%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW246+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:09:45 AM UTC 2026
% Result : Theorem 46.80s 12.00s
% Output : Refutation 50.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1199
% Syntax : Number of formulae : 2400 ( 495 unt; 0 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 : 0 ( 0 >; 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_decl,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
thf(t_a_decl,type,
t_a: $i ).
thf(tc_Nat_Onat_decl,type,
tc_Nat_Onat: $i ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i ).
thf(c_Groups_Oplus__class_Oplus_decl,type,
c_Groups_Oplus__class_Oplus: $i > $i ).
thf(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize_decl,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize: $i > $i > $i ).
thf(c_Groups_Oone__class_Oone_decl,type,
c_Groups_Oone__class_Oone: $i > $i ).
thf(tc_Polynomial_Opoly_decl,type,
tc_Polynomial_Opoly: $i > $i ).
thf(c_Polynomial_Opoly_decl,type,
c_Polynomial_Opoly: $i > $i > $i ).
thf(c_Groups_Otimes__class_Otimes_decl,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
thf(c_Power_Opower__class_Opower_decl,type,
c_Power_Opower__class_Opower: $i > $i ).
thf(c_Polynomial_OpCons_decl,type,
c_Polynomial_OpCons: $i > $i ).
thf(class_Rings_Oidom_decl,type,
class_Rings_Oidom: $i > $o ).
thf(class_Groups_Omonoid__add_decl,type,
class_Groups_Omonoid__add: $i > $o ).
thf(class_Fields_Ofield_decl,type,
class_Fields_Ofield: $i > $o ).
thf(c_Polynomial_Opdivmod__rel_decl,type,
c_Polynomial_Opdivmod__rel: $i > $i > $i > $i > $i > $o ).
thf(c_Divides_Odiv__class_Omod_decl,type,
c_Divides_Odiv__class_Omod: $i > $i > $i > $i ).
thf(class_Divides_Osemiring__div_decl,type,
class_Divides_Osemiring__div: $i > $o ).
thf(c_Divides_Odiv__class_Odiv_decl,type,
c_Divides_Odiv__class_Odiv: $i > $i > $i > $i ).
thf(tc_Int_Oint_decl,type,
tc_Int_Oint: $i ).
thf(class_Fields_Ofield__inverse__zero_decl,type,
class_Fields_Ofield__inverse__zero: $i > $o ).
thf(c_Groups_Ouminus__class_Ouminus_decl,type,
c_Groups_Ouminus__class_Ouminus: $i > $i ).
thf(c_Rings_Oinverse__class_Odivide_decl,type,
c_Rings_Oinverse__class_Odivide: $i > $i ).
thf(class_Orderings_Opreorder_decl,type,
class_Orderings_Opreorder: $i > $o ).
thf(c_Orderings_Oord__class_Oless_decl,type,
c_Orderings_Oord__class_Oless: $i > $i > $i > $o ).
thf(class_Rings_Osemiring__0_decl,type,
class_Rings_Osemiring__0: $i > $o ).
thf(class_Rings_Olinordered__semidom_decl,type,
class_Rings_Olinordered__semidom: $i > $o ).
thf(c_Nat_Osemiring__1__class_Oof__nat_decl,type,
c_Nat_Osemiring__1__class_Oof__nat: $i > $i > $i ).
thf(class_Rings_Ocomm__semiring__1_decl,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
thf(hBOOL_decl,type,
hBOOL: $i > $o ).
thf(c_Rings_Odvd__class_Odvd_decl,type,
c_Rings_Odvd__class_Odvd: $i > $i ).
thf(class_RealVector_Oreal__normed__field_decl,type,
class_RealVector_Oreal__normed__field: $i > $o ).
thf(c_Deriv_Oderiv_decl,type,
c_Deriv_Oderiv: $i > $i > $i > $i > $o ).
thf(c_Groups_Ominus__class_Ominus_decl,type,
c_Groups_Ominus__class_Ominus: $i > $i ).
thf(class_Groups_Ozero_decl,type,
class_Groups_Ozero: $i > $o ).
thf(c_Polynomial_Odegree_decl,type,
c_Polynomial_Odegree: $i > $i > $i ).
thf(c_Polynomial_Omonom_decl,type,
c_Polynomial_Omonom: $i > $i > $i > $i ).
thf(class_Rings_Oring__no__zero__divisors_decl,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
thf(class_Rings_Ocomm__semiring_decl,type,
class_Rings_Ocomm__semiring: $i > $o ).
thf(c_Polynomial_Ocoeff_decl,type,
c_Polynomial_Ocoeff: $i > $i > $i ).
thf(class_Orderings_Oord_decl,type,
class_Orderings_Oord: $i > $o ).
thf(tc_HOL_Obool_decl,type,
tc_HOL_Obool: $i ).
thf(class_Groups_Ouminus_decl,type,
class_Groups_Ouminus: $i > $o ).
thf(class_Rings_Osemiring__1_decl,type,
class_Rings_Osemiring__1: $i > $o ).
thf(c_Nat_Osemiring__1__class_Oof__nat__aux_decl,type,
c_Nat_Osemiring__1__class_Oof__nat__aux: $i > $i > $i > $i > $i ).
thf(c_Nat_OSuc_decl,type,
c_Nat_OSuc: $i ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(class_Groups_Oab__semigroup__add_decl,type,
class_Groups_Oab__semigroup__add: $i > $o ).
thf(c_Polynomial_Opoly__gcd_decl,type,
c_Polynomial_Opoly__gcd: $i > $i > $i > $i ).
thf(c_Polynomial_Osmult_decl,type,
c_Polynomial_Osmult: $i > $i ).
thf(c_Rings_Oinverse__class_Oinverse_decl,type,
c_Rings_Oinverse__class_Oinverse: $i > $i ).
thf(c_Orderings_Oord__class_Oless__eq_decl,type,
c_Orderings_Oord__class_Oless__eq: $i > $i > $i > $o ).
thf(c_COMBB_decl,type,
c_COMBB: $i > $i > $i > $i ).
thf(class_Groups_Ominus_decl,type,
class_Groups_Ominus: $i > $o ).
thf(tc_fun_decl,type,
tc_fun: $i > $i > $i ).
thf(class_Rings_Omult__zero_decl,type,
class_Rings_Omult__zero: $i > $o ).
thf(class_Rings_Ocomm__semiring__0_decl,type,
class_Rings_Ocomm__semiring__0: $i > $o ).
thf(class_Divides_Oring__div_decl,type,
class_Divides_Oring__div: $i > $o ).
thf(class_Rings_Ocomm__ring_decl,type,
class_Rings_Ocomm__ring: $i > $o ).
thf(class_Power_Opower_decl,type,
class_Power_Opower: $i > $o ).
thf(class_Rings_Olinordered__ring_decl,type,
class_Rings_Olinordered__ring: $i > $o ).
thf(c_Polynomial_OAbs__poly_decl,type,
c_Polynomial_OAbs__poly: $i > $i > $i ).
thf(class_Nat_Osemiring__char__0_decl,type,
class_Nat_Osemiring__char__0: $i > $o ).
thf(class_Groups_Oab__group__add_decl,type,
class_Groups_Oab__group__add: $i > $o ).
thf(class_Groups_Ocancel__semigroup__add_decl,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
thf(class_Groups_Ocancel__comm__monoid__add_decl,type,
class_Groups_Ocancel__comm__monoid__add: $i > $o ).
thf(class_Groups_Oab__semigroup__mult_decl,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
thf(class_Groups_Ocomm__monoid__add_decl,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
thf(class_Groups_Olinordered__ab__group__add_decl,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
thf(class_Rings_Odivision__ring_decl,type,
class_Rings_Odivision__ring: $i > $o ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $o ).
thf(class_Groups_Omonoid__mult_decl,type,
class_Groups_Omonoid__mult: $i > $o ).
thf(class_Groups_Ocancel__ab__semigroup__add_decl,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
thf(class_Rings_Ocomm__ring__1_decl,type,
class_Rings_Ocomm__ring__1: $i > $o ).
thf(c_COMBS_decl,type,
c_COMBS: $i > $i > $i > $i ).
thf(class_Groups_Oordered__ab__group__add_decl,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
thf(class_Groups_Ogroup__add_decl,type,
class_Groups_Ogroup__add: $i > $o ).
thf(c_Orderings_Oorder_Ostrict__mono_decl,type,
c_Orderings_Oorder_Ostrict__mono: $i > $i > $i > $i > $o ).
thf(c_fconj_decl,type,
c_fconj: $i ).
thf(c_fNot_decl,type,
c_fNot: $i ).
thf(c_COMBC_decl,type,
c_COMBC: $i > $i > $i > $i > $i ).
thf(c_Orderings_Oorder_Omono_decl,type,
c_Orderings_Oorder_Omono: $i > $i > $i > $i > $o ).
thf(class_Rings_Oring_decl,type,
class_Rings_Oring: $i > $o ).
thf(class_Rings_Olinordered__idom_decl,type,
class_Rings_Olinordered__idom: $i > $o ).
thf(class_Rings_Oring__1__no__zero__divisors_decl,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
thf(class_Rings_Odvd_decl,type,
class_Rings_Odvd: $i > $o ).
thf(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly_decl,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly: $i > $i > $i > $i ).
thf(class_Rings_Osemiring_decl,type,
class_Rings_Osemiring: $i > $o ).
thf(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_decl,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
thf(class_Rings_Ozero__neq__one_decl,type,
class_Rings_Ozero__neq__one: $i > $o ).
thf(class_Groups_Ocomm__monoid__mult_decl,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
thf(class_Groups_Oordered__ab__semigroup__add__imp__le_decl,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
thf(class_Groups_Oone_decl,type,
class_Groups_Oone: $i > $o ).
thf(class_Rings_Olinordered__semiring__strict_decl,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
thf(class_Rings_Ono__zero__divisors_decl,type,
class_Rings_Ono__zero__divisors: $i > $o ).
thf(c_If_decl,type,
c_If: $i > $i ).
thf(c_fequal_decl,type,
c_fequal: $i > $i ).
thf(class_Rings_Oordered__ring_decl,type,
class_Rings_Oordered__ring: $i > $o ).
thf(class_Lattices_Oboolean__algebra_decl,type,
class_Lattices_Oboolean__algebra: $i > $o ).
thf(c_Polynomial_Opos__poly_decl,type,
c_Polynomial_Opos__poly: $i > $i > $o ).
thf(class_Rings_Oring__1_decl,type,
class_Rings_Oring__1: $i > $o ).
thf(class_Rings_Olinordered__comm__semiring__strict_decl,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
thf(class_Int_Oring__char__0_decl,type,
class_Int_Oring__char__0: $i > $o ).
thf(class_Orderings_Owellorder_decl,type,
class_Orderings_Owellorder: $i > $o ).
thf(c_Orderings_Oord__class_OLeast_decl,type,
c_Orderings_Oord__class_OLeast: $i > $i > $i ).
thf(class_Rings_Olinordered__ring__strict_decl,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
thf(class_Rings_Odivision__ring__inverse__zero_decl,type,
class_Rings_Odivision__ring__inverse__zero: $i > $o ).
thf(class_Groups_Oordered__cancel__ab__semigroup__add_decl,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
thf(class_Groups_Oordered__comm__monoid__add_decl,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
thf(class_RealVector_Oreal__normed__algebra_decl,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
thf(c_Polynomial_Osynthetic__div_decl,type,
c_Polynomial_Osynthetic__div: $i > $i > $i > $i ).
thf(class_Fields_Olinordered__field_decl,type,
class_Fields_Olinordered__field: $i > $o ).
thf(c_Nat_Onat_Onat__case_decl,type,
c_Nat_Onat_Onat__case: $i > $i > $i > $i ).
thf(c_COMBI_decl,type,
c_COMBI: $i > $i ).
thf(class_Fields_Olinordered__field__inverse__zero_decl,type,
class_Fields_Olinordered__field__inverse__zero: $i > $o ).
thf(c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant_decl,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant: $i > $i > $i > $o ).
thf(c_Power_Opower_Opower_decl,type,
c_Power_Opower_Opower: $i > $i > $i > $i ).
thf(v_p_decl,type,
v_p: $i ).
thf(c_Polynomial_Oorder_decl,type,
c_Polynomial_Oorder: $i > $i > $i > $i ).
thf(class_Lattices_Oab__semigroup__idem__mult_decl,type,
class_Lattices_Oab__semigroup__idem__mult: $i > $o ).
thf(c_Polynomial_Opcompose_decl,type,
c_Polynomial_Opcompose: $i > $i > $i > $i ).
thf(c_COMBK_decl,type,
c_COMBK: $i > $i > $i ).
thf(c_Polynomial_Opoly__rec_decl,type,
c_Polynomial_Opoly__rec: $i > $i > $i > $i > $i > $i ).
thf(c_Transcendental_Odiffs_decl,type,
c_Transcendental_Odiffs: $i > $i > $i > $i ).
thf(c_Groups_Osgn__class_Osgn_decl,type,
c_Groups_Osgn__class_Osgn: $i > $i > $i ).
thf(class_RealVector_Oreal__field_decl,type,
class_RealVector_Oreal__field: $i > $o ).
thf(334,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__less) ).
thf(2163,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(583,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__right__disj) ).
thf(3021,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( ( ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(806,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__mult )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc2) ).
thf(3873,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__mult )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Odivision__ring )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__divide__distrib) ).
thf(1411,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Odivision__ring )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(98,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zminus__zminus) ).
thf(1469,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(885,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add1) ).
thf(4169,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(1032,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__poly__add__left) ).
thf(4729,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).
thf(695,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__less__cancel1) ).
thf(3434,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) )
<=> ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__eq__dvd__iff) ).
thf(1237,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ) )
& ( ( ( B @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(234,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__trans) ).
thf(1840,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(832,axiom,
! [A: $i,B: $i] :
( ( B @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__negative__iff__negative) ).
thf(3969,plain,
! [A: $i,B: $i] :
( ( B @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(446,axiom,
tc_Nat_Onat @ class_Groups_Oordered__ab__semigroup__add__imp__le,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(2559,plain,
tc_Nat_Onat @ class_Groups_Oordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(822,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ? [B: $i] :
( A
= ( B @ ( c_Nat_OSuc @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
thf(3927,plain,
! [A: $i] :
( ( ? [B: $i] :
( A
= ( B @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ? [B: $i] :
( A
= ( B @ ( c_Nat_OSuc @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(381,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__mult__pos2) ).
thf(2331,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(1105,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
thf(5028,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B = A )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
thf(227,axiom,
tc_Int_Oint @ class_Rings_Oidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).
thf(1818,plain,
tc_Int_Oint @ class_Rings_Oidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(271,axiom,
tc_Int_Oint @ class_Groups_Ocancel__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).
thf(1950,plain,
tc_Int_Oint @ class_Groups_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(144,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__ab__group__add )
=> ( ( ( C @ ( D @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq__diff__less) ).
thf(1586,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__ab__group__add )
=> ( ( ( C @ ( D @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
=> ( ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Divides_Odiv__class_Omod ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__imp__mod__0) ).
thf(1501,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Divides_Odiv__class_Omod ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(954,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( B @ ( A @ ( B @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__simps_I1_J) ).
thf(4447,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( B @ ( A @ ( B @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(48,axiom,
tc_Int_Oint @ class_Rings_Olinordered__ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).
thf(1337,plain,
tc_Int_Oint @ class_Rings_Olinordered__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(192,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Rings_Oring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Oring__1) ).
thf(1718,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Rings_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(1118,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone @ ( A @ c_Polynomial_Odegree ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__1) ).
thf(5088,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone @ ( A @ c_Polynomial_Odegree ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).
thf(497,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__field )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide_Oadd) ).
thf(2744,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__field )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(538,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__mono) ).
thf(2889,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(373,axiom,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).
thf(2295,plain,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(590,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL )
<=> ( ! [D: $i] :
( ( B
= ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( D @ ( C @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__split) ).
thf(3053,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ! [D: $i] :
( ( B
= ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( D @ ( C @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL )
=> ( ! [D: $i] :
( ( B
= ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( D @ ( C @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(955,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__iff__diff__less__0) ).
thf(4450,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(839,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= A )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__equal__zero) ).
thf(4005,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= A ) )
& ( ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= A )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(383,axiom,
! [A: $i,B: $i] :
( ( B @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__positive__iff__positive) ).
thf(2336,plain,
! [A: $i,B: $i] :
( ( B @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(578,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__Suc__eq__Suc__mod) ).
thf(3008,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(329,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__field )
=> ( ( A @ ( B @ ( C @ ( D @ c_Deriv_Oderiv ) ) ) )
=> ( ( ( B @ ( C @ hAPP ) )
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Oinverse @ ( D @ ( D @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Deriv_Oderiv ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DERIV__inverse__fun) ).
thf(2131,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__field )
=> ( ( A @ ( B @ ( C @ ( D @ c_Deriv_Oderiv ) ) ) )
=> ( ( ( B @ ( C @ hAPP ) )
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Oinverse @ ( D @ ( D @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Deriv_Oderiv ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(750,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(3661,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(215,axiom,
tc_HOL_Obool @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
thf(1767,plain,
tc_HOL_Obool @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(544,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( E @ c_Polynomial_Omonom ) ) @ ( C @ ( D @ ( E @ c_Polynomial_Omonom ) ) @ ( E @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Polynomial_Omonom ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__monom) ).
thf(2921,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( E @ c_Polynomial_Omonom ) ) @ ( C @ ( D @ ( E @ c_Polynomial_Omonom ) ) @ ( E @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Polynomial_Omonom ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(916,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ hAPP ) @ hBOOL )
=> ( ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_OLeast ) )
= ( c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_OLeast ) @ ( c_Nat_OSuc @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Least__Suc) ).
thf(4290,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ hAPP ) @ hBOOL )
=> ( ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_OLeast ) )
= ( c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_OLeast ) @ ( c_Nat_OSuc @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(703,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__semidom )
=> ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__one) ).
thf(3477,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__semidom )
=> ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(458,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__ring )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring) ).
thf(2595,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__ring )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(240,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__asym_H) ).
thf(1850,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(884,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__smult__left) ).
thf(4166,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(362,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ( ( B
!= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Odegree ) )
= ( B @ ( C @ c_Polynomial_Odegree ) @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( B
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Odegree ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__pCons__eq__if) ).
thf(2250,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ( ( B
!= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Odegree ) )
= ( B @ ( C @ c_Polynomial_Odegree ) @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( B
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Odegree ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(719,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Oab__semigroup__idem__mult )
=> ( ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__idem) ).
thf(3534,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Oab__semigroup__idem__mult )
=> ( ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(323,axiom,
tc_Nat_Onat @ class_Groups_Ocancel__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
thf(2104,plain,
tc_Nat_Onat @ class_Groups_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(901,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Osemiring )
=> ( ( A @ ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_combine__common__factor) ).
thf(4226,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Osemiring )
=> ( ( A @ ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(857,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel1) ).
thf(4075,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B = A )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(477,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__ring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring__1) ).
thf(2659,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__ring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(1154,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
thf(5242,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).
thf(683,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).
thf(3377,plain,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B = A )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ class_Fields_Ofield )
=> ( ( C @ ( D @ ( E @ ( F @ ( G @ c_Polynomial_Opdivmod__rel ) ) ) ) )
=> ( ( A @ ( B @ ( E @ ( F @ ( G @ c_Polynomial_Opdivmod__rel ) ) ) ) )
=> ( C = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pdivmod__rel__unique__mod) ).
thf(1401,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ class_Fields_Ofield )
=> ( ( C @ ( D @ ( E @ ( F @ ( G @ c_Polynomial_Opdivmod__rel ) ) ) ) )
=> ( ( A @ ( B @ ( E @ ( F @ ( G @ c_Polynomial_Opdivmod__rel ) ) ) ) )
=> ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(1090,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Divides_Osemiring__div )
=> ( ( D
!= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C
!= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( D @ ( E @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( E @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( D @ ( B @ ( E @ c_Divides_Odiv__class_Odiv ) ) )
= ( C @ ( A @ ( E @ c_Divides_Odiv__class_Odiv ) ) ) )
<=> ( ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__div__div__eq__mult) ).
thf(4960,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Divides_Osemiring__div )
=> ( ( D
!= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C
!= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( D @ ( E @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( E @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( D @ ( B @ ( E @ c_Divides_Odiv__class_Odiv ) ) )
= ( C @ ( A @ ( E @ c_Divides_Odiv__class_Odiv ) ) ) ) )
& ( ( ( D @ ( B @ ( E @ c_Divides_Odiv__class_Odiv ) ) )
= ( C @ ( A @ ( E @ c_Divides_Odiv__class_Odiv ) ) ) )
=> ( ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).
thf(991,axiom,
tc_Nat_Onat @ class_Orderings_Olinorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
thf(4603,plain,
tc_Nat_Onat @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(369,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__0__iff__less) ).
thf(2282,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add )
=> ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(1192,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( C @ ( B @ hAPP ) )
= ( C @ ( A @ hAPP ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ext) ).
thf(5405,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( C @ ( B @ hAPP ) )
= ( C @ ( A @ hAPP ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1192]) ).
