ( D = C )
=> ( B = A ) )
& ( ( B = A )
=> ( D = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(662,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ( c_Orderings_Oord__class_Oless @ A @ ( c_Groups_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( 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(3192,plain,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ( c_Orderings_Oord__class_Oless @ A @ ( c_Groups_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( 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)],[662]) ).
thf(1062,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__divide__inverse) ).
thf(4652,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) )
=> ( ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ D ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ D ) @ B ) @ A ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ D ) @ B ) @ ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ D ) @ A @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ D @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ D ) @ B ) @ ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ D ) @ A @ C ) ) ) @ ( c_Polynomial_Odegree @ D @ C ) ) ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ D @ C ) @ ( c_Polynomial_Odegree @ D @ C ) ) ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__pCons) ).
thf(1381,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) )
=> ( ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ D ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ D ) @ B ) @ A ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ D ) @ B ) @ ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ D ) @ A @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ D @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ D ) @ B ) @ ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ D ) @ A @ C ) ) ) @ ( c_Polynomial_Odegree @ D @ C ) ) ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ D @ C ) @ ( c_Polynomial_Odegree @ D @ C ) ) ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(242,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__semidom @ B )
=> ~ ( c_Orderings_Oord__class_Oless @ B @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__less__0__iff) ).
thf(1820,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__semidom @ B )
=> ~ ( c_Orderings_Oord__class_Oless @ B @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(483,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_COMBI @ B ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBI__1) ).
thf(2605,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_COMBI @ B ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(612,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( hAPP @ ( 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(3027,plain,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( hAPP @ ( 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)],[612]) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) )
= ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__int) ).
thf(1339,plain,
! [A: $i,B: $i] :
( ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) )
= ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(992,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(4420,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)],[992]) ).
thf(1119,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__reduce) ).
thf(4882,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( 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)],[1119]) ).
thf(886,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(4009,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)],[886]) ).
thf(401,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__pCons__0) ).
thf(2343,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(489,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__0 @ B )
=> ( ( hAPP @ ( hAPP @ ( 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(2625,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__0 @ B )
=> ( ( hAPP @ ( hAPP @ ( 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)],[489]) ).
thf(1174,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__pCons) ).
thf(5082,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).
thf(1040,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(4569,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)],[1040]) ).
thf(1006,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( hAPP @ ( 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(4462,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ A )
!= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(1128,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( c_Polynomial_Oorder @ C @ B @ A )
= ( c_Orderings_Oord__class_OLeast @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ tc_Nat_Onat ) @ c_fNot ) @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ ( tc_Polynomial_Opoly @ C ) @ tc_HOL_Obool @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_Polynomial_Opoly @ C ) @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_Polynomial_Opoly @ C ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ ( c_Groups_Oone__class_Oone @ C ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) ) @ c_Nat_OSuc ) ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__def) ).
thf(4911,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( c_Polynomial_Oorder @ C @ B @ A )
= ( c_Orderings_Oord__class_OLeast @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ tc_Nat_Onat ) @ c_fNot ) @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ ( tc_Polynomial_Opoly @ C ) @ tc_HOL_Obool @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_Polynomial_Opoly @ C ) @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_Polynomial_Opoly @ C ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ ( c_Groups_Oone__class_Oone @ C ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) ) @ c_Nat_OSuc ) ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).
thf(625,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ B ) @ A ) )
<=> ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
| ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__divide__iff) ).
thf(3073,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ B ) @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
| ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
| ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(900,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(4064,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)],[900]) ).
thf(1103,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( 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(4818,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).
thf(208,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(1731,plain,
class_Rings_Oring__1__no__zero__divisors @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(825,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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(3800,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( 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)],[825]) ).
thf(950,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ C )
=> ( ( ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B )
= ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__eq__imp__eq) ).
thf(4264,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ C )
=> ( ( ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B )
= ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(875,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Osemiring__1 @ C )
=> ( ( c_Nat_Osemiring__1__class_Oof__nat @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ B ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__mult) ).
thf(3977,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Osemiring__1 @ C )
=> ( ( c_Nat_Osemiring__1__class_Oof__nat @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ B ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(581,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(2923,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)],[581]) ).
thf(772,axiom,
class_Rings_Olinordered__semiring__strict @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).
thf(3614,plain,
class_Rings_Olinordered__semiring__strict @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(873,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( 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(3971,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(762,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 )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__dvd__not__less) ).
thf(3583,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 )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(376,axiom,
! [A: $i] :
( ( class_Groups_Oab__group__add @ A )
=> ( class_Groups_Ominus @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ominus) ).
thf(2252,plain,
! [A: $i] :
( ( class_Groups_Oab__group__add @ A )
=> ( class_Groups_Ominus @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(839,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__div__pos__less) ).
thf(3861,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ B ) @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zminus1__not__zero) ).
thf(1293,plain,
! [A: $i,B: $i] :
( ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ B ) @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(384,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(2278,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)],[384]) ).
thf(469,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__divide__distrib) ).
thf(2553,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(437,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__neg__neg) ).
thf(2461,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(591,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 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ B ) )
!= ( hAPP @ ( hAPP @ ( 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(2974,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 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ B ) )
!= ( hAPP @ ( hAPP @ ( 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)],[591]) ).
thf(646,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(3150,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)],[646]) ).
thf(1069,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__pos__neg) ).
thf(4684,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).
thf(938,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ C ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__power__divide) ).
thf(4232,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ C ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(547,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( c_Polynomial_Omonom @ C @ B @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( 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(2835,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( c_Polynomial_Omonom @ C @ B @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( c_Polynomial_Omonom @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(171,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ouminus @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ D ) ) @ B ) @ A )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ D ) @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__apply) ).
thf(1643,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ouminus @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ D ) ) @ B ) @ A )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ D ) @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(868,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Divides_Odiv__class_Odiv @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( c_Divides_Odiv__class_Odiv @ C @ A @ B ) ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__add__self1) ).
thf(3953,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Divides_Odiv__class_Odiv @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( c_Divides_Odiv__class_Odiv @ C @ A @ B ) ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(704,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ole__less__trans) ).
thf(3363,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(601,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(2999,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)],[601]) ).
thf(751,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(3539,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)],[751]) ).
thf(530,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ C ) @ B ) @ A )
= ( c_Polynomial_OAbs__poly @ C @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ C @ tc_Nat_Onat ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) ) @ ( c_Polynomial_Ocoeff @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__def) ).
thf(2770,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ C ) @ B ) @ A )
= ( c_Polynomial_OAbs__poly @ C @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ C @ tc_Nat_Onat ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) ) @ ( c_Polynomial_Ocoeff @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(1165,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Ofield @ B )
=> ( c_Polynomial_Opdivmod__rel @ B @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__by__0) ).
thf(5057,plain,
! [A: $i,B: $i] :
( ( class_Fields_Ofield @ B )
=> ( c_Polynomial_Opdivmod__rel @ B @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).
thf(430,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(2439,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)],[430]) ).
thf(515,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(2725,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)],[515]) ).
thf(195,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ C ) @ B ) @ A ) )
<=> ( ( c_Divides_Odiv__class_Omod @ C @ A @ B )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__eq__mod__eq__0) ).
thf(1699,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ C ) @ B ) @ A ) )
=> ( ( c_Divides_Odiv__class_Omod @ C @ A @ B )
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( ( ( c_Divides_Odiv__class_Omod @ C @ A @ B )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(1198,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( 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(5197,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( 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)],[1198]) ).
thf(321,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( 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 ) ) ) @ ( hAPP @ ( hAPP @ ( 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(2051,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( 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 ) ) ) @ ( hAPP @ ( hAPP @ ( 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)],[321]) ).
thf(1177,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_RealVector_Oreal__normed__field @ F )
=> ( ( c_Deriv_Oderiv @ F @ E @ D @ C )
=> ( ( c_Deriv_Oderiv @ F @ B @ D @ A )
=> ( ( ( hAPP @ B @ D )
!= ( c_Groups_Ozero__class_Ozero @ F ) )
=> ( c_Deriv_Oderiv @ F @ ( hAPP @ ( hAPP @ ( c_COMBS @ F @ F @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ ( tc_fun @ F @ F ) @ F ) @ ( c_Rings_Oinverse__class_Odivide @ F ) ) @ E ) ) @ B ) @ D @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ C ) @ ( hAPP @ B @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ A ) @ ( hAPP @ E @ D ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ F ) @ ( hAPP @ B @ D ) ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__quotient) ).
thf(5094,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_RealVector_Oreal__normed__field @ F )
=> ( ( c_Deriv_Oderiv @ F @ E @ D @ C )
=> ( ( c_Deriv_Oderiv @ F @ B @ D @ A )
=> ( ( ( hAPP @ B @ D )
!= ( c_Groups_Ozero__class_Ozero @ F ) )
=> ( c_Deriv_Oderiv @ F @ ( hAPP @ ( hAPP @ ( c_COMBS @ F @ F @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ ( tc_fun @ F @ F ) @ F ) @ ( c_Rings_Oinverse__class_Odivide @ F ) ) @ E ) ) @ B ) @ D @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ C ) @ ( hAPP @ B @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ A ) @ ( hAPP @ E @ D ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ F ) @ ( hAPP @ B @ D ) ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).
thf(723,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( 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(3423,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( 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)],[723]) ).
thf(468,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(2550,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)],[468]) ).
thf(444,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Orderings_Olinorder @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Olinorder) ).
thf(2481,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Orderings_Olinorder @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(345,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( c_Nat_Onat_Onat__case @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_COMBI @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc) ).
thf(2139,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( c_Nat_Onat_Onat__case @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_COMBI @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(826,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ocomm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ B ) @ ( c_Polynomial_Odegree @ C @ A ) )
=> ( ( c_Polynomial_Odegree @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ C ) ) @ B ) @ A ) )
= ( c_Polynomial_Odegree @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__add__eq__right) ).
thf(3806,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ocomm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ B ) @ ( c_Polynomial_Odegree @ C @ A ) )
=> ( ( c_Polynomial_Odegree @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ C ) ) @ B ) @ A ) )
= ( c_Polynomial_Odegree @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(325,axiom,
( ( c_Groups_Oone__class_Oone @ tc_Int_Oint )
= ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__numerals_I2_J) ).
thf(2064,plain,
( ( c_Groups_Oone__class_Oone @ tc_Int_Oint )
= ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(409,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ F @ E @ D ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBS__1) ).
thf(2369,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ F @ E @ D ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(224,axiom,
! [A: $i,B: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ A ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zminus1__eq__if) ).
thf(1775,plain,
! [A: $i,B: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ A ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(523,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oordered__ab__semigroup__add__imp__le @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(2752,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oordered__ab__semigroup__add__imp__le @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(798,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(3706,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)],[798]) ).
thf(696,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ 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_Odiff) ).
thf(3325,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ 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)],[696]) ).
thf(463,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(2535,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)],[463]) ).
thf(333,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_fequal @ B ) @ A ) )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__1) ).
thf(2101,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_fequal @ B ) @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(115,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ 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__neq__iff) ).
thf(1496,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( ( B != A )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
| ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
| ( c_Orderings_Oord__class_Oless @ C @ A @ B ) )
=> ( B != A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(935,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Ofield @ E )
=> ( ( c_Polynomial_Opdivmod__rel @ E @ D @ C @ B @ A )
<=> ( ( D
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ E ) ) @ B ) @ C ) ) @ A ) )
& ( ( C
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ E ) ) )
=> ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ E ) ) ) )
& ( ( C
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ E ) ) )
=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ E ) ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ E @ A ) @ ( c_Polynomial_Odegree @ E @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__def) ).
thf(4196,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Ofield @ E )
=> ( ( ( c_Polynomial_Opdivmod__rel @ E @ D @ C @ B @ A )
=> ( ( D
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ E ) ) @ B ) @ C ) ) @ A ) )
& ( ( C
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ E ) ) )
=> ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ E ) ) ) )
& ( ( C
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ E ) ) )
=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ E ) ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ E @ A ) @ ( c_Polynomial_Odegree @ E @ C ) ) ) ) ) )
& ( ( ( D
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ E ) ) @ B ) @ C ) ) @ A ) )
& ( ( C
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ E ) ) )
=> ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ E ) ) ) )
& ( ( C
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ E ) ) )
=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ E ) ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ E @ A ) @ ( c_Polynomial_Odegree @ E @ C ) ) ) ) )
=> ( c_Polynomial_Opdivmod__rel @ E @ D @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(657,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__right__mono) ).
thf(3178,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(1053,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(4626,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)],[1053]) ).
thf(1189,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ B ) @ A )
= ( c_Polynomial_OAbs__poly @ C @ ( c_Nat_Onat_Onat__case @ C @ B @ ( c_Polynomial_Ocoeff @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__def) ).
thf(5139,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ B ) @ A )
= ( c_Polynomial_OAbs__poly @ C @ ( c_Nat_Onat_Onat__case @ C @ B @ ( c_Polynomial_Ocoeff @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189]) ).
thf(1122,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( 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(4890,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).
thf(327,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ A ) )
= ( hAPP @ ( hAPP @ ( 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(2069,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ A ) )
= ( hAPP @ ( hAPP @ ( 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)],[327]) ).
thf(559,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(2867,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)],[559]) ).
thf(454,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Rings_Ocomm__ring @ D )
& ( class_Rings_Odvd @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ B ) )
=> ! [E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ E ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ F ) @ B ) ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__period_I4_J) ).