thf(1092,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( B = A )
| ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Ole__less) ).
thf(4973,plain,
! [A: $i,B: $i] :
( ( ( ( B = A )
| ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
| ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(1187,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Polynomial_OpCons @ hAPP ) @ ( A @ ( C @ c_Polynomial_Osmult @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ ( C @ c_COMBC ) ) ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ ( C @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ ( C @ tc_Polynomial_Opoly @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ c_COMBB ) ) @ ( C @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ tc_fun ) @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ ( C @ c_COMBC ) ) ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ c_COMBK ) @ ( C @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ ( C @ tc_Polynomial_Opoly @ c_Polynomial_Opoly__rec ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times__poly__def) ).
thf(5383,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Polynomial_OpCons @ hAPP ) @ ( A @ ( C @ c_Polynomial_Osmult @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ ( C @ c_COMBC ) ) ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ ( C @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ ( C @ tc_Polynomial_Opoly @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ c_COMBB ) ) @ ( C @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ tc_fun ) @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ ( C @ c_COMBC ) ) ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ c_COMBK ) @ ( C @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ ( C @ tc_Polynomial_Opoly @ c_Polynomial_Opoly__rec ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1187]) ).
thf(88,axiom,
! [A: $i,B: $i] : ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negative__zless) ).
thf(1437,plain,
! [A: $i,B: $i] : ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(964,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucE) ).
thf(4479,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(105,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zminus2__not__zero) ).
thf(1486,plain,
! [A: $i,B: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(755,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__0) ).
thf(3681,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(837,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0) ).
thf(3990,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(592,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( B @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zmod__equality2) ).
thf(3072,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( B @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(264,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Polynomial_Ocoeff ) @ ( B @ ( C @ c_Polynomial_Ocoeff ) @ ( C @ c_Groups_Ominus__class_Ominus @ ( tc_Nat_Onat @ ( C @ ( C @ tc_fun ) @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_OAbs__poly ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__poly__def) ).
thf(1924,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Polynomial_Ocoeff ) @ ( B @ ( C @ c_Polynomial_Ocoeff ) @ ( C @ c_Groups_Ominus__class_Ominus @ ( tc_Nat_Onat @ ( C @ ( C @ tc_fun ) @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_OAbs__poly ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(777,axiom,
! [A: $i] :
( ( A @ class_Fields_Ofield__inverse__zero )
=> ( ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_field__inverse__zero) ).
thf(3762,plain,
! [A: $i] :
( ( A @ class_Fields_Ofield__inverse__zero )
=> ( ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(817,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__equal__0__iff__equal) ).
thf(3905,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(118,axiom,
! [A: $i] :
( ( A @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__self) ).
thf(1522,plain,
! [A: $i] :
( ( A @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(426,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__field )
=> ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_COMBI @ ( B @ c_Deriv_Oderiv ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DERIV__ident) ).
thf(2495,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__field )
=> ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_COMBI @ ( B @ c_Deriv_Oderiv ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(1169,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__div__equality) ).
thf(5292,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).
thf(311,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__zminus) ).
thf(2062,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(725,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__ring )
=> ~ ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__square__less__zero) ).
thf(3549,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__ring )
=> ~ ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__trans) ).
thf(1422,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(1023,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ozero )
=> ( ( ( A
!= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) )
= ( A @ ( B @ c_Polynomial_Odegree ) @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( A
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psize__def) ).
thf(4697,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ozero )
=> ( ( ( A
!= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) )
= ( A @ ( B @ c_Polynomial_Odegree ) @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( A
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(829,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__imp__not__eq2) ).
thf(3959,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(818,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(3912,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(602,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Omonom ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Polynomial_Omonom ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__monom) ).
thf(3098,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Omonom ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Polynomial_Omonom ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(927,axiom,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__less__0) ).
thf(4326,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(394,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ~ ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__asym) ).
thf(2380,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ~ ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(223,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zdiv__equality_H) ).
thf(1793,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(1152,axiom,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__0__right) ).
thf(5237,plain,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152]) ).
thf(347,axiom,
! [A: $i] :
( ( A @ class_Groups_Oab__group__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__group__add) ).
thf(2195,plain,
! [A: $i] :
( ( A @ class_Groups_Oab__group__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(221,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
thf(1788,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(151,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( B @ ( A @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__div__mult__self) ).
thf(1608,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( B @ ( A @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(861,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Odvd ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Odvd) ).
thf(4090,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Odvd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(943,axiom,
! [A: $i,B: $i] :
( ( B @ class_Power_Opower )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__0) ).
thf(4418,plain,
! [A: $i,B: $i] :
( ( B @ class_Power_Opower )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(549,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Polynomial_Omonom ) ) )
= ( A @ ( B @ ( C @ c_Polynomial_Omonom ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_monom__Suc) ).
thf(2933,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Polynomial_Omonom ) ) )
= ( A @ ( B @ ( C @ c_Polynomial_Omonom ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B != A )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__cases) ).
thf(1275,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B != A )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(741,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
<=> ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__power__eq__Suc__0__iff) ).
thf(3616,plain,
! [A: $i,B: $i] :
( ( ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(44,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Rings_Ocomm__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Ocomm__ring) ).
thf(1327,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Rings_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(287,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( B @ ( A @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__diff__eq) ).
thf(1988,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( B @ ( A @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(210,axiom,
tc_Int_Oint @ class_Rings_Oring__1__no__zero__divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).
thf(1761,plain,
tc_Int_Oint @ class_Rings_Oring__1__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(667,axiom,
! [A: $i] :
( ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zminus__inverse2) ).
thf(3313,plain,
! [A: $i] :
( ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(950,axiom,
! [A: $i,B: $i] :
( ( B = A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oeq__refl) ).
thf(4435,plain,
! [A: $i,B: $i] :
( ( B = A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(814,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( B @ ( D @ c_Divides_Odiv__class_Odiv ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__mult2) ).
thf(3895,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( B @ ( D @ c_Divides_Odiv__class_Odiv ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(95,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( ( A @ ( C @ c_Polynomial_Odegree ) @ ( B @ ( C @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__poly__less) ).
thf(1458,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( ( A @ ( C @ c_Polynomial_Odegree ) @ ( B @ ( C @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(653,axiom,
! [A: $i] :
( ( A @ class_Rings_Odivision__ring__inverse__zero )
=> ( ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__zero) ).
thf(3276,plain,
! [A: $i] :
( ( A @ class_Rings_Odivision__ring__inverse__zero )
=> ( ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(461,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(2607,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(484,axiom,
tc_Nat_Onat @ class_Orderings_Owellorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Owellorder) ).
thf(2686,plain,
tc_Nat_Onat @ class_Orderings_Owellorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(208,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__imp__zdiv__neg__iff) ).
thf(1756,plain,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(37,axiom,
tc_HOL_Obool @ class_Groups_Ominus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ominus) ).
thf(1310,plain,
tc_HOL_Obool @ class_Groups_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(577,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__less__cancel1) ).
thf(3004,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(1006,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( ( B
!= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( C @ c_Polynomial_Opoly__gcd ) ) )
= ( B @ ( A @ ( C @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( C @ c_Polynomial_Opoly__gcd ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__gcd_Osimps_I2_J) ).
thf(4647,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( ( B
!= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( C @ c_Polynomial_Opoly__gcd ) ) )
= ( B @ ( A @ ( C @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( C @ c_Polynomial_Opoly__gcd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(825,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
thf(3942,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(616,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ~ ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__imp__not__less) ).
thf(3135,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ~ ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(865,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( B @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Divides_Odiv__class_Omod ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self1__is__0) ).
thf(4097,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( B @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Divides_Odiv__class_Omod ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(1071,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_RealVector_Oreal__field )
=> ( ( A @ ( B @ ( C @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( E @ ( F @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ ( F @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DERIV__mult__lemma) ).
thf(4884,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_RealVector_Oreal__field )
=> ( ( A @ ( B @ ( C @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( E @ ( F @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ ( F @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).
thf(1068,axiom,
! [A: $i,B: $i] :
( ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__if) ).
thf(4870,plain,
! [A: $i,B: $i] :
( ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).
thf(587,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mult__distrib) ).
thf(3044,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(200,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Groups_Ominus ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Ominus) ).
thf(1735,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Groups_Ominus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(248,axiom,
! [A: $i,B: $i] : ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negative__zle) ).
thf(1867,plain,
! [A: $i,B: $i] : ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(626,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__commute) ).
thf(3175,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(378,axiom,
! [A: $i] :
( ( A @ class_Groups_Oab__group__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ominus) ).
thf(2316,plain,
! [A: $i] :
( ( A @ class_Groups_Oab__group__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(698,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__less__divisor) ).
thf(3446,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(1159,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ozero )
=> ( ( ( A @ ( B @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ( A
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psize__eq__0__iff) ).
thf(5257,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ozero )
=> ( ( ( A
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).
thf(1003,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) ).
thf(4638,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(250,axiom,
! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__if) ).
thf(1872,plain,
! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(1007,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring )
=> ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
!= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__imp__inverse__nonzero) ).
thf(4650,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring )
=> ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
!= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(336,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Osynthetic__div ) ) )
= ( A @ ( B @ ( D @ c_Polynomial_Osynthetic__div ) ) @ ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( D @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_synthetic__div__pCons) ).
thf(2168,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Osynthetic__div ) ) )
= ( A @ ( B @ ( D @ c_Polynomial_Osynthetic__div ) ) @ ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( D @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(1100,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( ~ ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
& ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__divide__eq) ).
thf(5005,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( ( ( ~ ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
& ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) )
=> ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
& ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).
thf(730,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_Omonom ) ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
= ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__monom) ).
thf(3562,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_Omonom ) ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
= ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(1083,axiom,
tc_Nat_Onat @ class_Power_Opower,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Power_Opower) ).
thf(4941,plain,
tc_Nat_Onat @ class_Power_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).
thf(493,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( B @ ( C @ ( A @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__dvd) ).
thf(2723,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( B @ ( C @ ( A @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(407,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__ring )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__diff__left) ).
thf(2432,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__ring )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(711,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__Suc) ).
thf(3502,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(1128,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Oorder ) ) )
= ( A @ ( c_Nat_OSuc @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ ( tc_Nat_Onat @ ( C @ tc_Polynomial_Opoly @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ ( C @ tc_Polynomial_Opoly @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_Polynomial_Opoly @ ( tc_Nat_Onat @ c_COMBC ) ) ) @ hAPP ) @ ( c_fNot @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_OLeast ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__def) ).
thf(5123,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Oorder ) ) )
= ( A @ ( c_Nat_OSuc @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ ( tc_Nat_Onat @ ( C @ tc_Polynomial_Opoly @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ ( C @ tc_Polynomial_Opoly @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_Polynomial_Opoly @ ( tc_Nat_Onat @ c_COMBC ) ) ) @ hAPP ) @ ( c_fNot @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_OLeast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).
thf(164,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Rings_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Ocomm__semiring__1) ).
thf(1645,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Rings_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(121,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zminus__zminus) ).
thf(1529,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(436,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
!= A )
=> ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessI) ).
thf(2531,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
!= A )
=> ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(1046,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__cancel) ).
thf(4775,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( C = A )
=> ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).
thf(558,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring )
=> ~ ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__sum__squares__lt__zero) ).
thf(2957,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring )
=> ~ ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(503,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(2763,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(819,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
thf(3915,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(442,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( C @ c_Polynomial_Odegree ) @ ( B @ ( C @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) @ ( B @ ( C @ c_Polynomial_Odegree ) @ ( B @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_coeff__mult__degree__sum) ).
thf(2548,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( C @ c_Polynomial_Odegree ) @ ( B @ ( C @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) @ ( B @ ( C @ c_Polynomial_Odegree ) @ ( B @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(646,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Odivision__ring )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B
= ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) )
<=> ( ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__eq__divide__eq) ).
thf(3249,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Odivision__ring )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A )
=> ( B
= ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) )
& ( ( B
= ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) )
=> ( ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(90,axiom,
! [A: $i,B: $i] :
( ( B @ class_Fields_Ofield )
=> ( ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Polynomial_Opoly__gcd ) ) )
= ( A @ ( A @ ( B @ c_Polynomial_Odegree ) @ ( A @ ( B @ c_Polynomial_Ocoeff ) @ hAPP ) @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__gcd_Osimps_I1_J) ).
thf(1441,plain,
! [A: $i,B: $i] :
( ( B @ class_Fields_Ofield )
=> ( ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Polynomial_Opoly__gcd ) ) )
= ( A @ ( A @ ( B @ c_Polynomial_Odegree ) @ ( A @ ( B @ c_Polynomial_Ocoeff ) @ hAPP ) @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(149,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( A @ ( B @ ( D @ c_Polynomial_Opoly__gcd ) ) @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__poly__gcd__iff) ).
thf(1601,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( ( ( A @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( D @ c_Polynomial_Opoly__gcd ) ) @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ c_Polynomial_Opoly__gcd ) ) @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Divides_Osemiring__div )
=> ( ( C @ ( D @ ( E @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( E @ c_Divides_Odiv__class_Odiv ) ) @ ( D @ ( C @ ( E @ c_Divides_Odiv__class_Odiv ) ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Divides_Odiv__class_Odiv ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__div__if__dvd) ).
thf(1386,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Divides_Osemiring__div )
=> ( ( C @ ( D @ ( E @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( E @ c_Divides_Odiv__class_Odiv ) ) @ ( D @ ( C @ ( E @ c_Divides_Odiv__class_Odiv ) ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Divides_Odiv__class_Odiv ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(815,axiom,
! [A: $i,B: $i] :
( ( B @ class_Fields_Ofield )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone @ ( B @ c_Polynomial_Opoly__gcd ) ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__gcd__1__left) ).
thf(3898,plain,
! [A: $i,B: $i] :
( ( B @ class_Fields_Ofield )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone @ ( B @ c_Polynomial_Opoly__gcd ) ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(316,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__zero__left) ).
thf(2082,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(877,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_COMBK ) @ hAPP ) @ hAPP ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBK__1) ).
thf(4137,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_COMBK ) @ hAPP ) @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(196,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( B @ ( A @ ( C @ c_Divides_Odiv__class_Omod ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__eq__mod__eq__0) ).
thf(1724,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( ( ( B @ ( A @ ( C @ c_Divides_Odiv__class_Omod ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Divides_Odiv__class_Omod ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(100,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Rings_Ocomm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Ocomm__semiring) ).
thf(1475,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Rings_Ocomm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(788,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__diff__eq__iff) ).
thf(3809,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(993,axiom,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__1__right) ).
thf(4607,plain,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B = A )
| ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
thf(1366,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( ( B = A )
| ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B = A )
| ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(1012,axiom,
! [A: $i,B: $i] :
( ( B @ class_Fields_Ofield )
=> ( ( B @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Polynomial_Opoly__gcd ) ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__gcd__1__right) ).
thf(4665,plain,
! [A: $i,B: $i] :
( ( B @ class_Fields_Ofield )
=> ( ( B @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Polynomial_Opoly__gcd ) ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(1162,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__0) ).
thf(5269,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).
thf(994,axiom,
! [A: $i] : ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
thf(4610,plain,
! [A: $i] : ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(189,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__iff__less) ).
thf(1703,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Rings_Osemiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Osemiring__0) ).
thf(1228,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Rings_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(103,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Power_Opower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Oidom__Power_Opower) ).
thf(1482,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Power_Opower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(1186,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( C @ hAPP ) @ hBOOL )
<=> ( ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ! [D: $i,E: $i] :
( ( A @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B
= ( E @ ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( E @ ( C @ hAPP ) @ hBOOL ) ) ) )
& ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( B @ ( C @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__mod) ).
thf(5352,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ! [D: $i,E: $i] :
( ( A @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B
= ( E @ ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( E @ ( C @ hAPP ) @ hBOOL ) ) ) )
& ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( B @ ( C @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( C @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( C @ hAPP ) @ hBOOL )
=> ( ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ! [D: $i,E: $i] :
( ( A @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B
= ( E @ ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( E @ ( C @ hAPP ) @ hBOOL ) ) ) )
& ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( B @ ( C @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186]) ).
thf(1184,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__commute) ).
thf(5342,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).
thf(253,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ class_Fields_Ofield )
=> ( ( C @ ( D @ ( E @ ( F @ ( G @ c_Polynomial_Opdivmod__rel ) ) ) ) )
=> ( ( A @ ( B @ ( E @ ( F @ ( G @ c_Polynomial_Opdivmod__rel ) ) ) ) )
=> ( D = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pdivmod__rel__unique__div) ).
thf(1887,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ class_Fields_Ofield )
=> ( ( C @ ( D @ ( E @ ( F @ ( G @ c_Polynomial_Opdivmod__rel ) ) ) ) )
=> ( ( A @ ( B @ ( E @ ( F @ ( G @ c_Polynomial_Opdivmod__rel ) ) ) ) )
=> ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(159,axiom,
! [A: $i,B: $i] :
~ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__int__zless__negative) ).
thf(1628,plain,
! [A: $i,B: $i] :
~ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(1198,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).
thf(5429,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198]) ).
thf(380,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__minus) ).
thf(2328,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(1021,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ocomm__monoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult) ).
thf(4692,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ocomm__monoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(710,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Rings_Oidom )
& ( C @ class_Int_Oring__char__0 ) )
=> ( ( ( B @ ( C @ c_Polynomial_Opoly ) )
= ( A @ ( C @ c_Polynomial_Opoly ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__eq__iff) ).
thf(3495,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Rings_Oidom )
& ( C @ class_Int_Oring__char__0 ) )
=> ( ( ( B = A )
=> ( ( B @ ( C @ c_Polynomial_Opoly ) )
= ( A @ ( C @ c_Polynomial_Opoly ) ) ) )
& ( ( ( B @ ( C @ c_Polynomial_Opoly ) )
= ( A @ ( C @ c_Polynomial_Opoly ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(900,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( A @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__inverse__less) ).
thf(4224,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( A @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(1041,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__power__less__imp__less) ).
thf(4761,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(791,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Odvd )
=> ( ( C
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( C @ ( B @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvdI) ).
thf(3821,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Odvd )
=> ( ( C
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( C @ ( B @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(612,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Ozero__neq__one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ozero__neq__one) ).
thf(3125,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Ozero__neq__one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(94,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( A @ ( B @ ( D @ c_Polynomial_Opoly__gcd ) ) @ ( C @ ( D @ c_Polynomial_Opoly__gcd ) ) )
= ( A @ ( C @ ( D @ c_Polynomial_Opoly__gcd ) ) @ ( B @ ( D @ c_Polynomial_Opoly__gcd ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__gcd_Oleft__commute) ).
thf(1455,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( A @ ( B @ ( D @ c_Polynomial_Opoly__gcd ) ) @ ( C @ ( D @ c_Polynomial_Opoly__gcd ) ) )
= ( A @ ( C @ ( D @ c_Polynomial_Opoly__gcd ) ) @ ( B @ ( D @ c_Polynomial_Opoly__gcd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(489,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Divides_Osemiring__div )
=> ( ( ( D @ ( E @ ( F @ c_Divides_Odiv__class_Omod ) ) )
= ( D @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
=> ( ( ( D @ ( B @ ( F @ c_Divides_Odiv__class_Omod ) ) )
= ( D @ ( A @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
=> ( ( D @ ( B @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Divides_Odiv__class_Omod ) ) )
= ( D @ ( A @ ( C @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Divides_Odiv__class_Omod ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__cong) ).
thf(2703,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Divides_Osemiring__div )
=> ( ( ( D @ ( E @ ( F @ c_Divides_Odiv__class_Omod ) ) )
= ( D @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
=> ( ( ( D @ ( B @ ( F @ c_Divides_Odiv__class_Omod ) ) )
= ( D @ ( A @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
=> ( ( D @ ( B @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Divides_Odiv__class_Omod ) ) )
= ( D @ ( A @ ( C @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Divides_Odiv__class_Omod ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(648,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__right__mono__neg) ).
thf(3263,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(951,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zmod__equality) ).
thf(4439,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(584,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1__no__zero__divisors )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
!= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_field__power__not__zero) ).
thf(3029,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1__no__zero__divisors )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
!= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(1037,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__mult )
=> ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_realpow__minus__mult) ).
thf(4743,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__mult )
=> ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(691,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Osynthetic__div ) ) @ ( A @ ( C @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Polynomial_Osynthetic__div ) ) @ ( A @ ( B @ ( C @ c_Polynomial_Opoly ) @ hAPP ) @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_synthetic__div__correct) ).
thf(3425,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Osynthetic__div ) ) @ ( A @ ( C @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Polynomial_Osynthetic__div ) ) @ ( A @ ( B @ ( C @ c_Polynomial_Opoly ) @ hAPP ) @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(84,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Groups_Ocancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Ocancel__ab__semigroup__add) ).
thf(1430,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Groups_Ocancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(516,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict) ).
thf(2814,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(286,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__int__def__symmetric) ).
thf(1985,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(945,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__poly__code_I1_J) ).
thf(4422,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(170,axiom,
! [A: $i] :
~ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__less__0__conv) ).
thf(1660,plain,
! [A: $i] :
~ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(209,axiom,
tc_Int_Oint @ class_Rings_Ocomm__semiring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).
thf(1760,plain,
tc_Int_Oint @ class_Rings_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(1088,axiom,
tc_Nat_Onat @ class_Rings_Osemiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).
thf(4956,plain,
tc_Nat_Onat @ class_Rings_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).
thf(942,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( B
!= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ~ ( B @ ( B @ ( A @ ( C @ c_Polynomial_Oorder ) ) @ ( c_Nat_OSuc @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__2) ).
thf(4415,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( B
!= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ~ ( B @ ( B @ ( A @ ( C @ c_Polynomial_Oorder ) ) @ ( c_Nat_OSuc @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(365,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__minus) ).
thf(2269,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(411,axiom,
tc_Nat_Onat @ class_Nat_Osemiring__char__0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Nat_Osemiring__char__0) ).
thf(2444,plain,
tc_Nat_Onat @ class_Nat_Osemiring__char__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(245,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__int__def) ).
thf(1860,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(352,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Suc) ).
thf(2217,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(722,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__pos__nat) ).
thf(3542,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zminus2) ).
thf(1313,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(910,axiom,
tc_Nat_Onat @ class_Rings_Odvd,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Odvd) ).
thf(4275,plain,
tc_Nat_Onat @ class_Rings_Odvd,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(1140,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1__left) ).
thf(5182,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).
thf(845,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
thf(4023,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C = A )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(598,axiom,
tc_Nat_Onat @ class_Rings_Omult__zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).
thf(3089,plain,
tc_Nat_Onat @ class_Rings_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(423,axiom,
! [A: $i] :
( ( A @ class_Fields_Ofield )
=> ( A @ tc_Polynomial_Opoly @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Divides_Oring__div) ).
thf(2488,plain,
! [A: $i] :
( ( A @ class_Fields_Ofield )
=> ( A @ tc_Polynomial_Opoly @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(1168,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__distrib) ).
thf(5289,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).
thf(984,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
=> ( ( ( B != A )
& ( D != C ) )
<=> ( ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( B @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_crossproduct__noteq) ).
thf(4568,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
=> ( ( ( ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( B @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( ( B != A )
& ( D != C ) ) )
& ( ( ( B != A )
& ( D != C ) )
=> ( ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( B @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(786,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__minus__eq__add) ).
thf(3803,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(1125,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__smult__iff) ).
thf(5108,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( A @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).
thf(1043,axiom,
! [A: $i] :
( ( A @ class_Rings_Osemiring__1 )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__0) ).
thf(4766,plain,
! [A: $i] :
( ( A @ class_Rings_Osemiring__1 )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).
thf(947,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ozero )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_coeff__0) ).
thf(4428,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ozero )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(451,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
thf(2571,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(388,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__eq) ).
thf(2356,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(404,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(2420,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(871,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Omult__zero )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__zero__right) ).
thf(4119,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Omult__zero )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(1148,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__cancel1) ).
thf(5214,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B = A )
=> ( ( B @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).
thf(1145,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(5199,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).
thf(306,axiom,
tc_Int_Oint @ class_Groups_Oordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(2049,plain,
tc_Int_Oint @ class_Groups_Oordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(254,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__diff__nat) ).
thf(1890,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(998,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__cancel2) ).
thf(4622,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(471,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).
thf(2635,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(375,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
<=> ! [D: $i,E: $i] :
( ( ( A
= ( E @ ( D @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
& ( C @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
& ( E @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( E @ ( D @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__pos__lemma) ).
thf(2301,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ! [D: $i,E: $i] :
( ( ( A
= ( E @ ( D @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
& ( C @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
& ( E @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( E @ ( D @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i,E: $i] :
( ( ( A
= ( E @ ( D @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
& ( C @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
& ( E @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( E @ ( D @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(1116,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Opcompose ) ) )
= ( A @ ( B @ ( D @ c_Polynomial_Opcompose ) ) @ ( A @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pcompose__pCons) ).
thf(5077,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Opcompose ) ) )
= ( A @ ( B @ ( D @ c_Polynomial_Opcompose ) ) @ ( A @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__left) ).
thf(1232,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(238,axiom,
tc_Int_Oint @ class_Rings_Ono__zero__divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).
thf(1847,plain,
tc_Int_Oint @ class_Rings_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(263,axiom,
! [A: $i] :
( ( A @ class_Groups_Oab__group__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ogroup__add) ).
thf(1922,plain,
! [A: $i] :
( ( A @ class_Groups_Oab__group__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(487,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( D @ c_Polynomial_Opdivmod__rel ) ) ) ) )
<=> ( ( A
= ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pdivmod__rel__0__iff) ).
thf(2691,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( ( ( A
= ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) )
=> ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( D @ c_Polynomial_Opdivmod__rel ) ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( D @ c_Polynomial_Opdivmod__rel ) ) ) ) )
=> ( ( A
= ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(255,axiom,
tc_Int_Oint @ class_Rings_Olinordered__ring__strict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).
thf(1892,plain,
tc_Int_Oint @ class_Rings_Olinordered__ring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(682,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Opoly ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__0) ).
thf(3374,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Opoly ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(685,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__divide__eq__iff) ).
thf(3385,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(889,axiom,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
!= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__0__neq__1) ).
thf(4179,plain,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
!= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(1142,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring__1 )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_realpow__two__diff) ).
thf(5193,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring__1 )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).
thf(1057,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__inverse) ).
thf(4830,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).
thf(596,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__mult__distrib2) ).
thf(3084,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(980,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ~ ( C @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__trans) ).
thf(4551,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ~ ( C @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(138,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( ( B @ ( C @ c_Polynomial_Odegree ) @ ( B @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) ) )
=> ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__dvd__antisym) ).
thf(1568,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( ( B @ ( C @ c_Polynomial_Odegree ) @ ( B @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) ) )
=> ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(935,axiom,
tc_Nat_Onat @ class_Groups_Ocomm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
thf(4368,plain,
tc_Nat_Onat @ class_Groups_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(434,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__mult2) ).
thf(2520,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(1000,axiom,
! [A: $i] :
( ( A @ class_Groups_Ocomm__monoid__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__add) ).
thf(4632,plain,
! [A: $i] :
( ( A @ class_Groups_Ocomm__monoid__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(797,axiom,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__1) ).
thf(3835,plain,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(571,axiom,
tc_Nat_Onat @ class_Groups_Oordered__comm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
thf(2989,plain,
tc_Nat_Onat @ class_Groups_Oordered__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(277,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
thf(1963,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(1119,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__reduce) ).
thf(5091,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).
thf(961,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( A @ ( A @ ( B @ ( C @ c_Polynomial_Oorder ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__1) ).
thf(4471,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( A @ ( A @ ( B @ ( C @ c_Polynomial_Oorder ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(1102,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__mono2) ).
thf(5020,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).
thf(939,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__1__iff) ).
thf(4400,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(920,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult2__eq) ).
thf(4302,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(397,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( ( A
= ( C @ c_Groups_Oone__class_Oone ) )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( B @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__power) ).
thf(2388,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( ( A
= ( C @ c_Groups_Oone__class_Oone ) )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( B @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(1160,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__ring__1 )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).
thf(5264,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__ring__1 )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).
thf(97,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C = A )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I2_J) ).
thf(1465,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C = A )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(887,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__shift) ).
thf(4173,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(319,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr__implies__not0) ).
thf(2090,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(1180,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__less__m__mult__n) ).
thf(5333,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1180]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__zmod__imp__zdvd) ).
thf(1418,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(760,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0) ).
thf(3702,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(244,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__semidom )
=> ~ ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__less__0__iff) ).
thf(1858,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__semidom )
=> ~ ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(1030,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B @ ( C @ c_Polynomial_Opos__poly ) )
=> ( ( A @ ( C @ c_Polynomial_Opos__poly ) )
=> ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Opos__poly ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__poly__mult) ).
thf(4724,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B @ ( C @ c_Polynomial_Opos__poly ) )
=> ( ( A @ ( C @ c_Polynomial_Opos__poly ) )
=> ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Opos__poly ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(876,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Osemiring__1 )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__mult) ).
thf(4134,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Osemiring__1 )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(142,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__neq) ).
thf(1581,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(621,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
<=> ( ( A
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__zmult__eq__1__iff) ).
thf(3152,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( ( A
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) )
& ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
=> ( ( A
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(313,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J) ).
thf(2073,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(800,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B = A )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__add1__eq) ).
thf(3851,plain,
! [A: $i,B: $i] :
( ( ( ( B = A )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(106,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
thf(1489,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(895,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc) ).
thf(4205,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(1094,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__left) ).
thf(4988,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__div__less__self) ).
thf(1302,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(172,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ouminus )
=> ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( D @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_uminus__apply) ).
thf(1664,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ouminus )
=> ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( D @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(831,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( B @ ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self2) ).
thf(3966,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( B @ ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(299,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Oring__div )
=> ( ( ( B @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
=> ( ( B @ ( C @ ( D @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( D @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__minus__cong) ).
thf(2027,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Oring__div )
=> ( ( ( B @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
=> ( ( B @ ( C @ ( D @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( D @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(1076,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( D @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__lemma) ).
thf(4903,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( D @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).
thf(593,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
=> ( ( E
!= ( F @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( B != A )
& ( D = C ) )
=> ( ( B @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__scale__eq__noteq) ).
thf(3075,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
=> ( ( E
!= ( F @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( B != A )
& ( D = C ) )
=> ( ( B @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(856,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pow__divides__pow__nat) ).
thf(4072,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(985,axiom,
! [A: $i] :
( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0I) ).
thf(4578,plain,
! [A: $i] :
( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(324,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_RealVector_Oreal__normed__field )
=> ( ( C @ ( D @ ( E @ ( F @ c_Deriv_Oderiv ) ) ) )
=> ( ( A @ ( D @ ( B @ ( F @ c_Deriv_Oderiv ) ) ) )
=> ( D @ ( B @ hAPP ) @ ( C @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( E @ hAPP ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ ( F @ ( F @ ( F @ tc_fun ) @ ( F @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ ( F @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( F @ c_Deriv_Oderiv ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DERIV__mult_H) ).
thf(2105,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_RealVector_Oreal__normed__field )
=> ( ( C @ ( D @ ( E @ ( F @ c_Deriv_Oderiv ) ) ) )
=> ( ( A @ ( D @ ( B @ ( F @ c_Deriv_Oderiv ) ) ) )
=> ( D @ ( B @ hAPP ) @ ( C @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( E @ hAPP ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ ( F @ ( F @ ( F @ tc_fun ) @ ( F @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ ( F @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( F @ c_Deriv_Oderiv ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(1066,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Odivision__ring )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A )
=> ( B
= ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__divide__imp) ).
thf(4857,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Odivision__ring )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A )
=> ( B
= ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).
thf(907,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
thf(4258,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(574,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__smult__right) ).
thf(2996,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(765,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__imp__not__eq) ).
thf(3724,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(956,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield__inverse__zero )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( A @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__mult__distrib) ).
thf(4454,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield__inverse__zero )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( A @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(508,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Nat_Onat_Onat__case ) ) @ hAPP ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__case__0) ).
thf(2782,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Nat_Onat_Onat__case ) ) @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(231,axiom,
! [A: $i,B: $i] :
( ( B
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zminus2__eq__if) ).
thf(1828,plain,
! [A: $i,B: $i] :
( ( B
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(833,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oidom )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( B @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
| ( C
= ( D @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__cancel__left) ).
thf(3973,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oidom )
=> ( ( ( ( A @ ( B @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
| ( C
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
| ( C
= ( D @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(283,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semidom) ).
thf(1978,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(1040,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
| ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel__disj) ).
thf(4751,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
| ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
| ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(720,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__mono1) ).
thf(3537,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zminus2) ).
thf(1377,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(7,axiom,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= A )
& ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DIVISION__BY__ZERO) ).
thf(1215,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= A )
& ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(257,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__minus__iff) ).
thf(1896,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(762,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Oone__class_Oone @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc__less__one) ).
thf(3712,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Oone__class_Oone @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(156,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__right) ).
thf(1622,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(1097,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__divide__eq__iff) ).
thf(4996,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).
thf(370,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( D @ c_Polynomial_Omonom ) ) @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Omonom ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__monom) ).
thf(2286,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( D @ c_Polynomial_Omonom ) ) @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Omonom ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(1,conjecture,
? [A: $i,B: $i] :
( ? [C: $i] :
( ! [D: $i] :
( ( D @ ( t_a @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( t_a @ c_Polynomial_Opoly ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( t_a @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( t_a @ c_Polynomial_Opoly ) @ hAPP ) @ ( A @ ( D @ ( t_a @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( t_a @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( t_a @ c_Groups_Ozero__class_Ozero @ ( t_a @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( t_a @ c_Polynomial_Opoly ) @ hAPP ) @ ( t_a @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
& ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( C @ ( t_a @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( t_a @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( t_a @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) ) ) )
& ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
!= ( t_a @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ? [A: $i,B: $i] :
( ? [C: $i] :
( ! [D: $i] :
( ( D @ ( t_a @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( t_a @ c_Polynomial_Opoly ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( t_a @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( t_a @ c_Polynomial_Opoly ) @ hAPP ) @ ( A @ ( D @ ( t_a @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( t_a @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( t_a @ c_Groups_Ozero__class_Ozero @ ( t_a @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( t_a @ c_Polynomial_Opoly ) @ hAPP ) @ ( t_a @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
& ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( C @ ( t_a @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( t_a @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( t_a @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) ) ) )
& ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
!= ( t_a @ c_Groups_Ozero__class_Ozero ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(1201,plain,
~ ? [A: $i,B: $i] :
( ? [C: $i] :
( ! [D: $i] :
( ( D @ ( t_a @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( t_a @ c_Polynomial_Opoly ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( t_a @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( t_a @ c_Polynomial_Opoly ) @ hAPP ) @ ( A @ ( D @ ( t_a @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( t_a @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( t_a @ c_Groups_Ozero__class_Ozero @ ( t_a @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( t_a @ c_Polynomial_Opoly ) @ hAPP ) @ ( t_a @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
& ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( C @ ( t_a @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( t_a @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( t_a @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) ) ) )
& ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
!= ( t_a @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1025,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__mult__distrib) ).
thf(4707,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(636,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono1) ).
thf(3211,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(186,axiom,
tc_Int_Oint @ class_Rings_Osemiring__0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).
thf(1696,plain,
tc_Int_Oint @ class_Rings_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(521,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__poly__code_I2_J) ).
thf(2833,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(770,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__add__left) ).
thf(3739,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(712,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(3505,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(968,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Owellorder )
=> ( ( A @ ( B @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Orderings_Oord__class_OLeast ) @ ( B @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_LeastI) ).
thf(4504,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Owellorder )
=> ( ( A @ ( B @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Orderings_Oord__class_OLeast ) @ ( B @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(435,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
<=> ? [C: $i] :
( B
= ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__eq__0__iff) ).
thf(2523,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( B
= ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ? [C: $i] :
( B
= ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(224,axiom,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zminus2__eq__if) ).
thf(1796,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(120,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) @ ( C @ c_Polynomial_Odegree ) )
= ( B @ ( C @ c_Polynomial_Odegree ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__offset__poly) ).
thf(1526,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) @ ( C @ c_Polynomial_Odegree ) )
= ( B @ ( C @ c_Polynomial_Odegree ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(331,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone )
= ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__poly__def) ).
thf(2137,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone )
= ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(292,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__dvd__cancel) ).
thf(2002,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(828,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( C @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__le__trans) ).
thf(3955,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( C @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(644,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__1) ).
thf(3243,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(671,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( B
!= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ~ ( B @ ( B @ ( A @ ( C @ c_Polynomial_Oorder ) ) @ ( c_Nat_OSuc @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( B @ ( A @ ( C @ c_Polynomial_Oorder ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order) ).
thf(3327,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( B
!= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ~ ( B @ ( B @ ( A @ ( C @ c_Polynomial_Oorder ) ) @ ( c_Nat_OSuc @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( B @ ( A @ ( C @ c_Polynomial_Oorder ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
thf(1433,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(561,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Odivision__ring )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( A @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__inverse__mult__distrib) ).
thf(2965,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Odivision__ring )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( A @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(972,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__0__left) ).
thf(4519,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(187,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Oboolean__algebra )
=> ( B @ ( A @ tc_fun ) @ class_Lattices_Oboolean__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).
thf(1697,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Oboolean__algebra )
=> ( B @ ( A @ tc_fun ) @ class_Lattices_Oboolean__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(729,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ( B
!= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Odegree ) )
= ( B @ ( C @ c_Polynomial_Odegree ) @ ( c_Nat_OSuc @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__pCons__eq) ).
thf(3559,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ( B
!= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Odegree ) )
= ( B @ ( C @ c_Polynomial_Odegree ) @ ( c_Nat_OSuc @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(858,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(4082,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(136,axiom,
tc_Int_Oint @ class_Groups_Ocomm__monoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).
thf(1564,plain,
tc_Int_Oint @ class_Groups_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(246,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult) ).
thf(1863,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(557,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__poly__code_I1_J) ).
thf(2954,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(294,axiom,
tc_Int_Oint @ class_Rings_Osemiring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__1) ).
thf(2011,plain,
tc_Int_Oint @ class_Rings_Osemiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(893,axiom,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less0) ).
thf(4199,plain,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(926,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1) ).
thf(4323,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(987,axiom,
! [A: $i] :
( ~ ( A @ hBOOL )
| ~ ( A @ ( c_fNot @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__1) ).
thf(4589,plain,
! [A: $i] :
( ~ ( A @ hBOOL )
| ~ ( A @ ( c_fNot @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(452,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__add__strict) ).
thf(2574,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(628,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__less__0__iff) ).
thf(3186,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(1135,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0__right) ).
thf(5167,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).
thf(49,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Rings_Omult__zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Omult__zero) ).
thf(1338,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Rings_Omult__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(262,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ( ( B @ ( C @ c_Polynomial_Ocoeff ) )
= ( A @ ( C @ c_Polynomial_Ocoeff ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_coeff__inject) ).
thf(1915,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ( ( B = A )
=> ( ( B @ ( C @ c_Polynomial_Ocoeff ) )
= ( A @ ( C @ c_Polynomial_Ocoeff ) ) ) )
& ( ( ( B @ ( C @ c_Polynomial_Ocoeff ) )
= ( A @ ( C @ c_Polynomial_Ocoeff ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oord )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
thf(1311,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oord )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(197,axiom,
tc_Int_Oint @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).
thf(1730,plain,
tc_Int_Oint @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(579,axiom,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__1__left) ).
thf(3011,plain,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Ofield )
=> ( ( A @ ( B @ ( C @ ( D @ ( E @ c_Polynomial_Opdivmod__rel ) ) ) ) )
=> ( ( C @ ( D @ ( E @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__poly__eq) ).
thf(1206,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Ofield )
=> ( ( A @ ( B @ ( C @ ( D @ ( E @ c_Polynomial_Opdivmod__rel ) ) ) ) )
=> ( ( C @ ( D @ ( E @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(992,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__assoc) ).
thf(4604,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(835,axiom,
! [A: $i] :
( ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__nonzero) ).
thf(3984,plain,
! [A: $i] :
( ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(649,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__strict__left__mono__neg) ).
thf(3265,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(475,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__mono2) ).
thf(2646,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__of__nat__less) ).
thf(1306,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(975,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__minus__left) ).
thf(4531,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(1101,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Ofield )
=> ( ( D
!= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C
!= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__frac__eq) ).
thf(5017,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Ofield )
=> ( ( D
!= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C
!= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).
thf(718,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Odivision__ring )
=> ( ( ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( A @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) ) )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__inverse__eq__imp__eq) ).
thf(3531,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Odivision__ring )
=> ( ( ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( A @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) ) )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(743,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Ono__zero__divisors ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ono__zero__divisors) ).
thf(3635,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Ono__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(305,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__0__right) ).
thf(2047,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(1127,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq) ).
thf(5117,plain,
! [A: $i,B: $i] :
( ( ( B @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).
thf(846,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__left) ).
thf(4031,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(866,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__0__less__iff__less) ).
thf(4100,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(216,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ ( B @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__dvd__div) ).
thf(1768,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ ( B @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C @ ( A @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ ( B @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(395,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zmult__distrib2) ).
thf(2382,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(310,axiom,
tc_Int_Oint @ class_Groups_Oordered__comm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).
thf(2061,plain,
tc_Int_Oint @ class_Groups_Oordered__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(1165,axiom,
! [A: $i,B: $i] :
( ( B @ class_Fields_Ofield )
=> ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pdivmod__rel__by__0) ).
thf(5281,plain,
! [A: $i,B: $i] :
( ( B @ class_Fields_Ofield )
=> ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).
thf(1098,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(4999,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).
thf(290,axiom,
tc_Int_Oint @ class_Groups_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).
thf(2000,plain,
tc_Int_Oint @ class_Groups_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(162,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__add) ).
thf(1636,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(410,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__num__frac) ).
thf(2441,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(400,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Opreorder) ).
thf(2409,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield__inverse__zero )
=> ( ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__divide__right) ).
thf(1223,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield__inverse__zero )
=> ( ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(959,axiom,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_One__nat__def) ).