thf(2506,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Rings_Ocomm__ring @ D )
& ( class_Rings_Odvd @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ B ) )
=> ! [E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ E ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ F ) @ B ) ) ) @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ F ) @ B ) ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ E ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(140,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ~ ( c_Orderings_Oord__class_Oless @ B @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
thf(1562,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ~ ( c_Orderings_Oord__class_Oless @ B @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(904,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( B
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) )
<=> ( ( hAPP @ ( hAPP @ ( 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(4084,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( ( B
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( B
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(322,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(2054,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)],[322]) ).
thf(236,axiom,
class_Rings_Ono__zero__divisors @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).
thf(1809,plain,
class_Rings_Ono__zero__divisors @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(259,axiom,
class_Groups_Oab__semigroup__mult @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).
thf(1873,plain,
class_Groups_Oab__semigroup__mult @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(335,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 ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_positive__imp__inverse__positive) ).
thf(2107,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 ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(498,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 ) @ ( hAPP @ ( 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(2665,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 ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ A ) ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(1004,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__diff) ).
thf(4456,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(495,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(2652,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)],[495]) ).
thf(1118,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( ( c_Polynomial_Odegree @ A @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ A ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__1) ).
thf(4879,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( ( c_Polynomial_Odegree @ A @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ A ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).
thf(856,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(3921,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)],[856]) ).
thf(104,axiom,
! [A: $i,B: $i] :
( ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) )
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zminus2__not__zero) ).
thf(1472,plain,
! [A: $i,B: $i] :
( ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) )
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(290,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(1958,plain,
class_Groups_Ocancel__ab__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(970,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__0 @ B )
=> ( ( hAPP @ ( hAPP @ ( 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(4336,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__0 @ B )
=> ( ( hAPP @ ( hAPP @ ( 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)],[970]) ).
thf(987,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ B @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ B @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__1) ).
thf(4405,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ B @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ B @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(148,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ ( c_Polynomial_Opoly__gcd @ D @ B @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__poly__gcd__iff) ).
thf(1583,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ ( c_Polynomial_Opoly__gcd @ D @ B @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ ( c_Polynomial_Opoly__gcd @ D @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(1101,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(4813,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)],[1101]) ).
thf(1044,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 @ ( hAPP @ ( hAPP @ ( 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(4580,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 @ ( hAPP @ ( hAPP @ ( 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)],[1044]) ).
thf(599,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( 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(2994,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( 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)],[599]) ).
thf(1156,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(5025,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)],[1156]) ).
thf(269,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) ) @ ( c_Polynomial_Opoly__gcd @ C @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__dvd2) ).
thf(1905,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) ) @ ( c_Polynomial_Opoly__gcd @ C @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(85,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(1420,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)],[85]) ).
thf(453,axiom,
! [A: $i] :
( ( class_Rings_Osemiring__1 @ A )
=> ( ( c_Nat_Osemiring__1__class_Oof__nat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__1) ).
thf(2503,plain,
! [A: $i] :
( ( class_Rings_Osemiring__1 @ A )
=> ( ( c_Nat_Osemiring__1__class_Oof__nat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(189,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Polynomial_Opos__poly @ B @ A )
<=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ B @ A ) @ ( c_Polynomial_Odegree @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__def) ).
thf(1684,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( c_Polynomial_Opos__poly @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ B @ A ) @ ( c_Polynomial_Odegree @ B @ A ) ) ) )
& ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ B @ A ) @ ( c_Polynomial_Odegree @ B @ A ) ) )
=> ( c_Polynomial_Opos__poly @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(551,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( 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(2846,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ A ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(473,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(2564,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)],[473]) ).
thf(687,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__add @ B )
=> ( ( hAPP @ ( hAPP @ ( 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(3292,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__add @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(572,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 ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( 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(2899,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 ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( 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)],[572]) ).
thf(928,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ C ) )
<=> ( c_Orderings_Oord__class_Oless @ D @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__divide__eq) ).
thf(4168,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ C ) )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) ) )
& ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(477,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(2582,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)],[477]) ).
thf(1064,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( 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(4658,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ D ) @ A ) @ B ) )
=> ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(217,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ B ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__less__iff) ).
thf(1748,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ B ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ 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 @ C @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ B ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(389,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__field @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Deriv_Oderiv @ B @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ A @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ A ) ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__inverse) ).
thf(2298,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__field @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Deriv_Oderiv @ B @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ A @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ A ) ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(223,axiom,
! [A: $i,B: $i] :
( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) @ B )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) ) ) )
& ( ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B )
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zminus1__eq__if) ).
thf(1770,plain,
! [A: $i,B: $i] :
( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) @ B )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) ) ) )
& ( ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B )
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(893,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(4035,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)],[893]) ).
thf(417,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ D @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ D @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__smult) ).
thf(2397,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ D @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ D @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(853,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(3913,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)],[853]) ).
thf(1016,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(4490,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)],[1016]) ).
thf(1186,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__reduce) ).
thf(5125,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186]) ).
thf(411,axiom,
class_Nat_Osemiring__char__0 @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Nat_Osemiring__char__0) ).
thf(2375,plain,
class_Nat_Osemiring__char__0 @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(1067,axiom,
! [A: $i,B: $i] :
( ( ( B
= ( 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 ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__if) ).
thf(4673,plain,
! [A: $i,B: $i] :
( ( ( B
= ( 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 ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).
thf(173,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Groups_Oone @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Oone) ).
thf(1647,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Groups_Oone @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(641,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__def) ).
thf(3129,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(844,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( 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(3872,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(108,axiom,
! [A: $i] :
( ( class_Fields_Ofield @ A )
=> ( class_Divides_Osemiring__div @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Divides_Osemiring__div) ).
thf(1484,plain,
! [A: $i] :
( ( class_Fields_Ofield @ A )
=> ( class_Divides_Osemiring__div @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(1048,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ C ) ) )
=> ( ( B = A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oord__less__eq__trans) ).
thf(4593,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ C ) ) )
=> ( ( B = A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).
thf(1153,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 @ ( hAPP @ c_Nat_OSuc @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__trans__Suc) ).
thf(5018,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 @ ( hAPP @ c_Nat_OSuc @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153]) ).
thf(693,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(3315,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__idom @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(153,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( hAPP @ c_Nat_OSuc @ A ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negative__zless__0) ).
thf(1598,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( hAPP @ c_Nat_OSuc @ A ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ 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_order__less__imp__not__less) ).
thf(1225,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ 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)],[9]) ).
thf(953,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
<=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__diff__less__0) ).
thf(4272,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(978,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zmult1__eq) ).
thf(4366,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(156,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Odvd @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Odvd) ).
thf(1605,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Odvd @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(681,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(3260,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)],[681]) ).
thf(812,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Ofield @ B )
=> ( ( c_Polynomial_Opoly__gcd @ B @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) @ A )
= ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__1__left) ).
thf(3754,plain,
! [A: $i,B: $i] :
( ( class_Fields_Ofield @ B )
=> ( ( c_Polynomial_Opoly__gcd @ B @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) @ A )
= ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(1135,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( hAPP @ ( hAPP @ ( 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(4950,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).
thf(1024,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ 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_diff__mult__distrib) ).
thf(4517,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ 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)],[1024]) ).
thf(672,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__field @ C )
=> ( c_Deriv_Oderiv @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__cmult__Id) ).
thf(3228,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__field @ C )
=> ( c_Deriv_Oderiv @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(1058,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ B )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) @ B )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__times__mod__eq) ).
thf(4641,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ B )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) @ B )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(667,axiom,
( ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__Suc0__eq__1) ).
thf(3209,plain,
( ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(1088,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( A
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__pred_H) ).
thf(4754,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( A
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).
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(4961,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(421,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ C )
= A )
<=> ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__divide__eq__eq) ).
thf(2407,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ C )
= A )
=> ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) )
& ( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ C )
= A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(23,axiom,
class_Groups_Ouminus @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ouminus) ).
thf(1267,plain,
class_Groups_Ouminus @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(1173,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(5079,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)],[1173]) ).
thf(127,axiom,
class_Rings_Osemiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).
thf(1531,plain,
class_Rings_Osemiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(967,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(4324,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)],[967]) ).
thf(678,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oord__le__eq__trans) ).
thf(3246,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(941,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(4240,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)],[941]) ).
thf(862,axiom,
class_Groups_Ozero @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
thf(3940,plain,
class_Groups_Ozero @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(580,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__zero) ).
thf(2920,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(1152,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( 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(5015,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( 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)],[1152]) ).
thf(884,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__shift) ).
thf(4003,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(1035,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ D @ C )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( 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(4549,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ D @ C )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( 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)],[1035]) ).
thf(918,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ C @ B ) @ A ) ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult2__eq) ).
thf(4132,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ C @ B ) @ A ) ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(756,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__algebra @ E )
=> ( ( hAPP @ ( hAPP @ ( 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 ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ C ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ D ) @ B ) ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oprod__diff__prod) ).
thf(3564,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__algebra @ E )
=> ( ( hAPP @ ( hAPP @ ( 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 ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ C ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ D ) @ B ) ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(214,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ ( c_Divides_Odiv__class_Odiv @ D @ B @ C ) ) @ ( c_Divides_Odiv__class_Odiv @ D @ A @ C ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__dvd__div) ).
thf(1738,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ ( c_Divides_Odiv__class_Odiv @ D @ B @ C ) ) @ ( c_Divides_Odiv__class_Odiv @ D @ A @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ ( c_Divides_Odiv__class_Odiv @ D @ B @ C ) ) @ ( c_Divides_Odiv__class_Odiv @ D @ A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(1167,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zadd__distrib) ).
thf(5062,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).
thf(200,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(1711,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(626,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( 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(3080,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(689,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ 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_zdiff__zmult__distrib) ).
thf(3305,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ 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)],[689]) ).
thf(352,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 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B ) ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_division__ring__inverse__add) ).
thf(2165,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 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B ) ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ B ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__of__nat__less) ).
thf(1300,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ B ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(168,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Groups_Oab__group__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Oab__group__add) ).
thf(1637,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Groups_Oab__group__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(685,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield__inverse__zero @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ ( c_Groups_Oone__class_Oone @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ ( c_Groups_Oone__class_Oone @ C ) ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one__over) ).
thf(3273,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield__inverse__zero @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ ( c_Groups_Oone__class_Oone @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ ( c_Groups_Oone__class_Oone @ C ) ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(822,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( hAPP @ ( 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(3791,plain,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( hAPP @ ( 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 ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(936,axiom,
class_Rings_Ocomm__semiring__0 @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__0) ).
thf(4222,plain,
class_Rings_Ocomm__semiring__0 @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(258,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(1869,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)],[258]) ).
thf(428,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Divides_Osemiring__div @ F )
=> ( ( ( c_Divides_Odiv__class_Omod @ F @ E @ D )
= ( c_Divides_Odiv__class_Omod @ F @ C @ D ) )
=> ( ( ( c_Divides_Odiv__class_Omod @ F @ B @ D )
= ( c_Divides_Odiv__class_Omod @ F @ A @ D ) )
=> ( ( c_Divides_Odiv__class_Omod @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ E ) @ B ) @ D )
= ( c_Divides_Odiv__class_Omod @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ C ) @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__cong) ).
thf(2429,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Divides_Osemiring__div @ F )
=> ( ( ( c_Divides_Odiv__class_Omod @ F @ E @ D )
= ( c_Divides_Odiv__class_Omod @ F @ C @ D ) )
=> ( ( ( c_Divides_Odiv__class_Omod @ F @ B @ D )
= ( c_Divides_Odiv__class_Omod @ F @ A @ D ) )
=> ( ( c_Divides_Odiv__class_Omod @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ E ) @ B ) @ D )
= ( c_Divides_Odiv__class_Omod @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ C ) @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(1091,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ole__less) ).
thf(4768,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
| ( B = A ) ) )
& ( ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
| ( B = A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).
thf(298,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__divide__left) ).
thf(1980,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(340,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ C ) @ B @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) ) @ A ) )
= ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ C ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__mod__minus__right) ).
thf(2128,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ C ) @ B @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) ) @ A ) )
= ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ C ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(1200,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 @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( c_Groups_Oone__class_Oone @ C ) ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gt__half__sum) ).
thf(5203,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 @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( c_Groups_Oone__class_Oone @ C ) ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1200]) ).
thf(818,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(3774,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)],[818]) ).
thf(246,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ ( c_Polynomial_Opoly__gcd @ D @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__greatest) ).
thf(1830,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ ( c_Polynomial_Opoly__gcd @ D @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(222,axiom,
! [A: $i,B: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zminus2__eq__if) ).
thf(1763,plain,
! [A: $i,B: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(1149,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
<=> ( ( B
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__1__iff) ).
thf(5001,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( B
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
& ( ( ( B
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).
thf(509,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(2701,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)],[509]) ).
thf(446,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(2486,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(481,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(2599,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)],[481]) ).
thf(655,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(3174,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)],[655]) ).
thf(1081,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(4737,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Groups_Oone @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).
thf(913,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_Oplus__class_Oplus @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( 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(4117,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_Oplus__class_Oplus @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( 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)],[913]) ).
thf(146,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( 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(1579,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( 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)],[146]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( c_Polynomial_OAbs__poly @ B @ ( c_Polynomial_Ocoeff @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__inverse) ).
thf(1336,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( c_Polynomial_OAbs__poly @ B @ ( c_Polynomial_Ocoeff @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(816,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( hAPP @ ( hAPP @ ( 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(3769,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(795,axiom,
class_Rings_Olinordered__semidom @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
thf(3697,plain,
class_Rings_Olinordered__semidom @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(232,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__trans) ).