thf(4466,plain,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(793,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oorder__trans) ).
thf(3827,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(736,axiom,
tc_Nat_Onat @ class_Groups_Omonoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
thf(3603,plain,
tc_Nat_Onat @ class_Groups_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(949,axiom,
tc_Nat_Onat @ class_Groups_Oone,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
thf(4434,plain,
tc_Nat_Onat @ class_Groups_Oone,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(771,axiom,
tc_Nat_Onat @ class_Groups_Ocomm__monoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
thf(3742,plain,
tc_Nat_Onat @ class_Groups_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(874,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(4128,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(810,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Nat_Osemiring__char__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Nat_Osemiring__char__0) ).
thf(3884,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Nat_Osemiring__char__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(402,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( B @ ( A @ ( B @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__simps_I4_J) ).
thf(2414,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( B @ ( A @ ( B @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(751,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__Suc) ).
thf(3664,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(1109,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
<=> ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__cancel2) ).
thf(5049,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( C = A ) )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).
thf(456,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__add__right) ).
thf(2589,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(258,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oab__group__add )
=> ( ( ( C @ ( D @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
=> ( ( D = C )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq__diff__eq) ).
thf(1900,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oab__group__add )
=> ( ( ( C @ ( D @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
=> ( ( ( B = A )
=> ( D = C ) )
& ( ( D = C )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(195,axiom,
tc_Int_Oint @ class_Int_Oring__char__0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).
thf(1723,plain,
tc_Int_Oint @ class_Int_Oring__char__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(842,axiom,
tc_Nat_Onat @ class_Rings_Ono__zero__divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).
thf(4016,plain,
tc_Nat_Onat @ class_Rings_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(447,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__0) ).
thf(2560,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(803,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oorder) ).
thf(3867,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(1099,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ( A @ ( B @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Ocoeff ) )
= ( A @ ( C @ c_Polynomial_Ocoeff ) @ ( B @ ( C @ c_Nat_Onat_Onat__case ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_coeff__pCons) ).
thf(5002,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ( A @ ( B @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Ocoeff ) )
= ( A @ ( C @ c_Polynomial_Ocoeff ) @ ( B @ ( C @ c_Nat_Onat_Onat__case ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).
thf(1048,axiom,
tc_Nat_Onat @ class_Rings_Ocomm__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).
thf(4785,plain,
tc_Nat_Onat @ class_Rings_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).
thf(966,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( D @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__period) ).
thf(4499,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( D @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( D @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(914,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( A @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__self2) ).
thf(4284,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( A @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(155,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zero) ).
thf(1619,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(1054,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__0 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring) ).
thf(4821,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__0 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).
thf(570,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring )
=> ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__eq__divide) ).
thf(2986,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring )
=> ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(780,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).
thf(3778,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(812,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult1__eq) ).
thf(3889,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(701,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(3471,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(848,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq) ).
thf(4044,plain,
! [A: $i,B: $i] :
( ( ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(134,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Rings_Ozero__neq__one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Ozero__neq__one) ).
thf(1560,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Rings_Ozero__neq__one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(412,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( H @ class_Fields_Ofield )
=> ( ( D @ ( E @ ( F @ ( G @ ( H @ c_Polynomial_Opdivmod__rel ) ) ) ) )
=> ( ( A @ ( B @ ( C @ ( E @ ( H @ c_Polynomial_Opdivmod__rel ) ) ) ) )
=> ( D @ ( A @ ( F @ ( H @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( H @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( F @ ( H @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( G @ ( H @ c_Polynomial_Opdivmod__rel ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pdivmod__rel__mult) ).
thf(2445,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( H @ class_Fields_Ofield )
=> ( ( D @ ( E @ ( F @ ( G @ ( H @ c_Polynomial_Opdivmod__rel ) ) ) ) )
=> ( ( A @ ( B @ ( C @ ( E @ ( H @ c_Polynomial_Opdivmod__rel ) ) ) ) )
=> ( D @ ( A @ ( F @ ( H @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( H @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( F @ ( H @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( G @ ( H @ c_Polynomial_Opdivmod__rel ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(912,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__neg__neg) ).
thf(4280,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(878,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_offset__poly__0) ).
thf(4140,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(59,axiom,
tc_Int_Oint @ class_Groups_Ocancel__comm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__comm__monoid__add) ).
thf(1365,plain,
tc_Int_Oint @ class_Groups_Ocancel__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(421,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Odivision__ring )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= A )
<=> ( B
= ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__divide__eq__eq) ).
thf(2477,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Odivision__ring )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( B
= ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= A ) )
& ( ( ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= A )
=> ( B
= ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(132,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__smult) ).
thf(1555,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(272,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__mod__bound) ).
thf(1951,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(340,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Oadd) ).
thf(2179,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(1084,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
thf(4942,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).
thf(167,axiom,
tc_Int_Oint @ class_Divides_Osemiring__div,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Osemiring__div) ).
thf(1656,plain,
tc_Int_Oint @ class_Divides_Osemiring__div,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(74,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__imp__zdiv__neg__iff) ).
thf(1407,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(688,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__right) ).
thf(3408,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(784,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__int) ).
thf(3799,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(852,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Oboolean__algebra )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__compl) ).
thf(4063,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Oboolean__algebra )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(655,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__lessD1) ).
thf(3282,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(665,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oantisym) ).
thf(3307,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(1172,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_RealVector_Oreal__normed__field )
=> ( ( C @ ( D @ ( E @ ( F @ c_Deriv_Oderiv ) ) ) )
=> ( ( A @ ( D @ ( E @ hAPP ) @ ( B @ ( F @ c_Deriv_Oderiv ) ) ) )
=> ( C @ ( A @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( B @ ( F @ ( F @ ( F @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ c_Deriv_Oderiv ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DERIV__chain_H) ).
thf(5302,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_RealVector_Oreal__normed__field )
=> ( ( C @ ( D @ ( E @ ( F @ c_Deriv_Oderiv ) ) ) )
=> ( ( A @ ( D @ ( E @ hAPP ) @ ( B @ ( F @ c_Deriv_Oderiv ) ) ) )
=> ( C @ ( A @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( B @ ( F @ ( F @ ( F @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ c_Deriv_Oderiv ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).
thf(233,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield__inverse__zero )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__divide__divide) ).
thf(1837,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield__inverse__zero )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(279,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Rings_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Ocomm__ring__1) ).
thf(1968,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Rings_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(599,axiom,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gcd__lcm__complete__lattice__nat_Obot__least) ).
thf(3090,plain,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(449,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(2565,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(1096,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__field )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ ( C @ c_COMBK ) @ hAPP ) @ ( C @ c_Deriv_Oderiv ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DERIV__const) ).
thf(4994,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__field )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ ( C @ c_COMBK ) @ hAPP ) @ ( C @ c_Deriv_Oderiv ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).
thf(617,axiom,
tc_Nat_Onat @ class_Rings_Ocomm__semiring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
thf(3137,plain,
tc_Nat_Onat @ class_Rings_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(676,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__right__eq) ).
thf(3349,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(728,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__left) ).
thf(3556,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(228,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( C @ ( A @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mod__cancel) ).
thf(1819,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( C @ ( A @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(157,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Rings_Odvd ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Odvd) ).
thf(1624,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Rings_Odvd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(724,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__add) ).
thf(3546,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(1038,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pos__neg2) ).
thf(4746,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(1036,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
thf(4740,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).
thf(589,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pow__divides__pow__int) ).
thf(3050,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(377,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_RealVector_Oreal__normed__field )
=> ( ( C @ ( D @ ( E @ ( F @ c_Deriv_Oderiv ) ) ) )
=> ( ( A @ ( D @ ( B @ ( F @ c_Deriv_Oderiv ) ) ) )
=> ( ( ( D @ ( B @ hAPP ) )
!= ( F @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( D @ ( B @ hAPP ) @ ( F @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ ( E @ hAPP ) @ ( A @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ hAPP ) @ ( C @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( E @ ( F @ c_Rings_Oinverse__class_Odivide @ ( F @ ( F @ ( F @ tc_fun ) @ ( F @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ ( F @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( F @ c_Deriv_Oderiv ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DERIV__quotient) ).
thf(2313,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_RealVector_Oreal__normed__field )
=> ( ( C @ ( D @ ( E @ ( F @ c_Deriv_Oderiv ) ) ) )
=> ( ( A @ ( D @ ( B @ ( F @ c_Deriv_Oderiv ) ) ) )
=> ( ( ( D @ ( B @ hAPP ) )
!= ( F @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( D @ ( B @ hAPP ) @ ( F @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ ( E @ hAPP ) @ ( A @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ hAPP ) @ ( C @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( E @ ( F @ c_Rings_Oinverse__class_Odivide @ ( F @ ( F @ ( F @ tc_fun ) @ ( F @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ ( F @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( F @ c_Deriv_Oderiv ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(425,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J) ).
thf(2492,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(867,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__neg) ).
thf(4104,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(161,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( B @ ( C @ c_Polynomial_Opdivmod__rel ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pdivmod__rel) ).
thf(1634,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( B @ ( C @ c_Polynomial_Opdivmod__rel ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( C
!= ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( B @ ( D @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) )
= ( C @ ( C @ ( D @ c_Polynomial_Odegree ) @ ( C @ ( D @ c_Polynomial_Ocoeff ) @ hAPP ) @ ( C @ ( D @ c_Polynomial_Odegree ) @ ( C @ ( A @ ( D @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( D @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Ocoeff ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( D @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__pCons) ).
thf(1392,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( C
!= ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( B @ ( D @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) )
= ( C @ ( C @ ( D @ c_Polynomial_Odegree ) @ ( C @ ( D @ c_Polynomial_Ocoeff ) @ hAPP ) @ ( C @ ( D @ c_Polynomial_Odegree ) @ ( C @ ( A @ ( D @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( D @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Ocoeff ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( D @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(752,axiom,
! [A: $i] :
( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neq0__conv) ).
thf(3667,plain,
! [A: $i] :
( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(1033,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).
thf(4732,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).
thf(767,axiom,
! [A: $i] :
( ( A @ class_Groups_Ocomm__monoid__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__add) ).
thf(3731,plain,
! [A: $i] :
( ( A @ class_Groups_Ocomm__monoid__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(145,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__div__cancel) ).
thf(1592,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(1089,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__pred_H) ).
thf(4957,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).
thf(523,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
thf(2840,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(564,axiom,
tc_Nat_Onat @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
thf(2973,plain,
tc_Nat_Onat @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(109,axiom,
! [A: $i] :
( ( A @ class_Fields_Ofield )
=> ( A @ tc_Polynomial_Opoly @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Divides_Osemiring__div) ).
thf(1498,plain,
! [A: $i] :
( ( A @ class_Fields_Ofield )
=> ( A @ tc_Polynomial_Opoly @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(176,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) ) @ ( c_fNot @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oorder_Ostrict__mono ) ) ) )
=> ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Ostrict__monoD) ).
thf(1672,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) ) @ ( c_fNot @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oorder_Ostrict__mono ) ) ) )
=> ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(494,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0__eq__0) ).
thf(2726,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(1060,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__cancel) ).
thf(4840,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).
thf(840,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__imp__div__pos__less) ).
thf(4012,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(642,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ ( E @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( E @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pCons) ).
thf(3237,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ ( E @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( E @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(869,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Divides_Odiv__class_Odiv ) ) )
= ( C @ c_Groups_Oone__class_Oone @ ( B @ ( A @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__add__self1) ).
thf(4109,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Divides_Odiv__class_Odiv ) ) )
= ( C @ c_Groups_Oone__class_Oone @ ( B @ ( A @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(576,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Ozero) ).
thf(3001,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(781,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__lt__two__imp__zero__or__one) ).
thf(3782,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_RealVector_Oreal__normed__field )
=> ( ( B @ ( C @ ( D @ ( E @ c_Deriv_Oderiv ) ) ) )
=> ( ( A @ ( C @ ( D @ ( E @ c_Deriv_Oderiv ) ) ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DERIV__unique) ).
thf(1234,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_RealVector_Oreal__normed__field )
=> ( ( B @ ( C @ ( D @ ( E @ c_Deriv_Oderiv ) ) ) )
=> ( ( A @ ( C @ ( D @ ( E @ c_Deriv_Oderiv ) ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(124,axiom,
tc_Int_Oint @ class_Groups_Ogroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).
thf(1541,plain,
tc_Int_Oint @ class_Groups_Ogroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(705,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ~ ( C @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Ole__less__trans) ).
thf(3482,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ~ ( C @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(211,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Groups_Omonoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Omonoid__mult) ).
thf(1762,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Groups_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(432,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oab__group__add )
=> ( ( B @ ( C @ ( D @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( A @ ( D @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__diff__less) ).
thf(2515,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oab__group__add )
=> ( ( B @ ( C @ ( D @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( A @ ( D @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(22,axiom,
tc_HOL_Obool @ class_Orderings_Oord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
thf(1270,plain,
tc_HOL_Obool @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(217,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).
thf(1772,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Groups_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Ozero) ).
thf(1259,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Groups_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(611,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( B @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( C @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__self1) ).
thf(3122,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( B @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( C @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(554,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(2946,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(572,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__ring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Polynomial_Omonom ) ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__replicate__append) ).
thf(2990,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__ring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Polynomial_Omonom ) ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(393,axiom,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl) ).
thf(2377,plain,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(1013,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).
thf(4668,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(273,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mod__iff) ).
thf(1953,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(971,axiom,
! [A: $i,B: $i] :
( ( B @ class_Fields_Ofield__inverse__zero )
=> ( ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) )
<=> ( A
= ( B @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__eq__1__iff) ).
thf(4512,plain,
! [A: $i,B: $i] :
( ( B @ class_Fields_Ofield__inverse__zero )
=> ( ( ( A
= ( B @ c_Groups_Oone__class_Oone ) )
=> ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) )
& ( ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) )
=> ( A
= ( B @ c_Groups_Oone__class_Oone ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(1196,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).
thf(5423,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1196]) ).
thf(225,axiom,
! [A: $i,B: $i] :
( ( B
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zminus1__eq__if) ).
thf(1804,plain,
! [A: $i,B: $i] :
( ( B
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(1185,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__cancel) ).
thf(5345,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B = A )
=> ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185]) ).
thf(539,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__self__implies__10) ).
thf(2895,plain,
! [A: $i,B: $i] :
( ( B
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(491,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( B = A )
<=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__iff__diff__eq__0) ).
thf(2709,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(280,axiom,
! [A: $i,B: $i] :
( ( B @ class_Divides_Osemiring__div )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__by__0) ).
thf(1970,plain,
! [A: $i,B: $i] :
( ( B @ class_Divides_Osemiring__div )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(639,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
<=> ( ( B @ c_Groups_Ozero__class_Ozero )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__0__equal__iff__equal) ).
thf(3218,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( ( ( B @ c_Groups_Ozero__class_Ozero )
= A )
=> ( ( B @ c_Groups_Ozero__class_Ozero )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) )
& ( ( ( B @ c_Groups_Ozero__class_Ozero )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
=> ( ( B @ c_Groups_Ozero__class_Ozero )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(243,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Owellorder )
=> ( ( A @ ( C @ c_Orderings_Oord__class_OLeast ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__Least) ).
thf(1856,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Owellorder )
=> ( ( A @ ( C @ c_Orderings_Oord__class_OLeast ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(715,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Oab__semigroup__idem__mult )
=> ( ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times_Oidem) ).
thf(3518,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Oab__semigroup__idem__mult )
=> ( ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(830,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Odivision__ring )
=> ( ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Oone__class_Oone ) )
=> ( ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__unique) ).
thf(3963,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Odivision__ring )
=> ( ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Oone__class_Oone ) )
=> ( ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(863,axiom,
tc_Nat_Onat @ class_Groups_Ozero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
thf(4095,plain,
tc_Nat_Onat @ class_Groups_Ozero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(610,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( E @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( E @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( E @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__pCons) ).
thf(3119,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( E @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( E @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( E @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(773,axiom,
tc_Nat_Onat @ class_Rings_Olinordered__semiring__strict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).
thf(3746,plain,
tc_Nat_Onat @ class_Rings_Olinordered__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(696,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ozero )
=> ( ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( B @ c_Polynomial_Odegree ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__pCons__0) ).
thf(3440,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ozero )
=> ( ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( B @ c_Polynomial_Odegree ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(633,axiom,
tc_Nat_Onat @ class_Rings_Osemiring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__1) ).
thf(3205,plain,
tc_Nat_Onat @ class_Rings_Osemiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(597,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__strict__right__mono__neg) ).
thf(3087,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(582,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring__inverse__zero )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__zero) ).
thf(3018,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring__inverse__zero )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(1074,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucI) ).
thf(4898,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(1016,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(4676,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(180,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Rings_Ono__zero__divisors ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Ono__zero__divisors) ).
thf(1683,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Rings_Ono__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ouminus )
=> ( B @ ( A @ tc_fun ) @ class_Groups_Ouminus ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Groups_Ouminus) ).
thf(1361,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ouminus )
=> ( B @ ( A @ tc_fun ) @ class_Groups_Ouminus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(1045,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Ozero )
=> ( ( ( D @ ( F @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( F @ c_Groups_Ozero__class_Ozero @ ( E @ hAPP ) @ hAPP ) @ hAPP ) )
= D )
=> ( ( A @ ( B @ ( F @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( E @ ( D @ ( F @ ( C @ c_Polynomial_Opoly__rec ) ) ) ) )
= ( A @ ( E @ ( D @ ( F @ ( C @ c_Polynomial_Opoly__rec ) ) ) ) @ ( A @ ( B @ ( E @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__rec__pCons) ).
thf(4772,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Ozero )
=> ( ( ( D @ ( F @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( F @ c_Groups_Ozero__class_Ozero @ ( E @ hAPP ) @ hAPP ) @ hAPP ) )
= D )
=> ( ( A @ ( B @ ( F @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( E @ ( D @ ( F @ ( C @ c_Polynomial_Opoly__rec ) ) ) ) )
= ( A @ ( E @ ( D @ ( F @ ( C @ c_Polynomial_Opoly__rec ) ) ) ) @ ( A @ ( B @ ( E @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(520,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Odivision__ring )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Deriv_Oinverse__diff__inverse) ).
thf(2830,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Odivision__ring )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(533,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Polynomial_Ocoeff ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( tc_Nat_Onat @ ( C @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_OAbs__poly ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__def) ).
thf(2868,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Polynomial_Ocoeff ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( tc_Nat_Onat @ ( C @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_OAbs__poly ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(978,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Deriv_Oadd__diff__add) ).
thf(4545,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(585,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( ( ~ ( ( A
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Opoly__gcd ) ) @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( B @ ( C @ c_Polynomial_Opoly__gcd ) ) @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( C @ c_Groups_Oone__class_Oone ) ) )
& ( ( ( A
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Opoly__gcd ) ) @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( B @ ( C @ c_Polynomial_Opoly__gcd ) ) @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__gcd__monic) ).
thf(3032,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( ( ~ ( ( A
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Opoly__gcd ) ) @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( B @ ( C @ c_Polynomial_Opoly__gcd ) ) @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( C @ c_Groups_Oone__class_Oone ) ) )
& ( ( ( A
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Opoly__gcd ) ) @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( B @ ( C @ c_Polynomial_Opoly__gcd ) ) @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(630,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ~ ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__not__sym) ).
thf(3194,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ~ ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(303,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield__inverse__zero )
=> ( ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( B @ ( A @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__divide) ).
thf(2038,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield__inverse__zero )
=> ( ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( B @ ( A @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(746,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( ( A @ ( C @ c_Polynomial_Odegree ) @ ( B @ ( C @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Odiv ) ) )
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__poly__less) ).
thf(3643,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( ( A @ ( C @ c_Polynomial_Odegree ) @ ( B @ ( C @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Odiv ) ) )
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(957,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__increasing) ).
thf(4457,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(419,axiom,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oorder__refl) ).
thf(2472,plain,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(823,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
thf(3935,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(1008,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(4653,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Oring__div )
=> ( ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Divides_Odiv__class_Odiv ) ) )
= ( B @ ( A @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__neg__div) ).
thf(1329,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Oring__div )
=> ( ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Divides_Odiv__class_Odiv ) ) )
= ( B @ ( A @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(536,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
=> ( ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
<=> ( ( C = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_crossproduct__eq) ).
thf(2877,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
=> ( ( ( ( C = A )
| ( D = B ) )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( ( C = A )
| ( D = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(827,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( C @ c_Polynomial_Odegree ) @ ( B @ ( C @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Odegree ) )
= ( A @ ( C @ c_Polynomial_Odegree ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__add__eq__right) ).
thf(3952,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( C @ c_Polynomial_Odegree ) @ ( B @ ( C @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Odegree ) )
= ( A @ ( C @ c_Polynomial_Odegree ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(1086,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__zless__mono2__lemma) ).
thf(4951,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).
thf(268,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Odiv ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__power) ).
thf(1942,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Odiv ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(911,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__left__pos) ).
thf(4276,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(1117,axiom,
! [A: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
<=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__eq__0__conv) ).