thf(1802,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(906,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(4093,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)],[906]) ).
thf(951,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mono) ).
thf(4267,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(569,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(2892,plain,
class_Groups_Oordered__comm__monoid__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(705,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Divides_Odiv__class_Odiv @ D @ B @ C ) ) ) @ ( c_Divides_Odiv__class_Omod @ D @ B @ C ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mod__equality2) ).
thf(3366,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Divides_Odiv__class_Odiv @ D @ B @ C ) ) ) @ ( c_Divides_Odiv__class_Omod @ D @ B @ C ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(989,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).
thf(4414,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(790,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odvd @ D )
=> ( ( C
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvdI) ).
thf(3684,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odvd @ D )
=> ( ( C
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(161,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__add) ).
thf(1617,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(548,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ C )
=> ( ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inverse) ).
thf(2838,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ C )
=> ( ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(338,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( 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(2113,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( 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)],[338]) ).
thf(639,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_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ C ) ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__add) ).
thf(3124,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_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ C ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(427,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 ) ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__Suc) ).
thf(2426,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 ) ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(1015,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(4488,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)],[1015]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( c_Divides_Odiv__class_Omod @ C @ ( c_Divides_Odiv__class_Omod @ C @ B @ A ) @ A )
= ( c_Divides_Odiv__class_Omod @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mod__trivial) ).
thf(1284,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( c_Divides_Odiv__class_Omod @ C @ ( c_Divides_Odiv__class_Omod @ C @ B @ A ) @ A )
= ( c_Divides_Odiv__class_Omod @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( 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_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__neg__pos__less0) ).
thf(1353,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( 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_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(1085,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ 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_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zless__mono2__lemma) ).
thf(4748,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ 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_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).
thf(289,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ B )
=> ( ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ B ) @ A ) )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ B ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__minus__eq) ).
thf(1955,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ B )
=> ( ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ B ) @ A ) )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ B ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(550,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( ( c_Polynomial_Opcompose @ C @ B @ A )
= ( c_Polynomial_Opoly__rec @ ( tc_Polynomial_Opoly @ C ) @ C @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) ) @ C ) @ ( c_COMBK @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ ( tc_Polynomial_Opoly @ C ) ) ) @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ ( tc_fun @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) ) @ C ) @ ( c_COMBB @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_Polynomial_Opoly @ C ) @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ C ) ) ) @ ( hAPP @ ( c_COMBC @ C @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_OpCons @ C ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ C ) ) @ A ) ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pcompose__def) ).
thf(2843,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( ( c_Polynomial_Opcompose @ C @ B @ A )
= ( c_Polynomial_Opoly__rec @ ( tc_Polynomial_Opoly @ C ) @ C @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) ) @ C ) @ ( c_COMBK @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ ( tc_Polynomial_Opoly @ C ) ) ) @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ ( tc_fun @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) ) @ C ) @ ( c_COMBB @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_Polynomial_Opoly @ C ) @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ C ) ) ) @ ( hAPP @ ( c_COMBC @ C @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_OpCons @ C ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ C ) ) @ A ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(396,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ B )
=> ( ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__inverse__eq) ).
thf(2320,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ B )
=> ( ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(908,axiom,
class_Rings_Odvd @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Odvd) ).
thf(4106,plain,
class_Rings_Odvd @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(1147,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( ( hAPP @ ( hAPP @ ( 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(4991,plain,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( ( hAPP @ ( hAPP @ ( 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)],[1147]) ).
thf(895,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(4046,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)],[895]) ).
thf(1031,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 ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( 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(4538,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 ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( 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)],[1031]) ).
thf(939,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__add @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ D @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ D @ A ) @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__add__less) ).
thf(4235,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__add @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ D @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ D @ A ) @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(455,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( hAPP @ ( 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(2511,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ B ) @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(1056,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse) ).
thf(4634,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).
thf(541,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
<=> ( ( ( B
= ( hAPP @ 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
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__1) ).
thf(2807,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( ( B
= ( hAPP @ 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
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) )
& ( ( ( ( B
= ( hAPP @ 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
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(1179,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
| ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__less__0__iff) ).
thf(5100,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
| ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
| ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).
thf(604,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Power_Opower @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( hAPP @ 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(3007,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Power_Opower @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( hAPP @ 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)],[604]) ).
thf(379,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(2266,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)],[379]) ).
thf(923,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
thf(4150,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(478,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(2584,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)],[478]) ).
thf(948,axiom,
! [A: $i,B: $i] :
( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oeq__refl) ).
thf(4257,plain,
! [A: $i,B: $i] :
( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(735,axiom,
class_Groups_Omonoid__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
thf(3478,plain,
class_Groups_Omonoid__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(774,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pow__divides__eq__int) ).
thf(3620,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( 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)],[774]) ).
thf(436,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( ( hAPP @ c_Nat_OSuc @ B )
!= A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessI) ).
thf(2458,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( ( hAPP @ c_Nat_OSuc @ B )
!= A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(98,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Ocomm__semiring @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Ocomm__semiring) ).
thf(1459,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Ocomm__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(654,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ D @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ D ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ A ) @ ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ D @ B @ A ) ) ) @ ( hAPP @ ( hAPP @ ( 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(3171,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ D @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ D ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ A ) @ ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ D @ B @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ D ) @ C ) @ ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(749,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_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( 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(3533,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_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( 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)],[749]) ).
thf(177,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__int) ).
thf(1654,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(775,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oab__group__add @ B )
=> ( ( c_Polynomial_Odegree @ B @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ B ) ) @ A ) )
= ( c_Polynomial_Odegree @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__minus) ).
thf(3625,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oab__group__add @ B )
=> ( ( c_Polynomial_Odegree @ B @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ B ) ) @ A ) )
= ( c_Polynomial_Odegree @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(1042,axiom,
! [A: $i] :
( ( class_Rings_Osemiring__1 @ A )
=> ( ( c_Nat_Osemiring__1__class_Oof__nat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__0) ).
thf(4574,plain,
! [A: $i] :
( ( class_Rings_Osemiring__1 @ A )
=> ( ( c_Nat_Osemiring__1__class_Oof__nat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(727,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__add @ B )
=> ( ( hAPP @ ( hAPP @ ( 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(3433,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__add @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(955,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(4278,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)],[955]) ).
thf(275,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__mult__div__cancel) ).
thf(1918,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(920,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( A
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__0__iff) ).
thf(4138,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( A
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) )
& ( ( A
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(174,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Groups_Ogroup__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Ogroup__add) ).
thf(1649,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Groups_Ogroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(404,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( 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(2352,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(813,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( hAPP @ ( hAPP @ ( 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(3757,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( hAPP @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(1051,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ ( hAPP @ ( hAPP @ ( 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 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__dvd__iff) ).
thf(4606,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ ( hAPP @ ( hAPP @ ( 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 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ B ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(560,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 ) )
=> ( ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ A ) ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__mult__distrib) ).
thf(2870,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 ) )
=> ( ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ A ) ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(544,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(2828,plain,
! [A: $i] :
( ( class_Rings_Ocomm__ring @ A )
=> ( class_Rings_Oring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(248,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__less) ).
thf(1834,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(273,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ ( c_Divides_Odiv__class_Omod @ D @ A @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mod__iff) ).
thf(1913,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ ( c_Divides_Odiv__class_Omod @ D @ A @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ ( c_Divides_Odiv__class_Omod @ D @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(392,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__field @ E )
=> ( ( c_Deriv_Oderiv @ E @ D @ C @ B )
=> ( c_Deriv_Oderiv @ E @ ( hAPP @ ( c_COMBC @ E @ tc_Nat_Onat @ E @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ tc_Nat_Onat @ E ) @ E ) @ ( c_Power_Opower__class_Opower @ E ) ) @ D ) ) @ A ) @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ E @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ E ) @ ( hAPP @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__power) ).
thf(2310,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__field @ E )
=> ( ( c_Deriv_Oderiv @ E @ D @ C @ B )
=> ( c_Deriv_Oderiv @ E @ ( hAPP @ ( c_COMBC @ E @ tc_Nat_Onat @ E @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ tc_Nat_Onat @ E ) @ E ) @ ( c_Power_Opower__class_Opower @ E ) ) @ D ) ) @ A ) @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ E @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ E ) @ ( hAPP @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(250,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring__1 @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__dvd__iff) ).
thf(1844,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring__1 @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ C ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(753,axiom,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).
thf(3548,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(361,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( c_Polynomial_Odegree @ C @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ A ) @ B ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( c_Polynomial_Odegree @ C @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ A ) @ B ) )
= ( hAPP @ c_Nat_OSuc @ ( c_Polynomial_Odegree @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__pCons__eq__if) ).
thf(2194,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( c_Polynomial_Odegree @ C @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ A ) @ B ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( c_Polynomial_Odegree @ C @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ A ) @ B ) )
= ( hAPP @ c_Nat_OSuc @ ( c_Polynomial_Odegree @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(366,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Ofield @ B )
=> ( c_Polynomial_Opdivmod__rel @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__0) ).
thf(2215,plain,
! [A: $i,B: $i] :
( ( class_Fields_Ofield @ B )
=> ( c_Polynomial_Opdivmod__rel @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(121,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__relations_I2_J) ).
thf(1517,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ 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_Int_Oint @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(486,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( c_Polynomial_Opdivmod__rel @ D @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) @ C @ B @ A )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__0__iff) ).
thf(2611,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( ( c_Polynomial_Opdivmod__rel @ D @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) @ C @ B @ A )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) ) )
=> ( c_Polynomial_Opdivmod__rel @ D @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ D ) ) @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(932,axiom,
! [A: $i,B: $i] :
( ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ? [C: $i] :
( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__eq__0__iff) ).
thf(4185,plain,
! [A: $i,B: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ? [C: $i] :
( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ C ) ) )
& ( ? [C: $i] :
( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ C ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(520,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( hAPP @ ( hAPP @ ( 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(2743,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( hAPP @ ( hAPP @ ( 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)],[520]) ).
thf(448,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(2490,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)],[448]) ).
thf(885,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__0) ).
thf(4006,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(369,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( hAPP @ ( 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(2226,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( hAPP @ ( 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)],[369]) ).
thf(96,axiom,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) )
= ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zminus__zminus) ).
thf(1453,plain,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) )
= ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(493,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( 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(2643,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( 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)],[493]) ).
thf(210,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(1734,plain,
class_Rings_Oring__no__zero__divisors @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(899,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Osemiring @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ B ) ) @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_combine__common__factor) ).
thf(4061,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Osemiring @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ B ) ) @ C ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(575,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(2907,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)],[575]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( 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(1276,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( 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)],[27]) ).
thf(354,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ C ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__add__eq__iff) ).
thf(2174,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ C ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(332,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( c_Polynomial_Osynthetic__div @ D @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ D ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( 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(2098,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( c_Polynomial_Osynthetic__div @ D @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ D ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( 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)],[332]) ).
thf(1008,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ C ) @ B ) @ A ) ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__cancel) ).
thf(4468,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ C ) @ B ) @ A ) ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(107,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ A ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__div__cancel) ).
thf(1481,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ A ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(945,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__0) ).
thf(4250,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(216,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring__1 @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ C ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__minus__iff) ).
thf(1745,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring__1 @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ C ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ C ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ C ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(590,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ B ) ) @ B ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ C @ B ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zmod__equality2) ).
thf(2971,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ B ) ) @ B ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ C @ B ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(819,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(3780,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)],[819]) ).
thf(949,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ C ) ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ C ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zmod__equality) ).
thf(4261,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ C ) ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ C ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(172,axiom,
class_Orderings_Opreorder @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Opreorder) ).
thf(1646,plain,
class_Orderings_Opreorder @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(432,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__group__add @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ D @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ D @ A ) @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__diff__less) ).
thf(2443,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__group__add @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ D @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ D @ A ) @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(46,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(1326,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Power_Opower @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(803,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Omonoid__mult @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( hAPP @ 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(3729,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Omonoid__mult @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( hAPP @ 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)],[803]) ).
thf(17,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Oring__no__zero__divisors @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Oring__no__zero__divisors) ).
thf(1253,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Oring__no__zero__divisors @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(511,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(2707,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)],[511]) ).
thf(596,axiom,
class_Rings_Omult__zero @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).
thf(2988,plain,
class_Rings_Omult__zero @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(479,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__neg__pos) ).
thf(2594,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(185,axiom,
class_Rings_Osemiring__0 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).
thf(1674,plain,
class_Rings_Osemiring__0 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(821,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
thf(3789,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(169,axiom,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__less__0__conv) ).
thf(1639,plain,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(387,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) )
= ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__int) ).
thf(2290,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) )
= ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(832,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel__left) ).
thf(3825,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oidom @ D )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ B ) @ A ) ) ) )
& ( ( ( C
= ( c_Groups_Ozero__class_Ozero @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( 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)],[832]) ).
thf(268,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_RealVector_Oreal__normed__field @ F )
=> ( ( c_Deriv_Oderiv @ F @ E @ D @ C )
=> ( ( c_Deriv_Oderiv @ F @ B @ D @ A )
=> ( c_Deriv_Oderiv @ F @ ( hAPP @ ( hAPP @ ( c_COMBS @ F @ F @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ ( tc_fun @ F @ F ) @ F ) @ ( c_Groups_Ominus__class_Ominus @ F ) ) @ E ) ) @ B ) @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ F ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__diff) ).
thf(1903,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_RealVector_Oreal__normed__field @ F )
=> ( ( c_Deriv_Oderiv @ F @ E @ D @ C )
=> ( ( c_Deriv_Oderiv @ F @ B @ D @ A )
=> ( c_Deriv_Oderiv @ F @ ( hAPP @ ( hAPP @ ( c_COMBS @ F @ F @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ ( tc_fun @ F @ F ) @ F ) @ ( c_Groups_Ominus__class_Ominus @ F ) ) @ E ) ) @ B ) @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ F ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(343,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__field @ D )
=> ( ( c_Deriv_Oderiv @ D @ C @ B @ A )
=> ( ( ( hAPP @ C @ B )
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Deriv_Oderiv @ D @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ D @ D ) @ ( c_Rings_Oinverse__class_Oinverse @ D ) ) @ C ) @ B @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ C @ B ) ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__inverse__fun) ).
thf(2135,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__field @ D )
=> ( ( c_Deriv_Oderiv @ D @ C @ B @ A )
=> ( ( ( hAPP @ C @ B )
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Deriv_Oderiv @ D @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ D @ D ) @ ( c_Rings_Oinverse__class_Oinverse @ D ) ) @ C ) @ B @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ C @ B ) ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(1068,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ocomm__monoid__add @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ C ) ) @ B ) @ A )
= ( c_Polynomial_OAbs__poly @ C @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ C @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ C @ C ) @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ C ) ) @ ( c_Polynomial_Ocoeff @ C @ B ) ) ) @ ( c_Polynomial_Ocoeff @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__poly__def) ).
thf(4681,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ocomm__monoid__add @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ C ) ) @ B ) @ A )
= ( c_Polynomial_OAbs__poly @ C @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ C @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ C @ C ) @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ C ) ) @ ( c_Polynomial_Ocoeff @ C @ B ) ) ) @ ( c_Polynomial_Ocoeff @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).
thf(1196,axiom,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).
thf(5191,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1196]) ).
thf(706,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(3369,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)],[706]) ).
thf(916,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ B ) @ A ) ) )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__smult__cancel) ).
thf(4126,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ B ) @ A ) ) )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(542,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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__monom) ).
thf(2823,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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(635,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(3104,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)],[635]) ).
thf(306,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( 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(2004,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(810,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__minus__divide__divide) ).
thf(3748,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(313,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) )
= ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J) ).
thf(2026,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) )
= ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(755,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(3561,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)],[755]) ).
thf(484,axiom,
class_Orderings_Owellorder @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Owellorder) ).
thf(2608,plain,
class_Orderings_Owellorder @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(741,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel__right) ).
thf(3501,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oidom @ D )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ A ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( 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)],[741]) ).
thf(243,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_RealVector_Oreal__normed__field @ F )
=> ( ( c_Deriv_Oderiv @ F @ E @ D @ C )
=> ( ( c_Deriv_Oderiv @ F @ B @ D @ A )
=> ( ( ( hAPP @ B @ D )
!= ( c_Groups_Ozero__class_Ozero @ F ) )
=> ( c_Deriv_Oderiv @ F @ ( hAPP @ ( hAPP @ ( c_COMBS @ F @ F @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ ( tc_fun @ F @ F ) @ F ) @ ( c_Rings_Oinverse__class_Odivide @ F ) ) @ E ) ) @ B ) @ D @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ C ) @ ( hAPP @ B @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( hAPP @ E @ D ) ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( hAPP @ B @ D ) ) @ ( hAPP @ B @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__divide) ).
thf(1822,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_RealVector_Oreal__normed__field @ F )
=> ( ( c_Deriv_Oderiv @ F @ E @ D @ C )
=> ( ( c_Deriv_Oderiv @ F @ B @ D @ A )
=> ( ( ( hAPP @ B @ D )
!= ( c_Groups_Ozero__class_Ozero @ F ) )
=> ( c_Deriv_Oderiv @ F @ ( hAPP @ ( hAPP @ ( c_COMBS @ F @ F @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ ( tc_fun @ F @ F ) @ F ) @ ( c_Rings_Oinverse__class_Odivide @ F ) ) @ E ) ) @ B ) @ D @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ C ) @ ( hAPP @ B @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( hAPP @ E @ D ) ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( hAPP @ B @ D ) ) @ ( hAPP @ B @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(1150,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) )
= ( hAPP @ ( 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(5010,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).
thf(528,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( c_Divides_Odiv__class_Omod @ C @ B @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Divides_Odiv__class_Odiv @ C @ B @ A ) ) @ A ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__div__class_Omod__div__equality_H) ).
thf(2764,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( c_Divides_Odiv__class_Omod @ C @ B @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Divides_Odiv__class_Odiv @ C @ B @ A ) ) @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(1107,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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 ) @ ( hAPP @ ( 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(4834,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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 ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) )
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( ( ( hAPP @ ( c_Polynomial_Opoly @ C @ A ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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)],[1107]) ).
thf(745,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ B ) @ ( c_Polynomial_Odegree @ C @ A ) )
=> ( ( c_Divides_Odiv__class_Odiv @ ( tc_Polynomial_Opoly @ C ) @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__poly__less) ).
thf(3516,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ B ) @ ( c_Polynomial_Odegree @ C @ A ) )
=> ( ( c_Divides_Odiv__class_Odiv @ ( tc_Polynomial_Opoly @ C ) @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( C = B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__eq__less__trans) ).
thf(1558,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( C = B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(348,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( hAPP @ c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessI) ).
thf(2152,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( hAPP @ c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(585,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( 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(2944,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( 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)],[585]) ).
thf(931,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ B @ A ) @ ( c_Polynomial_Odegree @ B @ A ) )
!= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leading__coeff__neq__0) ).
thf(4182,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ B @ A ) @ ( c_Polynomial_Odegree @ B @ A ) )
!= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(112,axiom,
class_Rings_Olinordered__idom @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).
thf(1491,plain,
class_Rings_Olinordered__idom @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(442,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ C ) ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Polynomial_Odegree @ C @ B ) ) @ ( c_Polynomial_Odegree @ C @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ C @ B ) @ ( c_Polynomial_Odegree @ C @ B ) ) ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ C @ A ) @ ( c_Polynomial_Odegree @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__mult__degree__sum) ).
thf(2475,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ C ) ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Polynomial_Odegree @ C @ B ) ) @ ( c_Polynomial_Odegree @ C @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ C @ B ) @ ( c_Polynomial_Odegree @ C @ B ) ) ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ C @ A ) @ ( c_Polynomial_Odegree @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(960,axiom,
! [A: $i] :
( ( hAPP @ 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(4293,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(845,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__left) ).
thf(3879,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(39,axiom,
class_Rings_Omult__zero @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).
thf(1308,plain,
class_Rings_Omult__zero @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(326,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__group__add @ D )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ D @ C ) @ A ) ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ D @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__diff) ).
thf(2066,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__group__add @ D )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ D @ C ) @ A ) ) @ ( hAPP @ ( c_Polynomial_Ocoeff @ D @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(351,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( 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(2162,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( 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)],[351]) ).
thf(157,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ B ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__refl) ).
thf(1607,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ B ) @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(179,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Ono__zero__divisors @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Ono__zero__divisors) ).
thf(1661,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Ono__zero__divisors @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(394,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_RealVector_Oreal__normed__field @ F )
=> ( ( c_Deriv_Oderiv @ F @ E @ D @ C )
=> ( ( c_Deriv_Oderiv @ F @ B @ ( hAPP @ E @ D ) @ A )
=> ( c_Deriv_Oderiv @ F @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ F @ F ) @ B ) @ E ) @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__chain_H) ).
thf(2315,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_RealVector_Oreal__normed__field @ F )
=> ( ( c_Deriv_Oderiv @ F @ E @ D @ C )
=> ( ( c_Deriv_Oderiv @ F @ B @ ( hAPP @ E @ D ) @ A )
=> ( c_Deriv_Oderiv @ F @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ F @ F ) @ B ) @ E ) @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(425,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) ) @ A )
= ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J) ).
thf(2421,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) ) @ A )
= ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(1140,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(4964,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)],[1140]) ).
thf(965,axiom,
class_Groups_Oab__semigroup__mult @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
thf(4321,plain,
class_Groups_Oab__semigroup__mult @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(837,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ C ) @ B ) @ A )
<=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( 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 @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__less__eq) ).
thf(3844,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ C ) @ B ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( 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 @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( 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 @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(763,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ c_Nat_OSuc @ B )
= ( hAPP @ c_Nat_OSuc @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Oinject) ).
thf(3585,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ B )
= ( hAPP @ c_Nat_OSuc @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ c_Nat_OSuc @ B )
= ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(962,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( hAPP @ 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(4299,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( hAPP @ c_Nat_OSuc @ A ) )
=> ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(1181,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(5109,plain,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1181]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( c_Polynomial_Opoly__gcd @ D @ C @ ( c_Polynomial_Opoly__gcd @ D @ B @ A ) )
= ( c_Polynomial_Opoly__gcd @ D @ B @ ( c_Polynomial_Opoly__gcd @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd_Oleft__commute) ).
thf(1440,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( c_Polynomial_Opoly__gcd @ D @ C @ ( c_Polynomial_Opoly__gcd @ D @ B @ A ) )
= ( c_Polynomial_Opoly__gcd @ D @ B @ ( c_Polynomial_Opoly__gcd @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(1155,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(5023,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)],[1155]) ).
thf(503,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__strict__right__mono) ).
thf(2680,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( class_Divides_Osemiring__div @ B )
=> ( ( c_Divides_Odiv__class_Odiv @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__by__1) ).
thf(1212,plain,
! [A: $i,B: $i] :
( ( class_Divides_Osemiring__div @ B )
=> ( ( c_Divides_Odiv__class_Odiv @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1171,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Divides_Odiv__class_Odiv @ C @ B @ A ) ) @ A ) ) @ ( c_Divides_Odiv__class_Omod @ C @ B @ A ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__div__equality) ).
thf(5072,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Divides_Odiv__class_Odiv @ C @ B @ A ) ) @ A ) ) @ ( c_Divides_Odiv__class_Omod @ C @ B @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).
thf(880,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Divides_Odiv__class_Odiv @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self2__is__id) ).
thf(3993,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Divides_Odiv__class_Odiv @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(573,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less) ).
thf(2902,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(1185,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__cancel) ).
thf(5119,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185]) ).
thf(331,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( hAPP @ 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(2095,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( hAPP @ 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)],[331]) ).
thf(1000,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(4446,plain,
class_Groups_Ocancel__comm__monoid__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(266,axiom,
! [A: $i,B: $i] :
( ( ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B )
= ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__int__eq) ).
thf(1893,plain,
! [A: $i,B: $i] :
( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B )
= ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B )
= ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(40,axiom,
class_Rings_Ocomm__semiring__0 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__0) ).
thf(1309,plain,
class_Rings_Ocomm__semiring__0 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(1116,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ C @ B @ A )
= ( c_Polynomial_Opoly__rec @ ( tc_Polynomial_Opoly @ C ) @ C @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) ) @ C ) @ ( c_COMBK @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ ( tc_Polynomial_Opoly @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ C ) @ ( hAPP @ ( c_COMBS @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_Polynomial_Opoly @ C ) @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ ( tc_Polynomial_Opoly @ C ) ) @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ C ) ) ) @ ( hAPP @ ( c_Polynomial_Osmult @ C ) @ A ) ) ) ) @ ( c_Polynomial_OpCons @ C ) ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__def) ).
thf(4869,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ C @ B @ A )
= ( c_Polynomial_Opoly__rec @ ( tc_Polynomial_Opoly @ C ) @ C @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) ) @ C ) @ ( c_COMBK @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ ( tc_Polynomial_Opoly @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ C ) @ ( hAPP @ ( c_COMBS @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_Polynomial_Opoly @ C ) @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ ( tc_Polynomial_Opoly @ C ) ) @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ C ) ) ) @ ( hAPP @ ( c_Polynomial_Osmult @ C ) @ A ) ) ) ) @ ( c_Polynomial_OpCons @ C ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).
thf(579,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(2917,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)],[579]) ).
thf(980,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( 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(4372,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( 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)],[980]) ).
thf(303,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Ocomm__semiring__0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Ocomm__semiring__0) ).
thf(1994,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Ocomm__semiring__0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(754,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( 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(3552,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( hAPP @ ( 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 ) ) )
=> ( ( hAPP @ ( hAPP @ ( 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)],[754]) ).
thf(533,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(2779,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)],[533]) ).
thf(312,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B )
= A )
<=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__equation__iff) ).
thf(2019,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B )
= A )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A )
= B ) )
& ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A )
= B )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(346,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(2142,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)],[346]) ).
thf(582,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(2930,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)],[582]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ C @ B ) ) @ A ) @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ C ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmod__left) ).
thf(1348,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ C @ B ) ) @ A ) @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ C ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(386,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 ) @ ( hAPP @ ( hAPP @ ( 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(2287,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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(457,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__semigroup__add @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( 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(2517,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__semigroup__add @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(205,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ominus @ B )
=> ( class_Groups_Ominus @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ominus) ).
thf(1725,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ominus @ B )
=> ( class_Groups_Ominus @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(912,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( c_Divides_Odiv__class_Omod @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) @ A )
= ( c_Divides_Odiv__class_Omod @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__self2) ).
thf(4114,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( c_Divides_Odiv__class_Omod @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) @ A )
= ( c_Divides_Odiv__class_Omod @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(1076,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__right) ).
thf(4706,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).