thf(5080,plain,
! [A: $i] :
( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( ( ( B
!= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( C @ c_Polynomial_Opoly__gcd ) ) )
= ( B @ ( A @ ( C @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( C @ c_Polynomial_Opoly__gcd ) ) ) ) )
& ( ( B
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( C @ c_Polynomial_Opoly__gcd ) ) )
= ( A @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( C @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__gcd__code) ).
thf(1292,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( ( ( B
!= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( C @ c_Polynomial_Opoly__gcd ) ) )
= ( B @ ( A @ ( C @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( C @ c_Polynomial_Opoly__gcd ) ) ) ) )
& ( ( B
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( C @ c_Polynomial_Opoly__gcd ) ) )
= ( A @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( C @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(203,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
<=> ( A
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equation__minus__iff) ).
thf(1739,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( A
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
=> ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) )
& ( ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
=> ( A
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__less__iff) ).
thf(1461,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( ( B @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(946,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__mult )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1) ).
thf(4425,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__mult )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(763,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__dvd__not__less) ).
thf(3714,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(766,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__smult__left) ).
thf(3728,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(944,axiom,
tc_Nat_Onat @ class_Rings_Ozero__neq__one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).
thf(4421,plain,
tc_Nat_Onat @ class_Rings_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(923,axiom,
! [A: $i,B: $i] :
~ ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less2) ).
thf(4315,plain,
! [A: $i,B: $i] :
~ ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(81,axiom,
! [A: $i,B: $i] :
( ( B @ class_Divides_Osemiring__div )
=> ( ( A @ ( A @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__self) ).
thf(1424,plain,
! [A: $i,B: $i] :
( ( B @ class_Divides_Osemiring__div )
=> ( ( A @ ( A @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(76,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Groups_Ocancel__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Ocancel__comm__monoid__add) ).
thf(1414,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Groups_Ocancel__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(309,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ? [C: $i] :
( A
= ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__iff__Suc__zadd) ).
thf(2053,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( A
= ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ? [C: $i] :
( A
= ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(235,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mod__imp__dvd) ).
thf(1842,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(226,axiom,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zminus1__eq__if) ).
thf(1810,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(1067,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ozero )
=> ( ( ( C @ ( D @ ( E @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) ) )
<=> ( ( C = A )
& ( D = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pCons__eq__iff) ).
thf(4861,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ozero )
=> ( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( E @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) ) ) )
& ( ( ( C @ ( D @ ( E @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).
thf(849,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Int_Oring__char__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Int_Oring__char__0) ).
thf(4054,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Int_Oring__char__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(692,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__pos__pos) ).
thf(3428,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(443,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ozero )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Polynomial_Omonom ) ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_monom__0) ).
thf(2551,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ozero )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Polynomial_Omonom ) ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(317,axiom,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__0) ).
thf(2085,plain,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(706,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( C @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( B @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mod__equality2) ).
thf(3486,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( C @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( B @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(438,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__field )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide_Ozero) ).
thf(2536,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__field )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(93,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C = B )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I1_J) ).
thf(1451,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C = B )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(522,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Oordered__ring )
=> ( ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( F @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( F @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__iff1) ).
thf(2836,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Oordered__ring )
=> ( ( ( A @ ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( F @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( F @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( F @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( F @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(525,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Odivision__ring )
=> ( ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times__divide__eq__right) ).
thf(2845,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Odivision__ring )
=> ( ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(772,axiom,
! [A: $i] :
( ( A @ class_Rings_Ozero__neq__one )
=> ( ( A @ c_Groups_Ozero__class_Ozero )
!= ( A @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__neq__one) ).
thf(3743,plain,
! [A: $i] :
( ( A @ class_Rings_Ozero__neq__one )
=> ( ( A @ c_Groups_Ozero__class_Ozero )
!= ( A @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(174,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Groups_Oone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Oone) ).
thf(1668,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Groups_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(965,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL )
<=> ~ ( ? [D: $i] :
( ~ ( D @ ( C @ hAPP ) @ hBOOL )
& ( B
= ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
| ( ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__split__asm) ).
thf(4482,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( ? [D: $i] :
( ~ ( D @ ( C @ hAPP ) @ hBOOL )
& ( B
= ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
| ( ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL )
=> ~ ( ? [D: $i] :
( ~ ( D @ ( C @ hAPP ) @ hBOOL )
& ( B
= ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
| ( ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(416,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oord) ).
thf(2465,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(427,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Osemiring__0 )
& ( B @ class_Power_Opower ) )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__0__Suc) ).
thf(2497,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Osemiring__0 )
& ( B @ class_Power_Opower ) )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(824,axiom,
! [A: $i,B: $i] :
( ( B @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
& ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__less__inverse__iff) ).
thf(3937,plain,
! [A: $i,B: $i] :
( ( B @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
& ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
& ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(270,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zero) ).
thf(1947,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(285,axiom,
tc_Int_Oint @ class_Rings_Oring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring) ).
thf(1984,plain,
tc_Int_Oint @ class_Rings_Oring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(241,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Omonoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__mult) ).
thf(1852,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(531,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__div__class_Omod__div__equality_H) ).
thf(2862,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(193,axiom,
tc_Int_Oint @ class_Rings_Olinordered__comm__semiring__strict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).
thf(1720,plain,
tc_Int_Oint @ class_Rings_Olinordered__comm__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(332,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [E: $i] :
( ( B @ ( E @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( E @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( E @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( ( ( ~ ( ( A
= ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( C @ ( D @ c_Polynomial_Odegree ) @ ( C @ ( D @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( D @ c_Groups_Oone__class_Oone ) ) )
& ( ( ( A
= ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( C @ ( D @ c_Polynomial_Odegree ) @ ( C @ ( D @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( D @ c_Groups_Ozero__class_Ozero ) ) ) )
=> ( ( A @ ( B @ ( D @ c_Polynomial_Opoly__gcd ) ) )
= C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__gcd__unique) ).
thf(2140,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [E: $i] :
( ( B @ ( E @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( E @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( E @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( ( ( ~ ( ( A
= ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( C @ ( D @ c_Polynomial_Odegree ) @ ( C @ ( D @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( D @ c_Groups_Oone__class_Oone ) ) )
& ( ( ( A
= ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( C @ ( D @ c_Polynomial_Odegree ) @ ( C @ ( D @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( D @ c_Groups_Ozero__class_Ozero ) ) ) )
=> ( ( A @ ( B @ ( D @ c_Polynomial_Opoly__gcd ) ) )
= C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(230,axiom,
! [A: $i,B: $i] :
( ( B @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__0) ).
thf(1825,plain,
! [A: $i,B: $i] :
( ( B @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(562,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_RealVector_Oreal__normed__field )
=> ( ( B @ ( C @ ( D @ ( E @ c_Deriv_Oderiv ) ) ) )
=> ( B @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( E @ ( E @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ c_Deriv_Oderiv ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DERIV__cmult) ).
thf(2968,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_RealVector_Oreal__normed__field )
=> ( ( B @ ( C @ ( D @ ( E @ c_Deriv_Oderiv ) ) ) )
=> ( B @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( E @ ( E @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ c_Deriv_Oderiv ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(1111,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ tc_Polynomial_Opoly @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(5063,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ tc_Polynomial_Opoly @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).
thf(218,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring__1 )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__minus__iff) ).
thf(1776,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring__1 )
=> ( ( ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ( B = A )
<=> ! [D: $i] :
( ( D @ ( B @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_expand__poly__eq) ).
thf(1263,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ( ! [D: $i] :
( ( D @ ( B @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ! [D: $i] :
( ( D @ ( B @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(1062,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__gt1__lemma) ).
thf(4846,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).
thf(739,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__zmod) ).
thf(3611,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(504,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__strict__right__mono) ).
thf(2766,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(308,axiom,
tc_HOL_Obool @ class_Lattices_Oboolean__algebra,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Oboolean__algebra) ).
thf(2052,plain,
tc_HOL_Obool @ class_Lattices_Oboolean__algebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(148,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Groups_Ouminus ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Ouminus) ).
thf(1599,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Groups_Ouminus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(672,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oone )
=> ( ( ( B @ c_Groups_Oone__class_Oone )
= A )
<=> ( A
= ( B @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__reorient) ).
thf(3333,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oone )
=> ( ( ( A
= ( B @ c_Groups_Oone__class_Oone ) )
=> ( ( B @ c_Groups_Oone__class_Oone )
= A ) )
& ( ( ( B @ c_Groups_Oone__class_Oone )
= A )
=> ( A
= ( B @ c_Groups_Oone__class_Oone ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(1087,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__mod__minus__left) ).
thf(4953,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).
thf(606,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Power_Opower )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc) ).
thf(3109,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Power_Opower )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(855,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).
thf(4069,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(821,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__0__less__mult__iff) ).
thf(3920,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(366,axiom,
tc_Nat_Onat @ class_Groups_Ominus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).
thf(2272,plain,
tc_Nat_Onat @ class_Groups_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(638,axiom,
! [A: $i] :
( ( A @ class_Fields_Ofield )
=> ( ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_Polynomial_Opoly__gcd ) ) )
= ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__gcd__0__0) ).
thf(3215,plain,
! [A: $i] :
( ( A @ class_Fields_Ofield )
=> ( ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_Polynomial_Opoly__gcd ) ) )
= ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(119,axiom,
tc_Int_Oint @ class_Rings_Odvd,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Odvd) ).
thf(1525,plain,
tc_Int_Oint @ class_Rings_Odvd,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(1155,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oring__no__zero__divisors ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors) ).
thf(5245,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oring__no__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).
thf(654,axiom,
! [A: $i] :
( ( A @ class_Groups_Ozero )
=> ( ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) )
= ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pCons__0__0) ).
thf(3279,plain,
! [A: $i] :
( ( A @ class_Groups_Ozero )
=> ( ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) )
= ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(1091,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
=> ( ( B
= ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
<=> ( A
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__iff) ).
thf(4966,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
=> ( ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( B
= ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( B
= ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( A
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).
thf(625,axiom,
! [A: $i] :
( ( A @ class_Groups_Oab__group__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ouminus ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ouminus) ).
thf(3173,plain,
! [A: $i] :
( ( A @ class_Groups_Oab__group__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ouminus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(314,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Omult__zero )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__zero__left) ).
thf(2076,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Omult__zero )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(391,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Oring )
=> ( ( ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
<=> ( ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__add__iff1) ).
thf(2368,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Oring )
=> ( ( ( ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A )
=> ( ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(1194,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Odiv ) ) )
= ( C @ ( B @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self2) ).
thf(5417,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Odiv ) ) )
= ( C @ ( B @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194]) ).
thf(713,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Ofield )
=> ( ( D
!= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C
!= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__frac__eq) ).
thf(3508,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Ofield )
=> ( ( D
!= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C
!= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(1129,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__mult )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).
thf(5126,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__mult )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).
thf(405,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pow__divides__eq__nat) ).
thf(2423,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C @ ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(1136,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( A @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__less__imp__less__neg) ).
thf(5170,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( A @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136]) ).
thf(883,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Divides_Odiv__class_Odiv ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self2__is__id) ).
thf(4163,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Divides_Odiv__class_Odiv ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(619,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ominus__right) ).
thf(3147,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(288,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__bin__lemma) ).
thf(1991,plain,
! [A: $i,B: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(510,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__increasing__iff) ).
thf(2788,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(796,axiom,
tc_Nat_Onat @ class_Rings_Olinordered__semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
thf(3834,plain,
tc_Nat_Onat @ class_Rings_Olinordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Oring__div )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__minus__eq) ).
thf(1318,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Oring__div )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(785,axiom,
tc_Nat_Onat @ class_Divides_Osemiring__div,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Divides_Osemiring__div) ).
thf(3802,plain,
tc_Nat_Onat @ class_Divides_Osemiring__div,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(1175,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__less__n__mult__m) ).
thf(5310,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1175]) ).
thf(1133,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Rings_Osemiring__0 )
& ( C @ class_Rings_Odvd ) )
=> ( ? [D: $i] : ( D @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hBOOL )
<=> ? [D: $i] :
( ( D @ ( B @ hAPP ) @ hBOOL )
& ( C @ c_Groups_Ozero__class_Ozero @ ( D @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unity__coeff__ex) ).
thf(5153,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Rings_Osemiring__0 )
& ( C @ class_Rings_Odvd ) )
=> ( ( ? [D: $i] :
( ( D @ ( B @ hAPP ) @ hBOOL )
& ( C @ c_Groups_Ozero__class_Ozero @ ( D @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ? [D: $i] : ( D @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hBOOL ) )
& ( ? [D: $i] : ( D @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hBOOL )
=> ? [D: $i] :
( ( D @ ( B @ hAPP ) @ hBOOL )
& ( C @ c_Groups_Ozero__class_Ozero @ ( D @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).
thf(546,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__ring )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring) ).
thf(2926,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__ring )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(1005,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__diff) ).
thf(4644,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(640,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__zero__less__power__iff) ).
thf(3225,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(1191,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ( A @ ( B @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Polynomial_Ocoeff ) @ ( B @ ( C @ c_Nat_Onat_Onat__case ) ) @ ( C @ c_Polynomial_OAbs__poly ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pCons__def) ).
thf(5402,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ( A @ ( B @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Polynomial_Ocoeff ) @ ( B @ ( C @ c_Nat_Onat_Onat__case ) ) @ ( C @ c_Polynomial_OAbs__poly ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191]) ).
thf(999,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel1) ).
thf(4625,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(350,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__0 )
=> ( ( ( B @ ( C @ ( E @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( E @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) ) )
=> ( ( B
= ( C @ ( D @ ( E @ c_Polynomial_Osynthetic__div ) ) ) )
& ( A
= ( C @ ( D @ ( E @ c_Polynomial_Opoly ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_synthetic__div__unique) ).
thf(2208,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__0 )
=> ( ( ( B @ ( C @ ( E @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( E @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) ) )
=> ( ( B
= ( C @ ( D @ ( E @ c_Polynomial_Osynthetic__div ) ) ) )
& ( A
= ( C @ ( D @ ( E @ c_Polynomial_Opoly ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(1047,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__0__right) ).
thf(4782,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).
thf(734,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_fconj @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fconj__1) ).
thf(3592,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_fconj @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ hBOOL )
| ~ ( B @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(237,axiom,
tc_Int_Oint @ class_Divides_Oring__div,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Oring__div) ).
thf(1846,plain,
tc_Int_Oint @ class_Divides_Oring__div,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(171,axiom,
tc_Int_Oint @ class_Groups_Oordered__ab__semigroup__add__imp__le,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(1663,plain,
tc_Int_Oint @ class_Groups_Oordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(629,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__semidom )
=> ( ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__0__less__iff) ).
thf(3190,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__semidom )
=> ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(344,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessD) ).
thf(2189,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(690,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib) ).
thf(3422,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(1170,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
thf(5295,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170]) ).
thf(465,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__simps_I3_J) ).
thf(2617,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(753,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__less__mult) ).
thf(3675,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(922,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
<=> ( A
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__0__iff) ).
thf(4308,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( A
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(357,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) ).
thf(2235,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(26,axiom,
! [A: $i,B: $i] : ( B @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__Suc) ).
thf(1278,plain,
! [A: $i,B: $i] : ( B @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(291,axiom,
tc_Int_Oint @ class_Rings_Ocomm__ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring) ).
thf(2001,plain,
tc_Int_Oint @ class_Rings_Ocomm__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(116,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B != A )
<=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
thf(1510,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( B != A ) )
& ( ( B != A )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(212,axiom,
tc_Int_Oint @ class_Rings_Oring__no__zero__divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).
thf(1764,plain,
tc_Int_Oint @ class_Rings_Oring__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(875,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ozero )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ ( D @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Ocoeff ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_coeff__pCons__Suc) ).
thf(4131,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ozero )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ ( D @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Ocoeff ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(481,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__zpower) ).
thf(2677,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(543,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
<=> ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__1) ).
thf(2904,plain,
! [A: $i,B: $i] :
( ( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(455,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__nonneg) ).
thf(2585,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(708,axiom,
! [A: $i] :
( ( A @ class_Groups_Ozero )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ozero) ).
thf(3491,plain,
! [A: $i] :
( ( A @ class_Groups_Ozero )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(658,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add) ).
thf(3289,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(1051,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(4797,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(146,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Groups_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Ocomm__monoid__add) ).
thf(1595,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Groups_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(967,axiom,
tc_Nat_Onat @ class_Groups_Oab__semigroup__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
thf(4503,plain,
tc_Nat_Onat @ class_Groups_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(843,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( A @ ( B @ ( C @ c_Transcendental_Odiffs ) ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ hAPP ) @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diffs__def) ).
thf(4017,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( A @ ( B @ ( C @ c_Transcendental_Odiffs ) ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ hAPP ) @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(61,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Groups_Oab__semigroup__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Oab__semigroup__mult) ).
thf(1374,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Groups_Oab__semigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(364,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__gt__zero__iff) ).
thf(2260,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) ) )
=> ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(550,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Odivision__ring__inverse__zero )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__inverse) ).
thf(2936,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Odivision__ring__inverse__zero )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(495,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Oboolean__algebra )
=> ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__eq__compl__iff) ).
thf(2729,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Oboolean__algebra )
=> ( ( ( B = A )
=> ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) )
& ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(207,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ominus )
=> ( B @ ( A @ tc_fun ) @ class_Groups_Ominus ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Groups_Ominus) ).
thf(1754,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ominus )
=> ( B @ ( A @ tc_fun ) @ class_Groups_Ominus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(372,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Odivision__ring )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__minus__divide__right) ).
thf(2292,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Odivision__ring )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(275,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__mult__div__cancel) ).
thf(1959,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(445,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__distrib2) ).
thf(2556,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(932,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).
thf(4354,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(805,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__less__power__Suc) ).
thf(3871,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(368,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Power_Opower )
=> ( ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Oone__class_Oone ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_realpow__num__eq__if) ).
thf(2275,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Power_Opower )
=> ( ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Oone__class_Oone ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(301,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Oring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__diff__eq) ).
thf(2033,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Oring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(647,axiom,
! [A: $i,B: $i] :
( ( B != A )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oneq__le__trans) ).
thf(3257,plain,
! [A: $i,B: $i] :
( ( B != A )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(738,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_fequal @ hAPP ) @ hBOOL )
| ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__2) ).
thf(3607,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_fequal @ hAPP ) @ hBOOL )
| ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(594,axiom,
! [A: $i,B: $i] :
( ( B @ class_Fields_Olinordered__field )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negative__imp__inverse__negative) ).
thf(3079,plain,
! [A: $i,B: $i] :
( ( B @ class_Fields_Olinordered__field )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(204,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__zmod) ).
thf(1747,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(552,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_Groups_Oone__class_Oone @ ( A @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(2941,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ c_Groups_Oone__class_Oone @ ( A @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(129,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__mod__bound) ).
thf(1548,plain,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(265,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__zmod) ).
thf(1927,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(160,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zadd1__eq) ).
thf(1631,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(1108,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_Polynomial_Opoly ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__iff__poly__eq__0) ).
thf(5043,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_Polynomial_Opoly ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_Polynomial_Opoly ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).
thf(1049,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( B = A )
=> ( ~ ( C @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oord__less__eq__trans) ).
thf(4786,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( B = A )
=> ( ~ ( C @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).
thf(1011,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( A @ ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__divide) ).
thf(4662,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( A @ ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(563,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oab__group__add )
=> ( ( B @ ( A @ ( D @ c_Polynomial_Omonom ) ) @ ( B @ ( C @ ( D @ c_Polynomial_Omonom ) ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Omonom ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__monom) ).
thf(2970,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oab__group__add )
=> ( ( B @ ( A @ ( D @ c_Polynomial_Omonom ) ) @ ( B @ ( C @ ( D @ c_Polynomial_Omonom ) ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Omonom ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(779,axiom,
! [A: $i,B: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__1__eq__mult__iff) ).
thf(3768,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(252,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Opoly__gcd ) ) )
= ( B @ ( A @ ( C @ c_Polynomial_Opoly__gcd ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__gcd_Ocommute) ).
thf(1884,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Opoly__gcd ) ) )
= ( B @ ( A @ ( C @ c_Polynomial_Opoly__gcd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(643,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__def) ).
thf(3240,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(1112,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__ring )
=> ( ( A @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__diff__right) ).
thf(5065,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__ring )
=> ( ( A @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).
thf(206,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_RealVector_Oreal__normed__field )
=> ( ( C @ ( D @ ( E @ ( F @ c_Deriv_Oderiv ) ) ) )
=> ( ( A @ ( D @ ( B @ ( F @ c_Deriv_Oderiv ) ) ) )
=> ( A @ ( C @ ( F @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus @ ( F @ ( F @ ( F @ tc_fun ) @ ( F @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ ( F @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( F @ c_Deriv_Oderiv ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DERIV__diff) ).
thf(1752,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_RealVector_Oreal__normed__field )
=> ( ( C @ ( D @ ( E @ ( F @ c_Deriv_Oderiv ) ) ) )
=> ( ( A @ ( D @ ( B @ ( F @ c_Deriv_Oderiv ) ) ) )
=> ( A @ ( C @ ( F @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus @ ( F @ ( F @ ( F @ tc_fun ) @ ( F @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ ( F @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( F @ c_Deriv_Oderiv ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(872,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Divides_Odiv__class_Odiv ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self1__is__id) ).