thf(976,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
<=> ? [C: $i] :
( A
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
thf(4356,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ? [C: $i] :
( A
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) ) ) )
& ( ? [C: $i] :
( A
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( 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)],[976]) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Fields_Ofield @ F )
=> ( ( c_Polynomial_Opdivmod__rel @ F @ E @ D @ C @ B )
=> ( c_Polynomial_Opdivmod__rel @ F @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ F ) @ A ) @ E ) @ D @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ F ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ F ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__smult__left) ).
thf(1546,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Fields_Ofield @ F )
=> ( ( c_Polynomial_Opdivmod__rel @ F @ E @ D @ C @ B )
=> ( c_Polynomial_Opdivmod__rel @ F @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ F ) @ A ) @ E ) @ D @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ F ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ F ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(708,axiom,
( ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint )
= ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__numerals_I1_J) ).
thf(3373,plain,
( ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint )
= ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(261,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( ( c_Polynomial_Ocoeff @ C @ B )
= ( c_Polynomial_Ocoeff @ C @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__inject) ).
thf(1876,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ozero @ C )
=> ( ( ( ( c_Polynomial_Ocoeff @ C @ B )
= ( c_Polynomial_Ocoeff @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Polynomial_Ocoeff @ C @ B )
= ( c_Polynomial_Ocoeff @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(125,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( c_Polynomial_Opoly__gcd @ D @ ( c_Polynomial_Opoly__gcd @ D @ C @ B ) @ A )
= ( c_Polynomial_Opoly__gcd @ D @ C @ ( c_Polynomial_Opoly__gcd @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd_Oassoc) ).
thf(1527,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( c_Polynomial_Opoly__gcd @ D @ ( c_Polynomial_Opoly__gcd @ D @ C @ B ) @ A )
= ( c_Polynomial_Opoly__gcd @ D @ C @ ( c_Polynomial_Opoly__gcd @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(642,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__1) ).
thf(3132,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(220,axiom,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zdiv__trivial) ).
thf(1757,plain,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(792,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oorder__trans) ).
thf(3690,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(666,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( A
= ( hAPP @ ( 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(3203,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( A
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ B ) @ A ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( A
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(1160,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__ring__1 @ B )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( hAPP @ ( 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(5041,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__ring__1 @ B )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).
thf(170,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(1642,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(1130,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( 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(4917,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).
thf(982,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oring @ F )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) ) @ A ) )
<=> ( C
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ F ) @ B ) @ E ) ) @ D ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__add__iff2) ).
thf(4378,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oring @ F )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) ) @ A ) )
=> ( C
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ F ) @ B ) @ E ) ) @ D ) ) @ A ) ) )
& ( ( C
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ F ) @ B ) @ E ) ) @ D ) ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) ) @ C )
= ( hAPP @ ( hAPP @ ( 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)],[982]) ).
thf(462,axiom,
class_Groups_Oab__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
thf(2534,plain,
class_Groups_Oab__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(594,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ 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_diff__mult__distrib2) ).
thf(2983,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ 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)],[594]) ).
thf(841,axiom,
class_Rings_Ono__zero__divisors @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).
thf(3865,plain,
class_Rings_Ono__zero__divisors @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ B ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__less__imp__less) ).
thf(1229,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ B ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(767,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(3601,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)],[767]) ).
thf(846,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) )
= ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) )
<=> ( ( 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_negative__eq__positive) ).
thf(3882,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) )
= ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) )
=> ( ( 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 @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) )
= ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(73,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 @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) @ ( 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_pos__imp__zdiv__neg__iff) ).
thf(1395,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 @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) @ ( 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_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(163,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Ocomm__semiring__1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Ocomm__semiring__1) ).
thf(1625,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Ocomm__semiring__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(459,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ A ) @ B )
= ( c_Groups_Oone__class_Oone @ C ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__inverse__eq) ).
thf(2522,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ A ) @ B )
= ( c_Groups_Oone__class_Oone @ C ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ A ) @ B )
= ( c_Groups_Oone__class_Oone @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(633,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Owellorder @ B )
=> ( ? [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) )
=> ( hBOOL @ ( hAPP @ A @ ( c_Orderings_Oord__class_OLeast @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_LeastI__ex) ).
thf(3100,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Owellorder @ B )
=> ( ? [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) )
=> ( hBOOL @ ( hAPP @ A @ ( c_Orderings_Oord__class_OLeast @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(309,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
<=> ? [C: $i] :
( A
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( hAPP @ c_Nat_OSuc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__iff__Suc__zadd) ).
thf(2008,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
=> ? [C: $i] :
( A
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( hAPP @ c_Nat_OSuc @ C ) ) ) ) )
& ( ? [C: $i] :
( A
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( hAPP @ c_Nat_OSuc @ C ) ) ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Oord @ B )
=> ( class_Orderings_Oord @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
thf(1303,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Oord @ B )
=> ( class_Orderings_Oord @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(607,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(3015,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)],[607]) ).
thf(869,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Polynomial_Odegree @ C @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ C ) @ B ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Polynomial_Odegree @ C @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ C ) @ B ) @ A ) )
= ( c_Polynomial_Odegree @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__smult__eq) ).
thf(3956,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Polynomial_Odegree @ C @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ C ) @ B ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Polynomial_Odegree @ C @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ C ) @ B ) @ A ) )
= ( c_Polynomial_Odegree @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(60,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Groups_Oab__semigroup__mult @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Oab__semigroup__mult) ).
thf(1363,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Groups_Oab__semigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(399,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
<=> ( A
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__1__iff__1) ).
thf(2334,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
=> ( A
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( A
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(1055,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).
thf(4631,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ 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_Oplus__class_Oplus @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).
thf(1010,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ 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__divide) ).
thf(4474,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ 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)],[1010]) ).
thf(521,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oordered__ring @ F )
=> ( ( c_Orderings_Oord__class_Oless @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ F ) @ E ) @ B ) ) @ D ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__iff1) ).
thf(2746,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oordered__ring @ F )
=> ( ( ( c_Orderings_Oord__class_Oless @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ F ) @ E ) @ B ) ) @ D ) ) @ C ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ F ) @ E ) @ B ) ) @ D ) ) @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) ) @ C ) @ ( hAPP @ ( hAPP @ ( 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)],[521]) ).
thf(510,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 ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( 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(2704,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 ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( 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)],[510]) ).
thf(408,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 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ C ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B ) ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ C ) @ A ) @ B ) ) ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_division__ring__inverse__diff) ).
thf(2366,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 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ C ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B ) ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ C ) @ A ) @ B ) ) ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(724,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(3426,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)],[724]) ).
thf(613,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__1) ).
thf(3030,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(368,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( hAPP @ ( 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(2223,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(318,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(2040,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)],[318]) ).
thf(499,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 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B ) ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B ) ) ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__add) ).
thf(2668,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 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B ) ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B ) ) ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(1199,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(5200,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)],[1199]) ).
thf(1182,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__unique) ).
thf(5110,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182]) ).
thf(964,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( 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(4318,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ E ) @ D ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ D ) ) ) @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ D ) ) ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(831,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( hAPP @ ( 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(3822,plain,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(645,axiom,
! [A: $i,B: $i] :
( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oneq__le__trans) ).
thf(3145,plain,
! [A: $i,B: $i] :
( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(91,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(1436,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)],[91]) ).
thf(256,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ C @ A @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__minus__iff) ).
thf(1859,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(891,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( 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(4029,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( 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)],[891]) ).
thf(697,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__less__divisor) ).
thf(3328,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(974,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ C ) ) @ B ) @ A )
= ( c_Polynomial_Opoly__rec @ ( tc_Polynomial_Opoly @ C ) @ C @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) ) @ C ) @ ( c_COMBK @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ ( tc_Polynomial_Opoly @ C ) ) ) @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ ( tc_fun @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) ) @ C ) @ ( c_COMBB @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_Polynomial_Opoly @ C ) @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ C ) ) ) @ ( hAPP @ ( c_COMBC @ C @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_Osmult @ C ) ) @ A ) ) ) ) @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__poly__def) ).
thf(4350,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__0 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ C ) ) @ B ) @ A )
= ( c_Polynomial_Opoly__rec @ ( tc_Polynomial_Opoly @ C ) @ C @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) ) @ C ) @ ( c_COMBK @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ ( tc_Polynomial_Opoly @ C ) ) ) @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ ( tc_fun @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) ) @ C ) @ ( c_COMBB @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_Polynomial_Opoly @ C ) @ ( tc_fun @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ C ) ) ) @ ( hAPP @ ( c_COMBC @ C @ ( tc_Polynomial_Opoly @ C ) @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_Osmult @ C ) ) @ A ) ) ) ) @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(240,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Osemiring__1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Osemiring__1) ).
thf(1816,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Osemiring__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(114,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(1495,plain,
class_Groups_Oordered__ab__group__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(1124,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( hAPP @ ( 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 ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__right) ).
thf(4895,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( hAPP @ ( 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 ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).
thf(957,axiom,
( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_One__nat__def) ).
thf(4286,plain,
( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(191,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Oring__1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Oring__1) ).
thf(1693,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Oring__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(476,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(2572,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)],[476]) ).
thf(736,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 @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__total) ).
thf(3479,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 @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(423,axiom,
! [A: $i] :
( ( class_Fields_Ofield @ A )
=> ( class_Divides_Oring__div @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Divides_Oring__div) ).
thf(2417,plain,
! [A: $i] :
( ( class_Fields_Ofield @ A )
=> ( class_Divides_Oring__div @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(577,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__1__left) ).
thf(2913,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(420,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__assoc) ).
thf(2404,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(934,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ocomm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ B ) @ ( c_Polynomial_Odegree @ C @ A ) )
=> ( ( c_Polynomial_Odegree @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ C ) ) @ A ) @ B ) )
= ( c_Polynomial_Odegree @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__add__eq__left) ).
thf(4193,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ocomm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ B ) @ ( c_Polynomial_Odegree @ C @ A ) )
=> ( ( c_Polynomial_Odegree @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ C ) ) @ A ) @ B ) )
= ( c_Polynomial_Odegree @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(487,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(2619,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)],[487]) ).
thf(787,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ C ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__diff__eq__iff) ).
thf(3673,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ C ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(54,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Groups_Ocancel__semigroup__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Ocancel__semigroup__add) ).
thf(1346,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Groups_Ocancel__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(350,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__ring @ D )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ C ) @ A ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__diff) ).
thf(2159,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__ring @ D )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ D ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ C ) @ A ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Osemiring__1 @ D )
=> ( ( c_Nat_Osemiring__1__class_Oof__nat__aux @ D @ C @ ( hAPP @ c_Nat_OSuc @ B ) @ A )
= ( c_Nat_Osemiring__1__class_Oof__nat__aux @ D @ C @ B @ ( hAPP @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__aux_Osimps_I2_J) ).
thf(1268,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Osemiring__1 @ D )
=> ( ( c_Nat_Osemiring__1__class_Oof__nat__aux @ D @ C @ ( hAPP @ c_Nat_OSuc @ B ) @ A )
= ( c_Nat_Osemiring__1__class_Oof__nat__aux @ D @ C @ B @ ( hAPP @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(843,axiom,
! [A: $i,B: $i] :
( ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__power) ).
thf(3869,plain,
! [A: $i,B: $i] :
( ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(817,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(3772,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)],[817]) ).
thf(739,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(3489,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)],[739]) ).
thf(1106,axiom,
! [A: $i] :
( ( class_Rings_Odivision__ring @ A )
=> ( ( hAPP @ ( 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(4831,plain,
! [A: $i] :
( ( class_Rings_Odivision__ring @ A )
=> ( ( hAPP @ ( 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)],[1106]) ).
thf(1162,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( 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(5046,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( 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)],[1162]) ).
thf(1137,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ C ) )
<=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__less__divide__eq) ).
thf(4955,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ C ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).
thf(828,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( 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(3812,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(344,axiom,
class_Orderings_Oord @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
thf(2138,plain,
class_Orderings_Oord @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ C @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__eq__dvd__iff) ).
thf(1236,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ C @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ C ) @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ C ) @ A ) ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ C @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(374,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ C ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ C ) ) )
<=> ! [D: $i,E: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ E )
& ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ E @ C )
& ( A
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__pos__lemma) ).
thf(2241,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ C ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ C ) ) )
=> ! [D: $i,E: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ E )
& ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ E @ C )
& ( A
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ E ) ) ) )
& ( ! [D: $i,E: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ E )
& ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ E @ C )
& ( A
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ C ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(917,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ c_Nat_OSuc @ B )
= ( hAPP @ c_Nat_OSuc @ A ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__inject) ).
thf(4129,plain,
! [A: $i,B: $i] :
( ( ( hAPP @ c_Nat_OSuc @ B )
= ( hAPP @ c_Nat_OSuc @ A ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(297,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ 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) ).
thf(1977,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ 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)],[297]) ).
thf(874,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ozero @ D )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ D @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ D ) @ C ) @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( c_Polynomial_Ocoeff @ D @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__pCons__Suc) ).
thf(3974,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ozero @ D )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ D @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ D ) @ C ) @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( c_Polynomial_Ocoeff @ D @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(611,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 @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ A ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__inverse__less__neg) ).
thf(3025,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 @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ A ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(620,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add__distrib) ).
thf(3057,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(128,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__mod__bound) ).
thf(1532,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(1099,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ A ) )
<=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__divide__eq) ).
thf(4799,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).