thf(4122,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Divides_Odiv__class_Odiv ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(1121,axiom,
tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__0__less__1) ).
thf(5099,plain,
tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).
thf(1120,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_RealVector_Oreal__normed__field )
=> ( ( B @ ( C @ ( D @ ( E @ c_Deriv_Oderiv ) ) ) )
=> ( A @ ( C @ ( D @ hAPP ) @ ( E @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( E @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( E @ c_Groups_Oone__class_Oone @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( D @ ( E @ c_Power_Opower__class_Opower @ ( E @ ( E @ ( tc_Nat_Onat @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_Nat_Onat @ ( E @ c_COMBC ) ) ) @ hAPP ) @ ( E @ c_Deriv_Oderiv ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DERIV__power__Suc) ).
thf(5097,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_RealVector_Oreal__normed__field )
=> ( ( B @ ( C @ ( D @ ( E @ c_Deriv_Oderiv ) ) ) )
=> ( A @ ( C @ ( D @ hAPP ) @ ( E @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( E @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( E @ c_Groups_Oone__class_Oone @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( D @ ( E @ c_Power_Opower__class_Opower @ ( E @ ( E @ ( tc_Nat_Onat @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_Nat_Onat @ ( E @ c_COMBC ) ) ) @ hAPP ) @ ( E @ c_Deriv_Oderiv ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).
thf(278,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Odiv ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__div__mult) ).
thf(1965,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Odiv ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(330,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Ocoeff ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Polynomial_Ocoeff ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_coeff__diff) ).
thf(2134,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Ocoeff ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Polynomial_Ocoeff ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(930,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__divide__eq) ).
thf(4341,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(591,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__right__mono) ).
thf(3070,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(220,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ class_Fields_Ofield )
=> ( ( C @ ( D @ ( E @ ( F @ ( G @ c_Polynomial_Opdivmod__rel ) ) ) ) )
=> ( ( E
!= ( G @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B
= ( E @ ( G @ c_Polynomial_Odegree ) @ ( E @ ( G @ c_Polynomial_Ocoeff ) @ hAPP ) @ ( E @ ( G @ c_Polynomial_Odegree ) @ ( C @ ( A @ ( G @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( G @ c_Polynomial_Ocoeff ) @ hAPP ) @ ( G @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) )
=> ( E @ ( B @ ( G @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( G @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( G @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( G @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( A @ ( G @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( G @ c_Polynomial_Opdivmod__rel ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pdivmod__rel__pCons) ).
thf(1784,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ class_Fields_Ofield )
=> ( ( C @ ( D @ ( E @ ( F @ ( G @ c_Polynomial_Opdivmod__rel ) ) ) ) )
=> ( ( E
!= ( G @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B
= ( E @ ( G @ c_Polynomial_Odegree ) @ ( E @ ( G @ c_Polynomial_Ocoeff ) @ hAPP ) @ ( E @ ( G @ c_Polynomial_Odegree ) @ ( C @ ( A @ ( G @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( G @ c_Polynomial_Ocoeff ) @ hAPP ) @ ( G @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) )
=> ( E @ ( B @ ( G @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( G @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( G @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( G @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( A @ ( G @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( G @ c_Polynomial_Opdivmod__rel ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(68,axiom,
tc_Int_Oint @ class_Groups_Olinordered__ab__group__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).
thf(1389,plain,
tc_Int_Oint @ class_Groups_Olinordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(769,axiom,
! [A: $i] :
( ( A @ class_Groups_Ozero )
=> ( ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero )
= ( A @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ ( A @ c_COMBK ) @ hAPP ) @ ( A @ c_Polynomial_OAbs__poly ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__poly__def) ).
thf(3736,plain,
! [A: $i] :
( ( A @ class_Groups_Ozero )
=> ( ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero )
= ( A @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ ( A @ c_COMBK ) @ hAPP ) @ ( A @ c_Polynomial_OAbs__poly ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(595,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__minus__cancel) ).
thf(3081,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(826,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__cancel2) ).
thf(3945,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
=> ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(480,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Suc__right) ).
thf(2674,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(450,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__pCons) ).
thf(2568,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(492,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ozero )
=> ( ( ( C != B )
=> ( ( B @ ( C @ ( A @ ( D @ c_Polynomial_Omonom ) ) @ ( D @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( C = B )
=> ( ( B @ ( C @ ( A @ ( D @ c_Polynomial_Omonom ) ) @ ( D @ c_Polynomial_Ocoeff ) @ hAPP ) )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_coeff__monom) ).
thf(2716,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ozero )
=> ( ( ( C != B )
=> ( ( B @ ( C @ ( A @ ( D @ c_Polynomial_Omonom ) ) @ ( D @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( C = B )
=> ( ( B @ ( C @ ( A @ ( D @ c_Polynomial_Omonom ) ) @ ( D @ c_Polynomial_Ocoeff ) @ hAPP ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(737,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Polynomial_Opos__poly ) )
| ( A @ ( B @ c_Polynomial_Opos__poly ) )
| ( A
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__poly__total) ).
thf(3604,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Polynomial_Opos__poly ) )
| ( A @ ( B @ c_Polynomial_Opos__poly ) )
| ( A
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(117,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Rings_Oring__1__no__zero__divisors ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Oring__1__no__zero__divisors) ).
thf(1520,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Rings_Oring__1__no__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(995,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
thf(4612,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(1044,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( C @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_coeff__linear__power) ).
thf(4769,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( C @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Rings_Oring__no__zero__divisors ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Oring__no__zero__divisors) ).
thf(1256,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Rings_Oring__no__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).
thf(1226,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1103,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( C @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zmult2__eq) ).
thf(5022,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( C @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).
thf(559,axiom,
! [A: $i,B: $i] :
( ( B @ class_Fields_Ofield )
=> ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_field__inverse) ).
thf(2959,plain,
! [A: $i,B: $i] :
( ( B @ class_Fields_Ofield )
=> ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(637,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__left__mono) ).
thf(3213,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(353,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Odivision__ring )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_division__ring__inverse__add) ).
thf(2220,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Odivision__ring )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(190,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ c_Polynomial_Opos__poly ) )
<=> ( A @ ( B @ c_Polynomial_Odegree ) @ ( A @ ( B @ c_Polynomial_Ocoeff ) @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__poly__def) ).
thf(1707,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( A @ ( B @ c_Polynomial_Odegree ) @ ( A @ ( B @ c_Polynomial_Ocoeff ) @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Polynomial_Opos__poly ) ) )
& ( ( A @ ( B @ c_Polynomial_Opos__poly ) )
=> ( A @ ( B @ c_Polynomial_Odegree ) @ ( A @ ( B @ c_Polynomial_Ocoeff ) @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(941,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ ( C @ ( D @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( A @ ( D @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__add__less) ).
thf(4413,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ ( C @ ( D @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( A @ ( D @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ominus )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__diff__def) ).
thf(1332,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ominus )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(1065,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( ( B @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) ) )
=> ( B
= ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_synthetic__div__unique__lemma) ).
thf(4854,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( ( B @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) ) )
=> ( B
= ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).
thf(18,axiom,
tc_Int_Oint @ class_Rings_Ocomm__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).
thf(1258,plain,
tc_Int_Oint @ class_Rings_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(420,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__assoc) ).
thf(2474,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(55,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Groups_Ocancel__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Ocancel__semigroup__add) ).
thf(1356,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Groups_Ocancel__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(624,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Osemiring__1 )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__power) ).
thf(3170,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Osemiring__1 )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(178,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__int) ).
thf(1675,plain,
! [A: $i,B: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__zdiffD) ).
thf(1428,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(906,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
<=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__neg__iff__add__eq__0) ).
thf(4251,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) )
& ( ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(977,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
thf(4537,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(783,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self1) ).
thf(3796,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(1141,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__gr__0) ).
thf(5185,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).
thf(1197,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__strict__left__mono) ).
thf(5427,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197]) ).
thf(982,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__left__eq) ).
thf(4558,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(891,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__left__neg) ).
thf(4186,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(864,axiom,
t_a @ class_Rings_Oidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0) ).
thf(4096,plain,
t_a @ class_Rings_Oidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(23,axiom,
tc_Int_Oint @ class_Groups_Ouminus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ouminus) ).
thf(1271,plain,
tc_Int_Oint @ class_Groups_Ouminus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(1059,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__times__mod__eq) ).
thf(4837,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).
thf(747,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ( ( A @ ( B @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) )
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pCons__eq__0__iff) ).
thf(3646,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ( ( ( A
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) )
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) )
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(870,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Odegree ) )
= ( A @ ( C @ c_Polynomial_Odegree ) ) ) )
& ( ( B
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Odegree ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__smult__eq) ).
thf(4112,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Odegree ) )
= ( A @ ( C @ c_Polynomial_Odegree ) ) ) )
& ( ( B
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Odegree ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(886,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__neg__pos) ).
thf(4171,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(903,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) )
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_offset__poly__single) ).
thf(4236,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) )
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(247,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Polynomial_Opoly__gcd ) ) @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__gcd__greatest) ).
thf(1865,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Polynomial_Opoly__gcd ) ) @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(898,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ ( A @ ( D @ c_Polynomial_Omonom ) ) @ ( B @ ( C @ ( D @ c_Polynomial_Omonom ) ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Omonom ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__monom) ).
thf(4218,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ ( A @ ( D @ c_Polynomial_Omonom ) ) @ ( B @ ( C @ ( D @ c_Polynomial_Omonom ) ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Omonom ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(735,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__eq__zero__iff) ).
thf(3594,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(289,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring__inverse__zero )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__minus__eq) ).
thf(1997,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring__inverse__zero )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(759,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring__strict) ).
thf(3700,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(851,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Ofield__inverse__zero )
=> ( ( A @ ( B @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times__divide__times__eq) ).
thf(4060,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Ofield__inverse__zero )
=> ( ( A @ ( B @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(490,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__0 )
=> ( ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__0__right) ).
thf(2706,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__0 )
=> ( ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(795,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__mono) ).
thf(3832,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(213,axiom,
tc_HOL_Obool @ class_Groups_Ouminus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ouminus) ).
thf(1765,plain,
tc_HOL_Obool @ class_Groups_Ouminus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(663,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__mult__cancel) ).
thf(3302,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(732,axiom,
! [A: $i] :
( A
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
thf(3568,plain,
! [A: $i] :
( A
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(1199,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Oab__semigroup__idem__mult )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__idem) ).
thf(5432,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Oab__semigroup__idem__mult )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1199]) ).
thf(163,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__equal__iff__equal) ).
thf(1638,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( B = A )
=> ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) )
& ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(1072,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ~ ( C @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oord__eq__less__trans) ).
thf(4887,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ~ ( C @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
thf(1027,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Polynomial_Opoly__gcd ) ) )
= ( A @ ( B @ ( C @ c_Polynomial_Opoly__gcd ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__gcd__minus__right) ).
thf(4716,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Polynomial_Opoly__gcd ) ) )
= ( A @ ( B @ ( C @ c_Polynomial_Opoly__gcd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).
thf(603,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__mult )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__mult__distrib) ).
thf(3101,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__mult )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(1081,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__no__zero__divisors )
=> ( ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).
thf(4929,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__no__zero__divisors )
=> ( ( ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).
thf(351,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__ring )
=> ( ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__diff) ).
thf(2214,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__ring )
=> ( ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(1123,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pos__pos) ).
thf(5103,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).
thf(657,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__mult__pos) ).
thf(3287,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(363,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( D @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__pCons) ).
thf(2257,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( D @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(107,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__field )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( C @ ( D @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( B @ ( D @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DERIV__inverse__lemma) ).
thf(1492,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__field )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( C @ ( D @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( B @ ( D @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(1149,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__1__iff) ).
thf(5222,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).
thf(996,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring )
=> ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__inverse__minus__eq) ).
thf(4616,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring )
=> ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(184,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__int__nat__functions_I2_J) ).
thf(1690,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(684,axiom,
tc_Nat_Onat @ class_Rings_Osemiring__0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).
thf(3384,plain,
tc_Nat_Onat @ class_Rings_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(312,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= A )
<=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__equation__iff) ).
thf(2065,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= B )
=> ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= A ) )
& ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= A )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(315,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Oadd__right) ).
thf(2079,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(376,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__pos) ).
thf(2311,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__0) ).
thf(1209,plain,
! [A: $i,B: $i] :
( ( B @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1114,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(5071,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).
thf(677,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Odivision__ring )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B
= ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__eq__imp) ).
thf(3352,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Odivision__ring )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B
= ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(1024,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).
thf(4704,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(1132,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( ( A @ ( B @ ( C @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) )
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__eq__0__iff) ).
thf(5143,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( ( ( A
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) )
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( C @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) )
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__relations_I4_J) ).
thf(1282,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(936,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( C @ c_Polynomial_Odegree ) @ ( B @ ( C @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Odegree ) )
= ( A @ ( C @ c_Polynomial_Odegree ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__add__eq__left) ).
thf(4369,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( C @ c_Polynomial_Odegree ) @ ( B @ ( C @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Odegree ) )
= ( A @ ( C @ c_Polynomial_Odegree ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(474,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
thf(2642,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(790,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__diff__conv) ).
thf(3815,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(472,axiom,
! [A: $i] :
( ( A
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__self) ).
thf(2637,plain,
! [A: $i] :
( ( A
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(1179,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__less__0__iff) ).
thf(5325,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).
thf(726,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( B @ ( D @ c_Divides_Odiv__class_Odiv ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__mult1) ).
thf(3551,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( B @ ( D @ c_Divides_Odiv__class_Odiv ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(921,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ ( D @ c_Power_Opower_Opower ) ) @ hAPP ) @ hAPP ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power_Opower_Opower__0) ).
thf(4305,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ ( D @ c_Power_Opower_Opower ) ) @ hAPP ) @ hAPP ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__int) ).
thf(1349,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(651,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_COMBC ) ) ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBC__1) ).
thf(3270,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_COMBC ) ) ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(990,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).
thf(4601,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(605,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__mult1) ).
thf(3106,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(700,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__right__eq) ).
thf(3468,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(125,axiom,
tc_Int_Oint @ class_Orderings_Oord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).
thf(1542,plain,
tc_Int_Oint @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(529,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Oordered__ring )
=> ( ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( F @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( F @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__iff2) ).
thf(2856,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Oordered__ring )
=> ( ( ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( F @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( F @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( F @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( F @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(888,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc__0) ).
thf(4176,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(618,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( A @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Polynomial_Opdivmod__rel ) ) ) ) )
<=> ( ( A = C )
& ( B
= ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pdivmod__rel__by__0__iff) ).
thf(3138,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( ( ( A = C )
& ( B
= ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) )
=> ( A @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Polynomial_Opdivmod__rel ) ) ) ) ) )
& ( ( A @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Polynomial_Opdivmod__rel ) ) ) ) )
=> ( ( A = C )
& ( B
= ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(139,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__minus__self__iff) ).
thf(1571,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(534,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__cancel) ).
thf(2871,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(62,axiom,
tc_Int_Oint @ class_Rings_Olinordered__semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).
thf(1376,plain,
tc_Int_Oint @ class_Rings_Olinordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(970,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__commute) ).
thf(4509,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_RealVector_Oreal__normed__field )
=> ( ( C @ ( D @ ( E @ ( F @ c_Deriv_Oderiv ) ) ) )
=> ( ( A @ ( D @ ( B @ ( F @ c_Deriv_Oderiv ) ) ) )
=> ( A @ ( F @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( F @ c_Groups_Ouminus__class_Ouminus @ ( F @ ( F @ ( F @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_Groups_Oplus__class_Oplus @ ( F @ ( F @ ( F @ tc_fun ) @ ( F @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ ( F @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( F @ c_Deriv_Oderiv ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DERIV__add__minus) ).
thf(1439,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_RealVector_Oreal__normed__field )
=> ( ( C @ ( D @ ( E @ ( F @ c_Deriv_Oderiv ) ) ) )
=> ( ( A @ ( D @ ( B @ ( F @ c_Deriv_Oderiv ) ) ) )
=> ( A @ ( F @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( F @ c_Groups_Ouminus__class_Ouminus @ ( F @ ( F @ ( F @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_Groups_Oplus__class_Oplus @ ( F @ ( F @ ( F @ tc_fun ) @ ( F @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ ( F @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( F @ c_Deriv_Oderiv ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(1161,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ~ ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_Polynomial_Opos__poly ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__pos__poly__0) ).
thf(5267,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ~ ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_Polynomial_Opos__poly ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).
thf(348,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( ( ( A @ ( B @ ( C @ c_Polynomial_Opoly__gcd ) ) )
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__gcd__zero__iff) ).
thf(2197,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( ( ( ( A
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Opoly__gcd ) ) )
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( C @ c_Polynomial_Opoly__gcd ) ) )
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(963,axiom,
! [A: $i,B: $i] :
( ( B @ hBOOL )
| ~ ( A @ ( B @ ( c_fconj @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fconj__2) ).
thf(4477,plain,
! [A: $i,B: $i] :
( ( B @ hBOOL )
| ~ ( A @ ( B @ ( c_fconj @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(173,axiom,
tc_Int_Oint @ class_Orderings_Opreorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Opreorder) ).
thf(1667,plain,
tc_Int_Oint @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(1022,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Oring )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__diff__mult) ).
thf(4694,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Oring )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(1079,axiom,
! [A: $i,B: $i] :
( ( B = A )
<=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oeq__iff) ).
thf(4911,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).
thf(1053,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( A @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__power__div__base) ).
thf(4818,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( A @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(1181,axiom,
tc_Nat_Onat @ class_Groups_Oordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(5335,plain,
tc_Nat_Onat @ class_Groups_Oordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1181]) ).
thf(501,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zmult2__eq) ).
thf(2757,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(896,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).
thf(4208,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(928,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(4332,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(509,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__int__left) ).
thf(2785,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(535,axiom,
! [A: $i] :
( ( A @ class_Power_Opower )
=> ( ( A @ c_Power_Opower__class_Opower )
= ( A @ c_Groups_Otimes__class_Otimes @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Power_Opower_Opower ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__power__power) ).
thf(2874,plain,
! [A: $i] :
( ( A @ class_Power_Opower )
=> ( ( A @ c_Power_Opower__class_Opower )
= ( A @ c_Groups_Otimes__class_Otimes @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Power_Opower_Opower ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(918,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( A @ ( B @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__smult__cancel) ).
thf(4296,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( A @ ( B @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(565,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zmult__distrib) ).
thf(2974,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(182,axiom,
tc_Int_Oint @ class_Groups_Omonoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).
thf(1688,plain,
tc_Int_Oint @ class_Groups_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(341,axiom,
tc_Nat_Onat @ class_Rings_Olinordered__comm__semiring__strict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).
thf(2182,plain,
tc_Nat_Onat @ class_Rings_Olinordered__comm__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(1002,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Opcompose ) ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pcompose__0) ).
thf(4635,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Opcompose ) ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(1126,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zmult1__eq) ).
thf(5114,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).
thf(1146,axiom,
! [A: $i,B: $i] :
( ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__if) ).
thf(5202,plain,
! [A: $i,B: $i] :
( ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).
thf(774,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Ofield )
=> ( ( D
!= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C
!= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( D @ ( B @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) )
<=> ( ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_frac__eq__eq) ).
thf(3747,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Ofield )
=> ( ( D
!= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C
!= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( D @ ( B @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) )
& ( ( ( D @ ( B @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) )
=> ( ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(298,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__asym) ).
thf(2025,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(470,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__smult) ).
thf(2632,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(953,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mono) ).
thf(4445,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(462,axiom,
tc_Nat_Onat @ class_Groups_Oab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
thf(2610,plain,
tc_Nat_Onat @ class_Groups_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(1070,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__pos__neg) ).
thf(4882,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).
thf(133,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( C @ c_Divides_Odiv__class_Odiv ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__div__trivial) ).
thf(1557,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( C @ c_Divides_Odiv__class_Odiv ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(328,axiom,
! [A: $i] :
( ( A @ class_Groups_Ocomm__monoid__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Omonoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__add) ).
thf(2129,plain,
! [A: $i] :
( ( A @ class_Groups_Ocomm__monoid__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Omonoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(385,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Odivision__ring__inverse__zero )
=> ( ( ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( A @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__eq__iff__eq) ).
thf(2343,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Odivision__ring__inverse__zero )
=> ( ( ( B = A )
=> ( ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( A @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) ) ) )
& ( ( ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( A @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(1058,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl2) ).
thf(4833,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(198,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Oring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__diff__left__eq) ).
thf(1731,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Oring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(909,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
<=> ( ( B = A )
| ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).
thf(4264,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B = A )
| ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( B = A )
| ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(733,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= A )
<=> ( ( ( B
= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( B
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( C
= ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__eq__eq) ).
thf(3572,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( ( ( ( B
= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( B
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( C
= ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) )
=> ( ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= A ) )
& ( ( ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= A )
=> ( ( ( B
= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( B
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( C
= ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(1093,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__add__cancel) ).