thf(758,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(3570,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)],[758]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( class_Fields_Ofield @ G )
=> ( ( c_Polynomial_Opdivmod__rel @ G @ F @ E @ D @ C )
=> ( ( c_Polynomial_Opdivmod__rel @ G @ F @ E @ B @ A )
=> ( ( D = B )
& ( C = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__unique) ).
thf(1384,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( class_Fields_Ofield @ G )
=> ( ( c_Polynomial_Opdivmod__rel @ G @ F @ E @ D @ C )
=> ( ( c_Polynomial_Opdivmod__rel @ G @ F @ E @ B @ A )
=> ( ( D = B )
& ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(718,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(3411,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)],[718]) ).
thf(130,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(1537,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(703,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__eq__divide) ).
thf(3360,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(67,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(1378,plain,
class_Groups_Olinordered__ab__group__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(871,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Divides_Odiv__class_Odiv @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self1__is__id) ).
thf(3965,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Divides_Odiv__class_Odiv @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(609,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( c_Divides_Odiv__class_Omod @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) @ B )
= ( c_Divides_Odiv__class_Omod @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__self1) ).
thf(3020,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( c_Divides_Odiv__class_Omod @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) @ B )
= ( c_Divides_Odiv__class_Omod @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(969,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Ofield__inverse__zero @ B )
=> ( ( ( hAPP @ ( 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(4330,plain,
! [A: $i,B: $i] :
( ( class_Fields_Ofield__inverse__zero @ B )
=> ( ( ( ( hAPP @ ( 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 ) )
=> ( ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(202,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( B
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) )
<=> ( A
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equation__minus__iff) ).
thf(1713,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( ( B
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) )
=> ( A
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) )
& ( ( A
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) )
=> ( B
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(558,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Ofield @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( hAPP @ ( 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(2864,plain,
! [A: $i,B: $i] :
( ( class_Fields_Ofield @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ A ) ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(807,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Nat_Osemiring__char__0 @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Nat_Osemiring__char__0) ).
thf(3740,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Nat_Osemiring__char__0 @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(972,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc2) ).
thf(4345,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(1019,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono) ).
thf(4501,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).
thf(116,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Oring__1__no__zero__divisors @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Oring__1__no__zero__divisors) ).
thf(1505,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Oring__1__no__zero__divisors @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(855,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pow__divides__pow__nat) ).
thf(3918,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(381,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__field @ E )
=> ( ( c_Deriv_Oderiv @ E @ D @ C @ B )
=> ( c_Deriv_Oderiv @ E @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ E @ E ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ A ) ) @ D ) @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__cmult) ).
thf(2270,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__field @ E )
=> ( ( c_Deriv_Oderiv @ E @ D @ C @ B )
=> ( c_Deriv_Oderiv @ E @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ E @ E ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ A ) ) @ D ) @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(977,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oab__group__add @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Deriv_Oadd__diff__add) ).
thf(4363,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oab__group__add @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ E ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(410,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__num__frac) ).
thf(2372,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(1029,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(4533,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)],[1029]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__dvd__conv_I1_J) ).
thf(1331,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ B ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(524,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__divide__eq__right) ).
thf(2754,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Oring__div @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ C ) @ B ) @ A ) )
=> ( ( c_Divides_Odiv__class_Odiv @ C @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) @ B )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ ( c_Divides_Odiv__class_Odiv @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__neg__div) ).
thf(1320,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Oring__div @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ C ) @ B ) @ A ) )
=> ( ( c_Divides_Odiv__class_Odiv @ C @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) @ B )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ ( c_Divides_Odiv__class_Odiv @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(1025,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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(4520,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(293,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(1962,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)],[293]) ).
thf(1079,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( hAPP @ ( c_Polynomial_Opoly @ C @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( 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(4723,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( ( hAPP @ ( c_Polynomial_Opoly @ C @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ ( c_Groups_Oone__class_Oone @ C ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( 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)],[1079]) ).
thf(800,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( hAPP @ ( hAPP @ ( 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(3721,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( hAPP @ ( hAPP @ ( 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)],[800]) ).
thf(83,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Groups_Ocancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Ocancel__ab__semigroup__add) ).
thf(1417,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Groups_Ocancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(1063,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ C ) @ A @ B )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ C ) @ A @ B ) ) @ ( c_Polynomial_Odegree @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__mod__less) ).
thf(4655,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ C ) @ A @ B )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ C @ ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ C ) @ A @ B ) ) @ ( c_Polynomial_Odegree @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).
thf(492,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ B ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ A ) @ C ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__dvd) ).
thf(2640,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ B ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ D ) @ A ) @ C ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(867,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 ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ A ) )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__inverse) ).
thf(3950,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 ) @ ( hAPP @ ( c_Rings_Oinverse__class_Oinverse @ B ) @ A ) )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(1092,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add__cancel) ).
thf(4779,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(1157,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__1__left) ).
thf(5029,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Polynomial_Osmult @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).
thf(176,axiom,
class_Rings_Olinordered__semiring__strict @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).
thf(1653,plain,
class_Rings_Olinordered__semiring__strict @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(286,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__int__def__symmetric) ).
thf(1944,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(1037,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(4555,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)],[1037]) ).
thf(631,axiom,
class_Rings_Osemiring__1 @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__1) ).
thf(3096,plain,
class_Rings_Osemiring__1 @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(213,axiom,
class_Orderings_Oorder @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
thf(1737,plain,
class_Orderings_Oorder @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(188,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) @ ( hAPP @ ( 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(1681,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(567,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__asym_H) ).
thf(2887,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(716,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(3405,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)],[716]) ).
thf(373,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ C ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( 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(2238,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ C ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ B ) ) @ C ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(111,axiom,
class_Groups_Oab__group__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).
thf(1490,plain,
class_Groups_Oab__group__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(1143,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(4977,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).
thf(993,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
thf(4423,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(897,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( hAPP @ ( hAPP @ ( 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(4056,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ B ) @ A ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(1114,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(4863,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)],[1114]) ).
thf(665,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( 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(3200,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( 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)],[665]) ).
thf(360,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_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(2191,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_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)],[360]) ).
thf(3,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Groups_Omonoid__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Omonoid__add) ).
thf(1204,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Groups_Omonoid__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(95,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(1449,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)],[95]) ).
thf(238,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ 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_order__less__asym_H) ).
thf(1812,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ 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)],[238]) ).
thf(329,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( ( hAPP @ ( c_Polynomial_Ocoeff @ B @ A ) @ ( c_Polynomial_Odegree @ B @ A ) )
= ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leading__coeff__0__iff) ).
thf(2087,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( ( ( hAPP @ ( c_Polynomial_Ocoeff @ B @ A ) @ ( c_Polynomial_Odegree @ B @ A ) )
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
=> ( ( hAPP @ ( c_Polynomial_Ocoeff @ B @ A ) @ ( c_Polynomial_Odegree @ B @ A ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(859,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(3933,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Oordered__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(1005,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( c_Polynomial_Opoly__gcd @ C @ A @ B )
= ( c_Polynomial_Opoly__gcd @ C @ B @ ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ C ) @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd_Osimps_I2_J) ).
thf(4459,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
=> ( ( c_Polynomial_Opoly__gcd @ C @ A @ B )
= ( c_Polynomial_Opoly__gcd @ C @ B @ ( c_Divides_Odiv__class_Omod @ ( tc_Polynomial_Opoly @ C ) @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(102,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Power_Opower @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Power_Opower) ).
thf(1468,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Power_Opower @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(618,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( c_Groups_Oone__class_Oone @ C ) ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__half__sum) ).
thf(3047,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( c_Groups_Oone__class_Oone @ C ) ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(593,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__minus__cancel) ).
thf(2980,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ C ) @ B ) ) @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(615,axiom,
class_Rings_Ocomm__semiring__1 @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
thf(3035,plain,
class_Rings_Ocomm__semiring__1 @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(760,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(3575,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)],[760]) ).
thf(1036,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 ) @ ( hAPP @ ( hAPP @ ( 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(4552,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 ) @ ( hAPP @ ( hAPP @ ( 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)],[1036]) ).
thf(355,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(2177,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Rings_Osemiring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(5386,plain,
$false,
inference(e,[status(thm)],[1411,5116,5136,2072,3798,3666,2876,3698,2463,2544,3927,4728,1818,2250,4560,4447,3962,5088,1369,2889,4571,4450,2341,2109,2131,3399,2263,3930,3581,4852,3863,1850,2559,3449,4015,1950,1549,1924,2104,3317,4339,1882,2622,1522,3912,2380,2854,4623,1305,4592,1486,2363,1855,2495,3230,5069,2395,1443,2776,1808,2659,2953,1401,1422,2947,1569,1939,2671,1544,4603,3012,1671,4090,1310,2740,1999,1233,4247,3313,4435,4980,4762,3276,1705,3017,1788,1426,3530,4403,3439,3049,3745,4739,3004,2035,4839,4647,3135,3942,4026,3044,1735,4110,4528,2448,2933,4650,2168,1260,3253,1988,3414,1342,5161,1507,1222,2360,3236,3634,4496,3088,1921,2886,1475,2400,2531,3688,1887,3766,2432,1243,3915,1782,3513,5195,3308,1935,3809,1366,4665,4322,1709,2328,4743,4866,1985,4070,2217,1323,1511,2682,1832,2466,3855,4243,3891,4637,1409,3442,3263,1287,4546,2698,1760,1298,1907,2501,1313,4275,5130,2185,1577,1922,1379,1514,1609,2520,3835,2301,2989,1847,4353,4788,1704,1890,4179,2767,1741,1398,5052,3470,3902,1568,3180,4471,4793,5020,3866,4302,4514,4253,4967,4411,3322,4396,3431,1302,4583,4903,3163,2451,2880,4147,4815,1828,5032,5156,2254,1677,1960,3152,1283,4810,4432,2007,2950,4696,1415,4018,5013,4857,1373,2996,3724,1911,4600,3295,2782,2893,1632,4297,2469,3670,4001,3527,3983,1581,4686,5059,3068,1215,3421,3712,2483,2424,3157,1351,3243,1405,1600,4628,2718,1696,2762,3986,2058,2833,3189,2281,1796,3036,1526,3676,1433,4701,1943,1201,3211,2392,2154,3906,1975,3510,1564,1651,3097,1206,4753,4589,3567,4531,3186,2232,1736,4059,3795,4893,2910,3169,4480,2646,5142,4557,1470,1708,2093,1783,4076,2773,1636,1730,3679,1900,4712,2541,2596,1751,1666,1487,3610,3989,4785,2015,4044,1274,2441,5049,3735,1343,2805,4920,1355,1255,4375,5044,2133,3742,2969,3233,3371,3154,4493,5085,1370,3816,1619,2032,4821,2986,2414,3250,4160,4661,2528,3948,4053,1968,1296,1687,4327,2179,3546,5113,3727,3445,3166,2445,4280,2873,3980,1837,3269,4849,1365,2628,4192,1555,2826,4155,4994,4757,3065,3349,2200,2609,4417,4740,2211,1407,2547,2492,1392,3667,3647,2112,3033,3408,1910,1592,1983,2801,1375,3381,4525,3102,2268,3968,4123,2498,3909,3782,3615,1541,3482,5145,1534,2685,4974,1804,2841,1328,2709,1227,3218,4544,1856,4429,2692,1587,3650,4012,1755,3941,3060,3176,4898,4291,2798,1329,1659,2323,4983,2561,3596,2419,4938,1414,1937,2317,3311,2877,5075,4860,5107,2830,3094,1461,4425,1424,2312,3010,4750,3428,1810,1791,3194,2349,2038,1446,3643,4444,1612,2978,2472,3935,1419,1825,3611,3486,3126,2304,2487,1668,2006,4347,4953,1478,4384,1530,1539,1456,4508,1266,1231,1552,2851,2355,4482,1932,4244,3390,3819,4237,2566,1799,3937,1947,4120,3628,1874,3115,3760,1429,2862,4135,3692,1246,4152,1720,3109,4689,2272,4416,3083,4223,1627,1525,4163,4535,5153,2203,4288,4782,1695,2883,3999,3508,3841,2662,1996,1732,2634,2749,1991,1318,1814,4644,3225,2043,4889,3183,2057,1712,3592,1466,2402,4906,2915,2793,1663,1278,2729,3660,2677,3607,3491,4393,2602,4269,2235,2144,1727,1510,4872,2904,1698,1959,2556,3358,2275,2570,4256,4438,2941,1548,1927,3738,3375,1595,3839,4503,4577,3396,2376,4453,4144,3387,1916,1884,3519,3086,2991,3604,3213,3536,4943,3070,2727,2048,2859,1615,1389,2791,3240,5065,2849,2188,5067,1929,3945,2674,2016,2514,4032,4709,4465,3900,1403,5097,2695,1256,4505,3599,4485,4978,3751,2293,4112,3700,3832,4854,3416,1464,1356,1675,1786,3023,2029,4096,4796,1271,3695,3330,2738,4171,3663,1635,3002,2759,3436,1258,5158,4887,3355,2346,4790,4704,4929,2229,2214,4828,3419,1722,2116,4958,3384,1209,2721,3352,3996,3631,2538,1853,2478,4369,1574,1806,4914,4699,3270,1589,3732,1492,1603,3106,3468,3197,4073,2856,2802,3138,2378,2896,4477,4107,1969,3160,1667,2182,5035,4541,3572,2757,1862,3192,4652,1381,1820,2605,3027,1339,4420,4882,4009,2343,2625,5082,4569,4462,4911,3073,4064,4818,1731,3800,4264,3977,2923,3614,3971,3583,2252,3861,1293,2278,2553,2461,2974,3150,4684,4232,2835,1643,3953,3363,2999,3539,2770,5057,2439,2725,1699,5197,2051,5094,3423,2550,2481,2139,3806,2064,2369,1775,2752,3706,3325,2535,2101,1496,4196,3178,4626,5139,4890,2069,2867,2506,1562,4084,2054,1809,1873,2107,2665,4456,2652,4879,3921,1472,1958,4336,4405,1583,4813,4580,2994,5025,1905,1420,2503,1684,2846,2564,3292,2899,4168,2582,4658,1748,2298,1770,4035,2397,3913,4490,5125,2375,4673,1647,3129,3872,1484,4593,5018,3315,1598,1225,4272,4366,1605,3260,3754,4950,4517,3228,4641,3209,4754,4961,2407,1267,5079,1531,4324,3246,4240,3940,2920,5015,4003,4549,4132,3564,1738,5062,1711,3080,3305,2165,1300,1637,3273,3791,4222,1869,2429,4768,1980,2128,5203,3774,1830,1763,5001,2701,2486,2599,3174,4737,4117,1579,1336,3769,3697,1802,4093,4267,2892,3366,4414,3684,1617,2838,2113,3124,2426,4488,1284,1353,4748,1955,2843,2320,4106,4991,4046,4538,4235,2511,4634,2807,5100,3007,2266,4150,2584,4257,3478,3620,2458,1459,3171,3533,1654,3625,4574,3433,4278,1918,4138,1649,2352,3757,4606,2870,2828,1834,1913,2310,1844,3548,2194,2215,1517,2611,4185,2743,2490,4006,2226,1453,2643,1734,4061,2907,1276,2174,2098,4468,1481,4250,1745,2971,3780,4261,1646,2443,1326,3729,1253,2707,2988,2594,1674,3789,1639,2290,3825,1903,2135,4681,5191,3369,4126,2823,3104,2004,3748,2026,3561,2608,3501,1822,5010,2764,4834,3516,1558,2152,2944,4182,1491,2475,4293,3879,1308,2066,2162,1607,1661,2315,2421,4964,4321,3844,3585,4299,5109,1440,5023,2680,1212,5072,3993,2902,5119,2095,4446,1893,1309,4869,2917,4372,1994,3552,2779,2019,2142,2930,1348,2287,2517,1725,4114,4706,4356,1546,3373,1876,1527,3132,1757,3690,3203,5041,1642,4917,4378,2534,2983,3865,1229,3601,3882,1395,1625,2522,3100,2008,1303,3015,3956,1363,2334,4631,4474,2746,2704,2366,3426,3030,2223,2040,2668,5200,5110,4318,3822,3145,1436,1859,4029,3328,4350,1816,1495,4895,4286,1693,2572,3479,2417,2913,2404,4193,2619,3673,1346,2159,1268,3869,3772,3489,4831,5046,4955,3812,2138,1236,2241,4129,1977,3974,3025,3057,1532,4799,3570,1384,3411,1537,3360,1378,3965,3020,4330,1713,2864,3740,4345,4501,1505,3918,2270,4363,2372,4533,1331,2754,1320,4520,1962,4723,3721,1417,4655,2640,3950,4779,5029,1653,1944,4555,3096,1737,1681,2887,3405,2238,1490,4977,4423,4056,4863,3200,2191,1204,1449,1812,2087,3933,4459,1468,3047,2980,3035,3575,4552,2177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW246+1 : TPTP v8.1.2. Released v5.2.0.