thf(4985,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).
thf(1167,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__zadd__distrib) ).
thf(5286,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).
thf(1189,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring__inverse__zero )
=> ( ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__nonzero__iff__nonzero) ).
thf(5392,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring__inverse__zero )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189]) ).
thf(740,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__zless__mono2) ).
thf(3614,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(440,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Osemiring__1 )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat__aux ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__aux_Osimps_I1_J) ).
thf(2542,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Osemiring__1 )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat__aux ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(371,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Odegree ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__linear__power) ).
thf(2289,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Odegree ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(1031,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Polynomial_Opoly__gcd ) ) )
= ( A @ ( B @ ( C @ c_Polynomial_Opoly__gcd ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__gcd__minus__left) ).
thf(4726,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Polynomial_Opoly__gcd ) ) )
= ( A @ ( B @ ( C @ c_Polynomial_Opoly__gcd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).
thf(801,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__smult) ).
thf(3861,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(547,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(2928,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__zmod__right) ).
thf(1381,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(620,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__half__sum) ).
thf(3150,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(1019,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__diff) ).
thf(4684,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).
thf(721,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__commute) ).
thf(3539,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(386,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(2350,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(776,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Polynomial_Odegree ) )
= ( A @ ( B @ c_Polynomial_Odegree ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__minus) ).
thf(3759,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Polynomial_Odegree ) )
= ( A @ ( B @ c_Polynomial_Odegree ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(466,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( ( B @ ( A @ ( D @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( B
= ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_offset__poly__eq__0__lemma) ).
thf(2620,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( ( B @ ( A @ ( D @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( B
= ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(787,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Polynomial_Opoly ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__offset__poly) ).
thf(3806,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Polynomial_Opoly ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(859,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oab__semigroup__mult )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(4085,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oab__semigroup__mult )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(548,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__ring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1) ).
thf(2931,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__ring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(513,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
<=> ( ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
| ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_realpow__two__disj) ).
thf(2797,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( ( ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
| ( B = A ) )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
=> ( ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
| ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(322,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(2101,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(1171,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__algebra )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ozero__right) ).
thf(5299,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__algebra )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).
thf(854,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Olinordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add) ).
thf(4067,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Olinordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(807,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__left) ).
thf(3876,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(390,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__inverse) ).
thf(2365,plain,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(560,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__one__right) ).
thf(2962,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(1158,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self3) ).
thf(5254,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).
thf(399,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__1__iff__1) ).
thf(2401,plain,
! [A: $i] :
( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(188,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_RealVector_Oreal__normed__field )
=> ( ( B @ ( C @ ( D @ ( E @ c_Deriv_Oderiv ) ) ) )
=> ( ( B = A )
=> ( A @ ( C @ ( D @ ( E @ c_Deriv_Oderiv ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DERIV__cong) ).
thf(1699,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_RealVector_Oreal__normed__field )
=> ( ( B @ ( C @ ( D @ ( E @ c_Deriv_Oderiv ) ) ) )
=> ( ( B = A )
=> ( A @ ( C @ ( D @ ( E @ c_Deriv_Oderiv ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(742,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oidom )
=> ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
| ( B
= ( D @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__cancel__right) ).
thf(3627,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oidom )
=> ( ( ( ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
| ( B
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
| ( B
= ( D @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(337,axiom,
! [A: $i,B: $i] :
( ( B = A )
| ~ ( A @ ( B @ c_fequal @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__1) ).
thf(2171,plain,
! [A: $i,B: $i] :
( ( B = A )
| ~ ( A @ ( B @ c_fequal @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(1144,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__less__imp__less__exp) ).
thf(5197,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Omonom ) ) @ ( C @ c_Polynomial_Odegree ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__monom__eq) ).
thf(1245,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Omonom ) ) @ ( C @ c_Polynomial_Odegree ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(457,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oab__semigroup__add )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(2592,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oab__semigroup__add )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(360,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__eq__diff__pred) ).
thf(2244,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( B @ ( A @ ( B @ ( C @ c_Polynomial_Opoly__gcd ) ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__gcd__dvd1) ).
thf(1435,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( B @ ( A @ ( B @ ( C @ c_Polynomial_Opoly__gcd ) ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(297,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Odivision__ring )
=> ( ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__divide__left) ).
thf(2022,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Odivision__ring )
=> ( ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(680,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__add) ).
thf(3363,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(666,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__eq) ).
thf(3310,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(101,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__field )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide_Ominus) ).
thf(1477,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__field )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(670,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__power) ).
thf(3325,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(627,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__divide__iff) ).
thf(3178,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) )
=> ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(913,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add2) ).
thf(4282,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(575,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less) ).
thf(2999,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(333,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ozero )
=> ( ( ( A @ ( B @ c_Polynomial_Odegree ) @ ( A @ ( B @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
<=> ( A
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leading__coeff__0__iff) ).
thf(2156,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ozero )
=> ( ( ( A
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Polynomial_Odegree ) @ ( A @ ( B @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ c_Polynomial_Odegree ) @ ( A @ ( B @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(569,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ~ ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__asym_H) ).
thf(2984,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ~ ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(281,axiom,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ? [B: $i] :
( A
= ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negD) ).
thf(1973,plain,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ? [B: $i] :
( A
= ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(962,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).
thf(4473,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Fields_Ofield )
=> ( ( B @ ( C @ ( D @ ( E @ ( F @ c_Polynomial_Opdivmod__rel ) ) ) ) )
=> ( B @ ( A @ ( F @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( F @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( A @ ( F @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( F @ c_Polynomial_Opdivmod__rel ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pdivmod__rel__smult__left) ).
thf(1562,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Fields_Ofield )
=> ( ( B @ ( C @ ( D @ ( E @ ( F @ c_Polynomial_Opdivmod__rel ) ) ) ) )
=> ( B @ ( A @ ( F @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( F @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( A @ ( F @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( F @ c_Polynomial_Opdivmod__rel ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(464,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( B @ ( C @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mod__equality) ).
thf(2614,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( B @ ( C @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__refl) ).
thf(1304,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(325,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
<=> ( ( B != A )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__le) ).
thf(2107,plain,
! [A: $i,B: $i] :
( ( ( ( B != A )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( B != A )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(1104,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(5025,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).
thf(974,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc2) ).
thf(4529,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(1069,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Polynomial_Ocoeff ) @ ( B @ ( C @ c_Polynomial_Ocoeff ) @ ( C @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( C @ ( C @ tc_fun ) @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_OAbs__poly ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__poly__def) ).
thf(4879,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Polynomial_Ocoeff ) @ ( B @ ( C @ c_Polynomial_Ocoeff ) @ ( C @ c_Groups_Oplus__class_Oplus @ ( tc_Nat_Onat @ ( C @ ( C @ tc_fun ) @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_OAbs__poly ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).
thf(469,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Odivision__ring )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__divide__distrib) ).
thf(2629,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Odivision__ring )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_uminus__dvd__conv_I1_J) ).
thf(1340,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(99,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__minus) ).
thf(1472,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(382,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__minus) ).
thf(2333,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(541,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__zminus) ).
thf(2899,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(1200,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gt__half__sum) ).
thf(5435,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1200]) ).
thf(158,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( A @ ( A @ ( B @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__refl) ).
thf(1626,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( A @ ( A @ ( B @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(517,axiom,
! [A: $i,B: $i] :
( ( B @ class_Fields_Olinordered__field )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__less__inverse) ).
thf(2816,plain,
! [A: $i,B: $i] :
( ( B @ class_Fields_Olinordered__field )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(1020,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono) ).
thf(4690,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).
thf(379,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__power__nat__eq) ).
thf(2318,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(634,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_coeff__minus) ).
thf(3206,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(660,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__smult__right) ).
thf(3293,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(989,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).
thf(4598,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(622,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__add__distrib) ).
thf(3161,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(1034,axiom,
! [A: $i] :
( ( A @ class_Groups_Ocancel__comm__monoid__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ocancel__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add) ).
thf(4735,plain,
! [A: $i] :
( ( A @ class_Groups_Ocancel__comm__monoid__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ocancel__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
thf(1420,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(834,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__mult) ).
thf(3981,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(429,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( C @ ( B @ ( D @ c_Divides_Odiv__class_Odiv ) ) )
= A )
<=> ( B
= ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__div__eq__mult) ).
thf(2503,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B
= ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( C @ ( B @ ( D @ c_Divides_Odiv__class_Odiv ) ) )
= A ) )
& ( ( ( C @ ( B @ ( D @ c_Divides_Odiv__class_Odiv ) ) )
= A )
=> ( B
= ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(414,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ? [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B
= ( C @ ( c_Nat_OSuc @ hAPP ) ) ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).
thf(2449,plain,
! [A: $i,B: $i] :
( ( ( ? [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B
= ( C @ ( c_Nat_OSuc @ hAPP ) ) ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ? [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B
= ( C @ ( c_Nat_OSuc @ hAPP ) ) ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(115,axiom,
tc_Int_Oint @ class_Groups_Oordered__ab__group__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add) ).
thf(1509,plain,
tc_Int_Oint @ class_Groups_Oordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(459,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Odivision__ring )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( B @ ( A @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Oone__class_Oone ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__inverse__eq) ).
thf(2597,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Odivision__ring )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( A = B )
=> ( ( B @ ( A @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Oone__class_Oone ) ) )
& ( ( ( B @ ( A @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Oone__class_Oone ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(986,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ozero )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero )
= A )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__reorient) ).
thf(4581,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ozero )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ c_Groups_Ozero__class_Ozero )
= A ) )
& ( ( ( B @ c_Groups_Ozero__class_Ozero )
= A )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(1131,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
<=> ( ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
| ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_square__eq__iff) ).
thf(5133,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( ( ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
| ( B = A ) )
=> ( ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
| ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).
thf(1029,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__cancel) ).
thf(4722,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(128,axiom,
tc_Int_Oint @ class_Rings_Osemiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).
thf(1547,plain,
tc_Int_Oint @ class_Rings_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(745,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib2) ).
thf(3640,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(934,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ? [C: $i] :
( B
= ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__eq__0__iff) ).
thf(4360,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( B
= ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ? [C: $i] :
( B
= ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(607,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict) ).
thf(3112,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(478,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
<=> ( ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__cancel1) ).
thf(2661,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B = A ) )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(295,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Nat_Osemiring__char__0 )
=> ( ( ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__eq__iff) ).
thf(2012,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Nat_Osemiring__char__0 )
=> ( ( ( B = A )
=> ( ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) ) ) )
& ( ( ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(165,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__int) ).
thf(1647,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(976,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(4534,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(1115,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ozero )
=> ( ( ( B @ ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( D @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hAPP ) @ hAPP ) )
= B )
=> ( ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ ( B @ ( D @ ( A @ c_Polynomial_Opoly__rec ) ) ) ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__rec__0) ).
thf(5074,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ozero )
=> ( ( ( B @ ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( D @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hAPP ) @ hAPP ) )
= B )
=> ( ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ ( B @ ( D @ ( A @ c_Polynomial_Opoly__rec ) ) ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).
thf(614,axiom,
! [A: $i,B: $i] :
( ( B @ class_Fields_Olinordered__field )
=> ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__positive__imp__positive) ).
thf(3129,plain,
! [A: $i,B: $i] :
( ( B @ class_Fields_Olinordered__field )
=> ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(1004,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Odiff__left) ).
thf(4641,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(486,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__imp__less__div__pos) ).
thf(2689,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(836,axiom,
( ( t_a @ class_Rings_Oidom )
=> ~ ( t_a @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( t_a @ c_Polynomial_Opoly ) @ ( t_a @ ( t_a @ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C0_C) ).
thf(3988,plain,
( ( t_a @ class_Rings_Oidom )
=> ~ ( t_a @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( t_a @ c_Polynomial_Opoly ) @ ( t_a @ ( t_a @ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(431,axiom,
! [A: $i] :
( ( A @ ( c_fNot @ hAPP ) @ hBOOL )
| ~ ~ ( A @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__2) ).
thf(2513,plain,
! [A: $i] :
( ( A @ ( c_fNot @ hAPP ) @ hBOOL )
| ( A @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(374,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__add__mult__distrib) ).
thf(2298,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(687,axiom,
! [A: $i,B: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
<=> ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__is__add) ).
thf(3391,plain,
! [A: $i,B: $i] :
( ( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) ) )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(566,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less1) ).
thf(2977,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(152,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Odiv ) ) )
= ( C @ ( A @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ ( B @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__add) ).
thf(1611,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Odiv ) ) )
= ( C @ ( A @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ ( B @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(392,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_RealVector_Oreal__normed__field )
=> ( ( B @ ( C @ ( D @ ( E @ c_Deriv_Oderiv ) ) ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ hAPP ) @ ( E @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( E @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ ( E @ c_Power_Opower__class_Opower @ ( E @ ( E @ ( tc_Nat_Onat @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_Nat_Onat @ ( E @ c_COMBC ) ) ) @ hAPP ) @ ( E @ c_Deriv_Oderiv ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DERIV__power) ).
thf(2375,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_RealVector_Oreal__normed__field )
=> ( ( B @ ( C @ ( D @ ( E @ c_Deriv_Oderiv ) ) ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ hAPP ) @ ( E @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( E @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ ( E @ c_Power_Opower__class_Opower @ ( E @ ( E @ ( tc_Nat_Onat @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_Nat_Onat @ ( E @ c_COMBC ) ) ) @ hAPP ) @ ( E @ c_Deriv_Oderiv ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(1082,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oone) ).
thf(4939,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).
thf(1190,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Odivision__ring )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__power__inverse) ).
thf(5399,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Odivision__ring )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190]) ).
thf(346,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_COMBI @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Nat_Onat_Onat__case ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc) ).
thf(2192,plain,
! [A: $i,B: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_COMBI @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Nat_Onat_Onat__case ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(1015,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring )
=> ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__inverse__inverse__eq) ).
thf(4673,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring )
=> ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).
thf(915,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(4287,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(219,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__less__iff) ).
thf(1780,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(635,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Owellorder )
=> ( ? [C: $i] : ( C @ ( A @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Orderings_Oord__class_OLeast ) @ ( A @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_LeastI__ex) ).
thf(3209,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Owellorder )
=> ( ? [C: $i] : ( C @ ( A @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Orderings_Oord__class_OLeast ) @ ( A @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__less__imp__less) ).
thf(1230,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(527,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__field )
=> ( ( A @ ( B @ ( C @ ( D @ c_Deriv_Oderiv ) ) ) )
=> ( ( ( B @ ( C @ hAPP ) )
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( B @ ( C @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( A @ ( B @ ( C @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Oinverse @ ( D @ ( D @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Deriv_Oderiv ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DERIV__inverse_H) ).
thf(2850,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__field )
=> ( ( A @ ( B @ ( C @ ( D @ c_Deriv_Oderiv ) ) ) )
=> ( ( ( B @ ( C @ hAPP ) )
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( B @ ( C @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( A @ ( B @ ( C @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Oinverse @ ( D @ ( D @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Deriv_Oderiv ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(104,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Rings_Oring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Oring) ).
thf(1484,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Rings_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(645,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring )
=> ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Polynomial_Opoly ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Polynomial_Opoly ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__minus) ).
thf(3246,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring )
=> ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Polynomial_Opoly ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Polynomial_Opoly ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(1151,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__imp__le) ).
thf(5235,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).
thf(983,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Oring )
=> ( ( ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
<=> ( C
= ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__add__iff2) ).
thf(4561,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Oring )
=> ( ( ( C
= ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( C
= ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(488,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__poly__0__left) ).
thf(2700,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(844,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__power) ).
thf(4020,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(727,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__0 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Osemiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring__0) ).
thf(3554,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__0 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(674,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__field )
=> ( B @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( C @ c_Deriv_Oderiv ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DERIV__cmult__Id) ).
thf(3344,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__field )
=> ( B @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( C @ c_Deriv_Oderiv ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(249,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__less) ).
thf(1869,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(406,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__1) ).
thf(2429,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(748,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oab__group__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__left__minus) ).
thf(3655,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oab__group__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(284,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_RealVector_Oreal__normed__field )
=> ( ( B @ ( C @ ( D @ ( E @ c_Deriv_Oderiv ) ) ) )
=> ( ( B = A )
=> ( A @ ( C @ ( D @ ( E @ c_Deriv_Oderiv ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Deriv_Olemma__DERIV__subst) ).
thf(1980,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_RealVector_Oreal__normed__field )
=> ( ( B @ ( C @ ( D @ ( E @ c_Deriv_Oderiv ) ) ) )
=> ( ( B = A )
=> ( A @ ( C @ ( D @ ( E @ c_Deriv_Oderiv ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(723,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__one) ).
thf(3544,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(169,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Groups_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Oab__group__add) ).
thf(1658,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Groups_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(1052,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C
= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__dvd__iff) ).
thf(4800,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( ( ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C
= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) )
=> ( A @ ( B @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C
= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).
thf(141,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ~ ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
thf(1579,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ~ ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(191,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).
thf(1711,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A = B )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(498,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel1) ).
thf(2747,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(699,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( C
= ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) )
<=> ( ( ( A
= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( C
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__divide__eq) ).
thf(3448,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( ( ( ( A
= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( C
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= B ) ) )
=> ( C
= ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) )
& ( ( C
= ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) )
=> ( ( ( A
= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( C
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(973,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero )
= ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__zero__sym) ).
thf(4522,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ c_Groups_Ozero__class_Ozero )
= ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ c_Groups_Ozero__class_Ozero )
= ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(862,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( D @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pCons__right) ).
thf(4092,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( D @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(1077,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__right) ).
thf(4905,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).
thf(222,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zdiv__trivial) ).
thf(1790,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(1195,axiom,
! [A: $i,B: $i] :
( ( A @ hBOOL )
| ~ ( A @ ( B @ ( c_fconj @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fconj__3) ).
thf(5420,plain,
! [A: $i,B: $i] :
( ( A @ hBOOL )
| ~ ( A @ ( B @ ( c_fconj @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195]) ).
thf(664,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__two) ).
thf(3305,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(85,axiom,
tc_Int_Oint @ class_Rings_Ocomm__ring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).
thf(1432,plain,
tc_Int_Oint @ class_Rings_Ocomm__ring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(892,axiom,
! [A: $i,B: $i] :
( ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__eq__if) ).
thf(4190,plain,
! [A: $i,B: $i] :
( ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(335,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) ).
thf(2165,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(756,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__commute) ).
thf(3691,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(608,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Odiff__right) ).
thf(3114,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(652,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J) ).
thf(3273,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(41,axiom,
tc_Int_Oint @ class_Rings_Ocomm__semiring__0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__0) ).
thf(1317,plain,
tc_Int_Oint @ class_Rings_Ocomm__semiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(613,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( A @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__inverse__less__neg) ).
thf(3127,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( A @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(123,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ominus )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__apply) ).
thf(1538,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ominus )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(441,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( C @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
thf(2545,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( C @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(679,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oord__le__eq__trans) ).
thf(3359,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(1035,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__ab__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__imp__eq) ).
thf(4737,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__ab__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(202,axiom,
tc_Int_Oint @ class_Groups_Oone,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oone) ).
thf(1738,plain,
tc_Int_Oint @ class_Groups_Oone,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(586,axiom,
! [A: $i] :
( ( A @ class_Groups_Ozero )
=> ( ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_Polynomial_Odegree ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__0) ).
thf(3041,plain,
! [A: $i] :
( ( A @ class_Groups_Ozero )
=> ( ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_Polynomial_Odegree ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(794,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Osemiring__1 )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__Suc) ).
thf(3829,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Osemiring__1 )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(709,axiom,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__numerals_I1_J) ).
thf(3493,plain,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(454,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Rings_Odvd )
& ( D @ class_Rings_Ocomm__ring ) )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [E: $i,F: $i] :
( ( A @ ( E @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( F @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__period_I4_J) ).
thf(2579,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Rings_Odvd )
& ( D @ class_Rings_Ocomm__ring ) )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [E: $i,F: $i] :
( ( ( A @ ( B @ ( F @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( E @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( F @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(175,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Groups_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Ogroup__add) ).
thf(1670,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Groups_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(300,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ouminus )
=> ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( D @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__Compl__def) ).
thf(2030,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ouminus )
=> ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( D @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(551,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( A @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__less__imp__less) ).
thf(2939,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( A @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(881,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Opcompose ) ) )
= ( B @ ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Polynomial_OpCons @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ ( C @ c_COMBC ) ) ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ ( C @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ ( C @ tc_Polynomial_Opoly @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ c_COMBB ) ) @ ( C @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ tc_fun ) @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ ( C @ c_COMBC ) ) ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ c_COMBK ) @ ( C @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ ( C @ tc_Polynomial_Opoly @ c_Polynomial_Opoly__rec ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pcompose__def) ).
thf(4150,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Opcompose ) ) )
= ( B @ ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Polynomial_OpCons @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ ( C @ c_COMBC ) ) ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ ( C @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ ( C @ tc_Polynomial_Opoly @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ c_COMBB ) ) @ ( C @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ tc_fun ) @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ ( C @ c_COMBC ) ) ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ c_COMBK ) @ ( C @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ ( C @ tc_Polynomial_Opoly @ c_Polynomial_Opoly__rec ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(154,axiom,
! [A: $i] : ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negative__zless__0) ).