% 0.15/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n017.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 : Thu May 18 22:03:46 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.82/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.93/1.08 % [INFO] Parsing done (251ms).
% 1.93/1.09 % [INFO] Running in sequential loop mode.
% 2.40/1.29 % [INFO] eprover registered as external prover.
% 2.40/1.29 % [INFO] cvc4 registered as external prover.
% 2.40/1.29 % [INFO] Scanning for conjecture ...
% 2.75/1.45 % [INFO] Found a conjecture and 1198 axioms. Running axiom selection ...
% 3.93/1.66 % [INFO] Axiom selection finished. Selected 1198 axioms (removed 0 axioms).
% 5.12/2.06 % [INFO] Problem is first-order (TPTP FOF).
% 5.43/2.09 % [INFO] Type checking passed.
% 5.43/2.09 % [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 ...
% 23.61/6.71 % External prover 'e' found a proof!
% 23.61/6.71 % [INFO] Killing All external provers ...
% 23.61/6.71 % Time passed: 6183ms (effective reasoning time: 5618ms)
% 23.61/6.71 % 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)>
% 23.61/6.72 % Axioms used in derivation (1198): fact_dvd_Oord__less__eq__trans, fact_div__mult__mult1, arity_Polynomial__Opoly__Rings_Osemiring__0, fact_int__0, arity_fun__Orderings_Oorder, fact_nat_Osimps_I3_J, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_dvd_Oless__trans, fact_mod__div__equality, fact_minus__mult__left, fact_zadd__int, fact_mult__strict__left__mono__neg, fact_Nat_Oadd__0__right, fact_div__add, fact_one__dvd, fact_right__inverse__eq, fact_real__squared__diff__one__factored, fact_minus__monom, fact_int__mult, fact_xt1_I1_J, clrel_Rings_Oidom__Groups_Ozero, fact_smult__minus__left, fact_coeff__pCons__0, arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, arity_Nat__Onat__Groups_Ocancel__semigroup__add, clrel_Rings_Oidom__Groups_Ogroup__add, fact_power__strict__decreasing, arity_Int__Oint__Rings_Ocomm__semiring, fact_pdivmod__rel__mult, fact_pos__add__strict, arity_Int__Oint__Rings_Osemiring, clrel_Rings_Oidom__Groups_Oab__group__add, fact_mult__poly__0__right, fact_nonzero__inverse__inverse__eq, fact_add__strict__right__mono, arity_Int__Oint__Orderings_Olinorder, fact_zdvd__zmod, fact_div__power, fact_mult__1__left, fact_diff__0__eq__0, fact_add__poly__code_I2_J, fact_dvd__mult__cancel__left, fact_zdvd__not__zless, fact_neg__equal__0__iff__equal, fact_mod__mult2__eq, fact_diff__add__inverse, fact_dvdI, arity_Polynomial__Opoly__Rings_Ocomm__semiring__0, fact_DERIV__inverse_H, fact_trans__less__add1, fact_poly__eq__0__iff__dvd, fact_of__nat__add, fact_inverse__1, fact_minus__poly__def, fact_pdivmod__rel__unique__div, fact_order, fact_diff__0__right, fact_mult__less__cancel__left__disj, fact_nat__add__left__commute, fact_dvd_Oeq__iff, fact_less__imp__inverse__less, fact_power__power__power, fact_degree__add__eq__right, fact_mult__left_Ominus, tfree_0, fact_inf__period_I4_J, arity_Nat__Onat__Rings_Ono__zero__divisors, clrel_Rings_Oidom__Rings_Omult__zero, fact_nat__less__cases, fact_zero__less__int__conv, fact_one__is__add, arity_Int__Oint__Rings_Olinordered__semiring__strict, arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add, fact_minus__mult__right, clrel_Rings_Oidom__Rings_Oring__1, fact_odd__nonzero, fact_diff__Suc, fact_dvd_Oorder__trans, fact_zdiff__zmod__right, fact_zminus__zminus, fact_combine__common__factor, fact_mod__mult__cong, fact_dvd__triv__right, fact_zpower__zmod, fact_poly__gcd__greatest, fact_zmult__int, fact_n__less__m__mult__n, fact_inverse__inverse__eq, fact_unity__coeff__ex, fact_Suc__mono, fact_one__less__inverse__iff, arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le, fact_add__less__mono, fact_mult__pCons__right, fact_order__less__asym_H, fact_mult__eq__0__iff, fact_pow__divides__pow__int, fact_zpower__int, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, fact_smult__dvd__cancel, arity_Nat__Onat__Orderings_Oorder, fact_positive__imp__inverse__positive, fact_dvd_Oless__asym_H, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, fact_Suc__times__mod__eq, arity_Int__Oint__Rings_Osemiring__1, 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_zadd__commute, arity_HOL__Obool__Lattices_Oboolean__algebra, fact_zless__int, arity_Nat__Onat__Groups_Omonoid__mult, fact_diff__Suc__less, fact_transfer__int__nat__numerals_I2_J, fact_divide__inverse, fact_mult__0, fact_inverse__zero__imp__zero, arity_Polynomial__Opoly__Rings_Olinordered__ring__strict, fact_mod__mult__eq, fact_dvd_Oless__imp__not__less, arity_Polynomial__Opoly__Rings_Oidom, fact_zero__less__diff, fact_nonzero__inverse__eq__imp__eq, fact_Divides_Otransfer__int__nat__functions_I2_J, fact_linorder__neqE, fact_neg__0__less__iff__less, fact_dvd__smult, fact_mult__poly__0__left, arity_Nat__Onat__Rings_Ozero__neq__one, fact_poly__zero, fact_eq__neg__iff__add__eq__0, arity_Polynomial__Opoly__Groups_Oab__semigroup__mult, fact_add__right__imp__eq, fact_realpow__two__diff, arity_HOL__Obool__Orderings_Opreorder, fact_nat__add__right__cancel, fact_dvd__mod, clrel_Rings_Oidom__Power_Opower, fact_gr0__conv__Suc, arity_Polynomial__Opoly__Groups_Ominus, fact_coeff__eq__0, fact_poly__dvd__antisym, fact_zdvd__mult__cancel, fact_inverse__zero, fact_dvd_Oord__eq__less__trans, fact_DERIV__chain2, fact_field__power__not__zero, help_c__fconj__3, fact_zmod__zdiv__equality, fact_Suc__diff__diff, fact_mod__diff__cong, fact_divide__pos__neg, fact_minus__add__cancel, fact_smult__smult, arity_Polynomial__Opoly__Rings_Ocomm__ring, fact_fun__Compl__def, fact_zmult__div__cancel, arity_Int__Oint__Orderings_Oord, fact_nat__add__left__cancel__less, fact_mod__mult__distrib2, fact_mod__less, fact_coeff__add, fact_mult_Oadd__right, fact_mult_Ominus__right, help_c__fequal__2, fact_mult__eq__self__implies__10, fact_minus__pCons, fact_poly__mod__minus__left, fact_dvd__div__mult__self, fact_degree__linear__power, fact_pow__divides__pow__nat, fact_poly__add, fact_degree__pCons__0, fact_pdivmod__rel, fact_order__1, fact_int__0__less__1, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_linorder__antisym__conv3, fact_order__less__imp__not__eq, fact_inverse__positive__imp__positive, clrel_Rings_Oidom__Groups_Ouminus, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, fact_of__nat__less__imp__less, fact_linorder__neqE__linordered__idom, fact_coeff__inverse, help_c__COMBC__1, arity_Polynomial__Opoly__Orderings_Olinorder, fact_mod__if, fact_Least__Suc, fact_Nat__Transfer_Otransfer__int__nat__relations_I2_J, fact_smult__1__left, fact_DERIV__inverse, fact_mult__right_Ozero, clrel_Rings_Oidom__Groups_Ocancel__semigroup__add, fact_mod__mult__self1, fact_pow__divides__eq__nat, fact_pdivmod__rel__by__0, fact_mult__smult__right, fact_smult__pCons, fact_mod__by__1, arity_Polynomial__Opoly__Rings_Olinordered__semidom, fact_synthetic__div__correct_H, fact_neg__less__0__iff__less, fact_divide__1, fact_mult__strict__left__mono, fact_mod__mult__self4, fact_zdvd__mult__div__cancel, fact_dvd__reduce, fact_synthetic__div__0, arity_Int__Oint__Groups_Ozero, fact_zdiv__zero, fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J, fact_mult_Ozero__left, fact_zdvd__zmod__imp__zdvd, fact_even__less__0__iff, fact_power__commutes, fact_gr0I, clrel_Rings_Oidom__Rings_Osemiring, fact_poly__smult, arity_Polynomial__Opoly__Orderings_Oord, fact_times__poly__def, fact_power__strict__increasing, fact_power__one__over, arity_Nat__Onat__Rings_Osemiring__0, arity_Int__Oint__Groups_Ocomm__monoid__add, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_add__monom, fact_add__0__left, fact_zmod__zminus1__eq__if, fact_poly__0, fact_add__eq__if, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_coeff__1, arity_Int__Oint__Rings_Olinordered__ring, fact_add__0__iff, fact_int__int__eq, fact_minus__add, fact_divide__eq__imp, arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add, fact_power__minus, fact_DERIV__unique, fact_of__nat__mult, fact_degree__1, arity_Int__Oint__Groups_Ocancel__comm__monoid__add, fact_of__nat__aux_Osimps_I1_J, fact_one__less__power, fact_mod__mult__left__eq, fact_nat__dvd__not__less, fact_DERIV__mult_H, fact_leading__coeff__neq__0, fact_mult__eq__1__iff, fact_dvd__div__eq__mult, fact_smult__add__right, fact_degree__pCons__eq__if, fact_divide__add__eq__iff, fact_nat__mult__1__right, fact_order__less__imp__not__less, fact_poly__gcd__monic, arity_Int__Oint__Rings_Oidom, fact_dvd__eq__mod__eq__0, fact_ord__less__eq__trans, fact_poly__gcd_Oassoc, fact_zdiv__zmult1__eq, fact_one__reorient, fact_diff__commute, fact_minus__less__iff, fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J, arity_fun__Groups_Ouminus, fact_power__eq__0__iff, help_c__COMBS__1, fact_negative__imp__inverse__negative, fact_diff__Suc__eq__diff__pred, fact_xt1_I9_J, fact_less__add__eq__less, fact_divide__strict__left__mono__neg, fact_mod__1, help_c__COMBI__1, fact_minus__mult__commute, fact_linorder__less__linear, arity_Polynomial__Opoly__Groups_Omonoid__add, fact_division__ring__inverse__add, fact_mult__left_Odiff, fact_eq__iff__diff__eq__0, fact_add__lessD1, fact_div__mult__self1__is__id, arity_Polynomial__Opoly__Int_Oring__char__0, fact_lessI, fact_transfer__int__nat__numerals_I1_J, fact_coeff__linear__power, fact_inverse__less__imp__less, fact_dvd_Oantisym__conv, fact_zero__reorient, fact_pos__imp__zdiv__neg__iff, arity_Int__Oint__Groups_Oordered__ab__group__add, fact_mult__right_Odiff, fact_DERIV__const, fact_dvd__0__right, fact_mod__add__self1, fact_minus__divide__divide, 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clrel_Rings_Oidom__Groups_Omonoid__mult, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, fact_mult__zero__left, fact_left__add__mult__distrib, fact_add__scale__eq__noteq, fact_eq__add__iff2, fact_zadd__zmult__distrib2, fact_less__not__refl2, fact_field__class_Onormalizing__field__rules_I2_J, fact_mult__cancel1, clrel_Rings_Oidom__Groups_Oab__semigroup__add, fact_zdvd__mono, fact_monom__eq__0, fact_zmod__zmult1__eq, fact_power__eq__if, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, fact_leading__coeff__0__iff, fact_less__add__Suc1, fact_nat__case__Suc, fact_One__nat__def, fact_mult__diff__mult, fact_add__less__imp__less__left, fact_times__divide__times__eq, fact_divide_Oadd, fact_Deriv_Oadd__diff__add, fact_xt1_I2_J, fact_coeff__smult, fact_nonzero__minus__divide__divide, fact_smult__0__right, fact_ab__left__minus, fact_add__neg__neg, fact_dvd__mod__iff, arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict, fact_minus__diff__eq, fact_less__imp__inverse__less__neg, fact_comm__semiring__class_Odistrib, fact_square__eq__iff, fact_smult__dvd__iff, fact_nonzero__minus__divide__right, fact_add__is__0, clrel_Rings_Oidom__Groups_Ocomm__monoid__add, fact_divide__diff__eq__iff, fact_realpow__num__eq__if, fact_DERIV__cmult__Id, fact_mod__eq__0__iff, arity_Int__Oint__Rings_Oordered__ring, fact_mod__mult__mult2, fact_power_Opower_Opower__Suc, fact_inverse__less__imp__less__neg, fact_ab__diff__minus, fact_pCons__def, arity_Polynomial__Opoly__Rings_Oordered__ring, fact_diff__minus__eq__add, fact_Suc__eq__plus1, fact_add__eq__0__iff, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, fact_neg__equal__iff__equal, fact_pos__poly__add, fact_diff__add__0, fact_zmod__simps_I2_J, fact_uminus__dvd__conv_I1_J, fact_add__pos__pos, fact_nat__case__0, arity_Nat__Onat__Groups_Oab__semigroup__mult, fact_diff__cancel2, fact_add__0, fact_poly__mod__minus__right, fact_dvd_Ostrict__monoD, fact_dvd__mult__cancel, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J, fact_fun__diff__def, fact_diff__self__eq__0, arity_Int__Oint__Rings_Olinordered__idom, arity_Int__Oint__Rings_Ocomm__semiring__1, fact_offset__poly__def, fact_minus__poly__code_I2_J, fact_realpow__two__disj, fact_inverse__minus__eq, fact_div__neg__pos__less0, fact_degree__minus, fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J, fact_compl__eq__compl__iff, fact_coeff__pCons__Suc, fact_smult__dvd, fact_pos__poly__pCons, arity_Polynomial__Opoly__Rings_Osemiring, fact_Zero__neq__Suc, fact_poly__gcd__0__0, fact_degree__add__eq__left, fact_dvd__minus__iff, fact_int__less__0__conv, arity_Nat__Onat__Groups_Oab__semigroup__add, arity_Nat__Onat__Rings_Olinordered__semidom, arity_Int__Oint__Groups_Ocomm__monoid__mult, fact_ord__eq__less__trans, fact_zmult__zless__mono2, fact_degree__mod__less, fact_Suc__pred, arity_Int__Oint__Groups_Oab__semigroup__add, fact_nat__dvd__1__iff__1, fact_power__Suc__0, fact_nat__mult__eq__1__iff, fact_n__less__n__mult__m, fact_mult__right_Ominus, fact_less__not__refl, fact_mult__less__cancel__left__neg, fact_poly__gcd__unique, fact_synthetic__div__eq__0__iff, fact_power__mult__distrib, fact_less__1__mult, fact_right__inverse, fact_coeff__monom, fact_power__one, fact_zmod__zmult2__eq, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, fact_poly__diff, arity_Int__Oint__Orderings_Oorder, fact_mod__smult__left, fact_int__eq__0__conv, fact_mult__pos__pos, fact_minus__mult__minus, fact_crossproduct__eq, fact_monom__eq__iff, fact_square__eq__1__iff, fact_dvd_Oantisym, fact_neg__less__divide__eq, fact_mod__mod__cancel, fact_inf__period_I3_J, arity_fun__Groups_Ominus, fact_divide__less__eq, fact_zmod__simps_I1_J, fact_gr__implies__not0, fact_dvd_Ole__neq__trans, fact_mult__strict__right__mono__neg, fact_zdiv__zminus__zminus, arity_Int__Oint__Groups_Oone, fact_DERIV__add, clrel_Rings_Oidom__Rings_Ono__zero__divisors, help_c__COMBK__1, arity_Polynomial__Opoly__Orderings_Opreorder, fact_power__less__power__Suc, arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors, fact_less__add__one, fact_degree__monom__eq, arity_Nat__Onat__Rings_Olinordered__semiring__strict, fact_less__Suc__eq, fact_nonzero__power__inverse, fact_divide__strict__left__mono, fact_zmod__zminus2, fact_dvd__smult__iff, arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add, fact_diff__Suc__1, fact_dvd__antisym, fact_div__mod__equality, fact_poly__gcd_Osimps_I1_J, fact_zero__neq__one, fact_nat__add__commute, fact_mult__smult__left, fact_add__poly__code_I1_J, fact_synthetic__div__unique, arity_Int__Oint__Rings_Ono__zero__divisors, fact_of__nat__eq__iff, fact_degree__diff__less, fact_Suc__less__eq, fact_mult__neg__neg, arity_Int__Oint__Rings_Oring__1, fact_right__minus__eq, fact_div__mult__swap, arity_Int__Oint__Rings_Odvd, fact_poly__gcd__1__left, fact_mult_Odiff__left, fact_coeff__0, arity_Polynomial__Opoly__Groups_Ogroup__add, fact_zmult__zminus, fact_zero__less__Suc, fact_mod__poly__eq, fact_div__self, fact_diff__add__inverse2, fact_plus__nat_Oadd__0, fact_less__divide__eq, fact_mult_Ocomm__neutral, fact_dvd_Oless__le, fact_mult__left__idem, fact_zmult__zless__mono2__lemma, clrel_Rings_Oidom__Rings_Ocomm__semiring, fact_not__pos__poly__0, fact_zdiv__zminus2, fact_zero__poly__def, fact_dvd_Oless__le__trans, fact_nat__mult__commute, fact_nat__power__eq__Suc__0__iff, fact_divide_Odiff, arity_Polynomial__Opoly__Divides_Oring__div, fact_mod__Suc__eq__Suc__mod, fact_neg__divide__less__eq, fact_diff__eq__diff__eq, fact_of__nat__Suc, fact_zdiv__self, fact_pow__divides__eq__int, fact_neq0__conv, fact_Suc__n__not__n, fact_zless__linear, fact_mult__less__cancel__left__pos, fact_add__divide__distrib, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, clrel_Rings_Oidom__Groups_Oone, arity_Int__Oint__Rings_Olinordered__comm__semiring__strict, clrel_Rings_Oidom__Rings_Oring__1__no__zero__divisors, arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le, arity_Polynomial__Opoly__Rings_Ocomm__ring__1, fact_add__frac__num, fact_minus__equation__iff, fact_divide__strict__right__mono, fact_mult__0__right, fact_synthetic__div__unique__lemma, fact_zdvd__period, fact_zadd__0__right, fact_dvd_Ostrict__mono__mono, fact_zero__less__mult__pos, arity_Polynomial__Opoly__Rings_Odvd, arity_Polynomial__Opoly__Rings_Ocomm__semiring, fact_zless__iff__Suc__zadd, arity_Int__Oint__Groups_Ominus, fact_zmult__1__right, arity_Polynomial__Opoly__Rings_Ono__zero__divisors, fact_double__eq__0__iff, fact_mult__Suc__right, fact_zdvd__zdiffD, fact_dvd__0__left, fact_pcompose__pCons, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J, fact_mult__less__cancel2, fact_mult__1__right, fact_gcd__lcm__complete__lattice__nat_Obot__least, arity_Polynomial__Opoly__Groups_Ozero, fact_order__less__irrefl, arity_Int__Oint__Rings_Ocomm__ring__1, fact_add__diff__inverse, arity_Nat__Onat__Rings_Osemiring, fact_smult__minus__right, fact_termination__basic__simps_I1_J, fact_less__iff__Suc__add, fact_semiring__1__class_Oof__nat__code, fact_order__less__trans, fact_dvd__1__iff__1, fact_DIVISION__BY__ZERO, fact_mod__lemma, fact_mod__0, fact_negative__eq__positive, fact_zero__less__two, fact_pdivmod__rel__unique__mod, fact_DERIV__add__minus, fact_sum__squares__eq__zero__iff, fact_nat__zero__less__power__iff, fact_mod__add__right__eq, fact_of__nat__1, fact_dvd__iff__poly__eq__0, fact_less__Suc0, fact_div__mult1__eq, fact_pos__poly__def, fact_dvd_Ole__less__trans, fact_diff__monom, arity_Int__Oint__Groups_Olinordered__ab__group__add, fact_nat__mult__eq__cancel__disj, fact_DERIV__divide, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, arity_Int__Oint__Rings_Ozero__neq__one, fact_add__imp__eq, fact_power__gt1, fact_no__zero__divisors, fact_zadd__zmult__distrib, arity_Polynomial__Opoly__Rings_Olinordered__ring, arity_Polynomial__Opoly__Groups_Ocomm__monoid__add, fact_zadd__zminus__inverse2, fact_div__mult__self2__is__id, fact_DERIV__mult__lemma, fact_ab__semigroup__add__class_Oadd__ac_I1_J, arity_Nat__Onat__Groups_Oone, fact_mod__mult__self2, fact_diff__Suc__Suc, fact_dvd__mult__left, fact_coeff__inject, arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_degree__0, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_mod__minus__cong, fact_dvd_Ole__imp__less__or__eq, fact_power__0__Suc, fact_minus__poly__code_I1_J, fact_DERIV__cong, fact_less__iff__diff__less__0, fact_mult__eq__if, fact_Deriv_Oinverse__diff__inverse, fact_less__SucE, fact_gt__half__sum, fact_zless__add1__eq, fact_linorder__cases, fact_add__less__mono1, fact_eq__divide__eq, fact_divisors__zero, fact_smult__diff__left, arity_Polynomial__Opoly__Groups_Oone, fact_poly__eq__iff, fact_degree__mult__eq, fact_inverse__negative__imp__negative, fact_field__inverse__zero, fact_nonzero__eq__divide__eq, fact_double__add__less__zero__iff__single__add__less__zero, fact_minus__divide__left, fact_zmod__zminus1__not__zero, fact_pdivmod__rel__0, fact_odd__less__0, fact_dvd_Oless__imp__not__eq2, fact_pdivmod__rel__pCons, fact_field__inverse, arity_Int__Oint__Groups_Omonoid__add, fact_dvd__mult__cancel__right, fact_DERIV__power, fact_pdivmod__rel__def, fact_mod__add__eq, fact_less__half__sum, arity_Int__Oint__Rings_Ocomm__semiring__0, fact_negative__zless__0, fact_add__Suc__shift, fact_less__SucI, fact_Suc__not__Zero, fact_dvd__power, fact_poly__gcd_Osimps_I2_J, fact_not__square__less__zero, fact_Suc__lessI, fact_add__Suc__right, fact_mult__pCons__left, fact_not__less__Least, fact_mult__1, fact_less__bin__lemma, arity_Int__Oint__Rings_Olinordered__ring__strict, fact_mult_Odiff__right, fact_mod__mult__distrib, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, arity_Int__Oint__Divides_Oring__div, fact_DERIV__quotient, fact_dvd__imp__mod__0, arity_Int__Oint__Orderings_Opreorder, fact_divide__self, fact_nonzero__power__divide, fact_coeff__diff, fact_dvd__mod__imp__dvd
% 23.61/6.72 % No. of inferences in proof: 2400
% 23.61/6.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6183 ms resp. 5618 ms w/o parsing
% 25.30/7.17 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 25.30/7.18 % [INFO] Killing All external provers ...
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