thf(1617,plain,
! [A: $i] : ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(73,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__geq) ).
thf(1404,plain,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__zmod__left) ).
thf(1358,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(361,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__add) ).
thf(2247,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(267,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__int__eq) ).
thf(1934,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) ) ) )
& ( ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(758,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__poly__code_I2_J) ).
thf(3697,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(401,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_coeff__pCons__0) ).
thf(2411,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(428,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Divides_Osemiring__div )
=> ( ( ( D @ ( E @ ( F @ c_Divides_Odiv__class_Omod ) ) )
= ( D @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
=> ( ( ( D @ ( B @ ( F @ c_Divides_Odiv__class_Omod ) ) )
= ( D @ ( A @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
=> ( ( D @ ( B @ ( E @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( F @ c_Divides_Odiv__class_Omod ) ) )
= ( D @ ( A @ ( C @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( F @ c_Divides_Odiv__class_Omod ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__cong) ).
thf(2500,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Divides_Osemiring__div )
=> ( ( ( D @ ( E @ ( F @ c_Divides_Odiv__class_Omod ) ) )
= ( D @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
=> ( ( ( D @ ( B @ ( F @ c_Divides_Odiv__class_Omod ) ) )
= ( D @ ( A @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
=> ( ( D @ ( B @ ( E @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( F @ c_Divides_Odiv__class_Omod ) ) )
= ( D @ ( A @ ( C @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( F @ c_Divides_Odiv__class_Omod ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_Opoly__gcd ) ) @ ( D @ c_Polynomial_Opoly__gcd ) ) )
= ( A @ ( B @ ( D @ c_Polynomial_Opoly__gcd ) ) @ ( C @ ( D @ c_Polynomial_Opoly__gcd ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__gcd_Oassoc) ).
thf(1543,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_Opoly__gcd ) ) @ ( D @ c_Polynomial_Opoly__gcd ) ) )
= ( A @ ( B @ ( D @ c_Polynomial_Opoly__gcd ) ) @ ( C @ ( D @ c_Polynomial_Opoly__gcd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(214,axiom,
tc_Int_Oint @ class_Orderings_Olinorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).
thf(1766,plain,
tc_Int_Oint @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(678,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__frac__num) ).
thf(3356,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(1153,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__trans__Suc) ).
thf(5240,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Limits_Ominus__diff__minus) ).
thf(1353,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(1039,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__1) ).
thf(4748,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).
thf(524,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(2843,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(868,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring )
=> ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__inverse) ).
thf(4106,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring )
=> ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(1095,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__diff__minus) ).
thf(4991,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).
thf(114,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B != A )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
thf(1506,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B != A )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(205,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Fields_Ofield )
=> ( ( E
!= ( F @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ ( D @ ( F @ c_Polynomial_Opdivmod__rel ) ) ) ) )
=> ( A @ ( B @ ( E @ ( F @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( F @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( F @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( D @ ( F @ c_Polynomial_Opdivmod__rel ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pdivmod__rel__smult__right) ).
thf(1749,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Fields_Ofield )
=> ( ( E
!= ( F @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ ( D @ ( F @ c_Polynomial_Opdivmod__rel ) ) ) ) )
=> ( A @ ( B @ ( E @ ( F @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( F @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( F @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( D @ ( F @ c_Polynomial_Opdivmod__rel ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(879,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__int) ).
thf(4143,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(82,axiom,
tc_Int_Oint @ class_Groups_Omonoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).
thf(1427,plain,
tc_Int_Oint @ class_Groups_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(948,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring )
=> ( ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__minus__right) ).
thf(4431,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring )
=> ( ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(686,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield__inverse__zero )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__one__over) ).
thf(3388,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield__inverse__zero )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(112,axiom,
tc_Int_Oint @ class_Groups_Oab__group__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).
thf(1504,plain,
tc_Int_Oint @ class_Groups_Oab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(894,axiom,
! [A: $i] :
( ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__self__eq__0) ).
thf(4202,plain,
! [A: $i] :
( ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(143,axiom,
tc_Int_Oint @ class_Groups_Ozero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).
thf(1585,plain,
tc_Int_Oint @ class_Groups_Ozero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(430,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).
thf(2511,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(1001,axiom,
tc_Nat_Onat @ class_Groups_Ocancel__comm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__comm__monoid__add) ).
thf(4634,plain,
tc_Nat_Onat @ class_Groups_Ocancel__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(609,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__0 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Omult__zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Omult__zero) ).
thf(3117,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__0 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Omult__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(530,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pos__neg) ).
thf(2860,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(555,axiom,
( ( t_a @ class_Rings_Oidom )
=> ~ ( v_p @ ( t_a @ c_Polynomial_Opoly ) @ ( t_a @ ( t_a @ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_assms) ).
thf(2949,plain,
( ( t_a @ class_Rings_Oidom )
=> ~ ( v_p @ ( t_a @ c_Polynomial_Opoly ) @ ( t_a @ ( t_a @ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(514,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Odiff) ).
thf(2807,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Osemiring__1 )
=> ( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ ( D @ c_Nat_Osemiring__1__class_Oof__nat__aux ) ) ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( C @ ( D @ c_Nat_Osemiring__1__class_Oof__nat__aux ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__aux_Osimps_I2_J) ).
thf(1272,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Osemiring__1 )
=> ( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ ( D @ c_Nat_Osemiring__1__class_Oof__nat__aux ) ) ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( C @ ( D @ c_Nat_Osemiring__1__class_Oof__nat__aux ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(1122,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(5100,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).
thf(526,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__1__mult) ).
thf(2848,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(681,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__dvd__1__iff__1) ).
thf(3366,plain,
! [A: $i] :
( ( ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
=> ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(532,axiom,
! [A: $i,B: $i] :
( ( B @ class_Fields_Olinordered__field )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__negative__imp__negative) ).
thf(2865,plain,
! [A: $i,B: $i] :
( ( B @ class_Fields_Olinordered__field )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(545,axiom,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__0) ).
thf(2924,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(979,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zmult1__eq) ).
thf(4548,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(1064,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( ( B
!= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( C @ c_Polynomial_Odegree ) @ ( B @ ( A @ ( C @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) @ ( C @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( ( B @ ( A @ ( C @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) )
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__mod__less) ).
thf(4851,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( ( B
!= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( C @ c_Polynomial_Odegree ) @ ( B @ ( A @ ( C @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) @ ( C @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( ( B @ ( A @ ( C @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) )
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(731,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__eq) ).
thf(3565,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(181,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Omonom ) ) )
= ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ c_fequal @ ( C @ c_If @ ( tc_Nat_Onat @ ( C @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_fun ) @ ( C @ ( tc_Nat_Onat @ c_COMBC ) ) ) @ hAPP ) @ ( C @ ( C @ ( tc_Nat_Onat @ c_COMBC ) ) ) @ hAPP ) @ ( C @ c_Polynomial_OAbs__poly ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_monom__def) ).
thf(1685,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Omonom ) ) )
= ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ c_fequal @ ( C @ c_If @ ( tc_Nat_Onat @ ( C @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_fun ) @ ( C @ ( tc_Nat_Onat @ c_COMBC ) ) ) @ hAPP ) @ ( C @ ( C @ ( tc_Nat_Onat @ c_COMBC ) ) ) @ hAPP ) @ ( C @ c_Polynomial_OAbs__poly ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(131,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Oidom__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(1553,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(236,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Groups_Oab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Oab__semigroup__add) ).
thf(1844,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Groups_Oab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(463,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(2611,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( C @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mod__trivial) ).
thf(1289,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( C @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(1017,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(4678,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(408,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Odivision__ring )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ ( A @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_division__ring__inverse__diff) ).
thf(2435,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Odivision__ring )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ ( A @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(656,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( D @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) )
= ( A @ ( B @ ( D @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) @ ( C @ ( D @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) @ ( A @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_offset__poly__pCons) ).
thf(3284,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( D @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) )
= ( A @ ( B @ ( D @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) @ ( C @ ( D @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) @ ( A @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(502,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__pred) ).
thf(2760,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(468,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Osynthetic__div ) ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_synthetic__div__0) ).
thf(2626,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Osynthetic__div ) ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(40,axiom,
tc_Int_Oint @ class_Rings_Omult__zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).
thf(1316,plain,
tc_Int_Oint @ class_Rings_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(1139,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone @ ( B @ c_Polynomial_Opoly ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__1) ).
thf(5179,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone @ ( B @ c_Polynomial_Opoly ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139]) ).
thf(600,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__divide__less__eq) ).
thf(3092,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(1085,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
| ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Ole__imp__less__or__eq) ).
thf(4945,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
| ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).
thf(518,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1__no__zero__divisors )
=> ( ( ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) )
<=> ( ( A
= ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
| ( A
= ( B @ c_Groups_Oone__class_Oone ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_square__eq__1__iff) ).
thf(2818,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1__no__zero__divisors )
=> ( ( ( ( A
= ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
| ( A
= ( B @ c_Groups_Oone__class_Oone ) ) )
=> ( ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) )
& ( ( ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) )
=> ( ( A
= ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
| ( A
= ( B @ c_Groups_Oone__class_Oone ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(1042,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring )
=> ( ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__zero__imp__zero) ).
thf(4763,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring )
=> ( ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(519,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add) ).
thf(2828,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(1188,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__reduce) ).
thf(5386,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_uminus__dvd__conv_I2_J) ).
thf(1321,plain,
! [A: $i,B: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(1009,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__cancel) ).
thf(4656,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(232,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__field )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide_Odiff) ).
thf(1834,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__field )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(261,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__triv__left) ).
thf(1913,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Oring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__diff__right__eq) ).
thf(1448,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Oring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(424,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring) ).
thf(2490,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(675,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oab__group__add )
=> ( ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__poly__code_I2_J) ).
thf(3346,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oab__group__add )
=> ( ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__not__sym) ).
thf(1390,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(140,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( C = B )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord__eq__less__trans) ).
thf(1575,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( C = B )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(199,axiom,
tc_Int_Oint @ class_Rings_Oring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).
thf(1734,plain,
tc_Int_Oint @ class_Rings_Oring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(1113,axiom,
! [A: $i] :
( ( A @ class_Groups_Ogroup__add )
=> ( ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__zero) ).
thf(5068,plain,
! [A: $i] :
( ( A @ class_Groups_Ogroup__add )
=> ( ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).
thf(511,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pCons__left) ).
thf(2792,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(1177,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring__inverse__zero )
=> ( ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) )
& ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__self__if) ).
thf(5315,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring__inverse__zero )
=> ( ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) )
& ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).
thf(367,axiom,
! [A: $i,B: $i] :
( ( B @ class_Fields_Ofield )
=> ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pdivmod__rel__0) ).
thf(2273,plain,
! [A: $i,B: $i] :
( ( B @ class_Fields_Ofield )
=> ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(338,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__antisym) ).
thf(2174,plain,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(321,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring__1 )
=> ( ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( C @ c_Polynomial_Opoly ) @ hAPP ) @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( C @ c_Polynomial_Osynthetic__div ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_synthetic__div__correct_H) ).
thf(2098,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring__1 )
=> ( ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( C @ c_Polynomial_Opoly ) @ hAPP ) @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( C @ c_Polynomial_Osynthetic__div ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(177,axiom,
tc_Int_Oint @ class_Rings_Olinordered__semiring__strict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).
thf(1674,plain,
tc_Int_Oint @ class_Rings_Olinordered__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(1018,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Ominus) ).
thf(4681,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(242,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Rings_Osemiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Osemiring__1) ).
thf(1854,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Rings_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(641,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B @ ( C @ c_Polynomial_Opos__poly ) )
=> ( ( A @ ( C @ c_Polynomial_Opos__poly ) )
=> ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Opos__poly ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__poly__add) ).
thf(3235,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B @ ( C @ c_Polynomial_Opos__poly ) )
=> ( ( A @ ( C @ c_Polynomial_Opos__poly ) )
=> ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Opos__poly ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(229,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_RealVector_Oreal__normed__field )
=> ( ( C @ ( D @ ( E @ ( F @ c_Deriv_Oderiv ) ) ) )
=> ( ( A @ ( D @ ( B @ ( F @ c_Deriv_Oderiv ) ) ) )
=> ( ( ( D @ ( B @ hAPP ) )
!= ( F @ c_Groups_Ozero__class_Ozero ) )
=> ( D @ ( B @ hAPP ) @ ( D @ ( B @ hAPP ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( E @ hAPP ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ hAPP ) @ ( C @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( E @ ( F @ c_Rings_Oinverse__class_Odivide @ ( F @ ( F @ ( F @ tc_fun ) @ ( F @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ ( F @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( F @ c_Deriv_Oderiv ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DERIV__divide) ).
thf(1822,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_RealVector_Oreal__normed__field )
=> ( ( C @ ( D @ ( E @ ( F @ c_Deriv_Oderiv ) ) ) )
=> ( ( A @ ( D @ ( B @ ( F @ c_Deriv_Oderiv ) ) ) )
=> ( ( ( D @ ( B @ hAPP ) )
!= ( F @ c_Groups_Ozero__class_Ozero ) )
=> ( D @ ( B @ hAPP ) @ ( D @ ( B @ hAPP ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( E @ hAPP ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ hAPP ) @ ( C @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( E @ ( F @ c_Rings_Oinverse__class_Odivide @ ( F @ ( F @ ( F @ tc_fun ) @ ( F @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ ( F @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( F @ c_Deriv_Oderiv ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(1055,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Odivision__ring )
=> ( ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__inverse) ).
thf(4823,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Odivision__ring )
=> ( ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).
thf(1075,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) ).
thf(4900,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).
thf(1026,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
thf(4710,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).
thf(802,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(3864,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(194,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__ring__1 )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__diff) ).
thf(1721,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__ring__1 )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(528,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__mult )
=> ( ( B @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__commutes) ).
thf(2853,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__mult )
=> ( ( B @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(1163,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( B @ ( A @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( A @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__div__equality2) ).
thf(5272,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( B @ ( A @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( A @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).
thf(792,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__gt1) ).
thf(3825,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(444,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Olinorder) ).
thf(2554,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(960,axiom,
! [A: $i,B: $i] :
( ( B @ class_Divides_Osemiring__div )
=> ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( A @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__self) ).
thf(4468,plain,
! [A: $i,B: $i] :
( ( B @ class_Divides_Osemiring__div )
=> ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( A @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(604,axiom,
! [A: $i] :
( ( A @ class_Groups_Ocancel__comm__monoid__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ocancel__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add) ).
thf(3104,plain,
! [A: $i] :
( ( A @ class_Groups_Ocancel__comm__monoid__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ocancel__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(293,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ozero )
=> ( ( ( B @ ( C @ ( D @ c_Polynomial_Omonom ) ) )
= ( B @ ( A @ ( D @ c_Polynomial_Omonom ) ) ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_monom__eq__iff) ).
thf(2004,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ozero )
=> ( ( ( C = A )
=> ( ( B @ ( C @ ( D @ c_Polynomial_Omonom ) ) )
= ( B @ ( A @ ( D @ c_Polynomial_Omonom ) ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_Polynomial_Omonom ) ) )
= ( B @ ( A @ ( D @ c_Polynomial_Omonom ) ) ) )
=> ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(908,axiom,
! [A: $i] :
( ( A @ class_Rings_Ozero__neq__one )
=> ( ( A @ c_Groups_Oone__class_Oone )
!= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__neq__zero) ).
thf(4261,plain,
! [A: $i] :
( ( A @ class_Rings_Ozero__neq__one )
=> ( ( A @ c_Groups_Oone__class_Oone )
!= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(398,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__minus__eq) ).
thf(2394,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( B = A )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(890,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).
thf(4182,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(757,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Oprod__diff__prod) ).
thf(3694,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(917,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ominus__left) ).
thf(4293,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(1193,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( ( A @ ( B @ ( C @ c_Polynomial_Opoly ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( ( B @ ( A @ ( C @ c_Polynomial_Oorder ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__root) ).
thf(5408,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( ( ( ( B @ ( A @ ( C @ c_Polynomial_Oorder ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Opoly ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( C @ c_Polynomial_Opoly ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( B @ ( A @ ( C @ c_Polynomial_Oorder ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__field )
=> ( ( A @ ( B @ ( C @ ( D @ c_Deriv_Oderiv ) ) ) )
=> ( A @ ( D @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Ouminus__class_Ouminus @ ( D @ ( D @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Deriv_Oderiv ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DERIV__minus) ).
thf(1308,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__field )
=> ( ( A @ ( B @ ( C @ ( D @ c_Deriv_Oderiv ) ) ) )
=> ( A @ ( D @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Ouminus__class_Ouminus @ ( D @ ( D @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ c_Deriv_Oderiv ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(453,axiom,
! [A: $i] :
( ( A @ class_Rings_Osemiring__1 )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__1) ).
thf(2576,plain,
! [A: $i] :
( ( A @ class_Rings_Osemiring__1 )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(838,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( A @ ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( ~ ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
& ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__less__eq) ).
thf(3993,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( ( ( ~ ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
& ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) )
=> ( A @ ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
& ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(320,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ozero__left) ).
thf(2095,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(153,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Odiv ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__swap) ).
thf(1614,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Odiv ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(413,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).
thf(2447,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(553,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__power__same) ).
thf(2944,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(183,axiom,
tc_Int_Oint @ class_Rings_Oordered__ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).
thf(1689,plain,
tc_Int_Oint @ class_Rings_Oordered__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(1173,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__pCons) ).
thf(5304,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173]) ).
thf(925,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
thf(4321,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(304,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__int__conv) ).
thf(2041,plain,
! [A: $i] :
( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(882,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Rings_Ozero__neq__one )
& ( C @ class_Rings_Ono__zero__divisors )
& ( C @ class_Rings_Omult__zero )
& ( C @ class_Power_Opower ) )
=> ( ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__eq__0__iff) ).
thf(4153,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Rings_Ozero__neq__one )
& ( C @ class_Rings_Ono__zero__divisors )
& ( C @ class_Rings_Omult__zero )
& ( C @ class_Power_Opower ) )
=> ( ( ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(808,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self4) ).
thf(3879,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(799,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Osemiring__0 )
& ( B @ class_Power_Opower ) )
=> ( ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__0__left) ).
thf(3844,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Osemiring__0 )
& ( B @ class_Power_Opower ) )
=> ( ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(476,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C = B )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__cases) ).
thf(2648,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C = B )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(693,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oidom) ).
thf(3430,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(988,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone @ ( B @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone @ ( B @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_coeff__1) ).
thf(4591,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone @ ( B @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone @ ( B @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(650,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__1) ).
thf(3267,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(919,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__inject) ).
thf(4299,plain,
! [A: $i,B: $i] :
( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(415,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__minus) ).
thf(2462,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(1107,axiom,
! [A: $i] :
( ( A @ class_Rings_Odivision__ring )
=> ( ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( A @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__1) ).
thf(5040,plain,
! [A: $i] :
( ( A @ class_Rings_Odivision__ring )
=> ( ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( A @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).
thf(754,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).
thf(3677,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(389,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__field )
=> ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ ( B @ c_Deriv_Oderiv ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DERIV__inverse) ).
thf(2362,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__field )
=> ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ ( B @ c_Deriv_Oderiv ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(482,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__mult) ).
thf(2680,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(342,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Oadd) ).
thf(2183,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ class_Divides_Osemiring__div )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__by__1) ).
thf(1212,plain,
! [A: $i,B: $i] :
( ( B @ class_Divides_Osemiring__div )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(542,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__0 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__0) ).
thf(2902,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__0 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(326,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__cancel1) ).
thf(2120,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
=> ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(1147,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diffs0__imp__equal) ).
thf(5211,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147]) ).
thf(355,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__add__eq__iff) ).
thf(2230,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(256,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__0__left) ).
thf(1893,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(302,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Rings_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Ocomm__semiring__0) ).
thf(2036,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Rings_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B = A )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord__less__eq__trans) ).
thf(1444,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B = A )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(1143,axiom,
tc_Nat_Onat @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(5196,plain,
tc_Nat_Onat @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).
thf(937,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Ofield )
=> ( ( A @ ( B @ ( C @ ( D @ ( E @ c_Polynomial_Opdivmod__rel ) ) ) ) )
<=> ( ( ( C
!= ( E @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( E @ c_Polynomial_Odegree ) @ ( A @ ( E @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( A
= ( E @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) )
& ( ( C
= ( E @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( B
= ( E @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) )
& ( D
= ( A @ ( C @ ( B @ ( E @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pdivmod__rel__def) ).
thf(4372,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Ofield )
=> ( ( ( ( ( C
!= ( E @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( E @ c_Polynomial_Odegree ) @ ( A @ ( E @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( A
= ( E @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) )
& ( ( C
= ( E @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( B
= ( E @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) )
& ( D
= ( A @ ( C @ ( B @ ( E @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
=> ( A @ ( B @ ( C @ ( D @ ( E @ c_Polynomial_Opdivmod__rel ) ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ ( E @ c_Polynomial_Opdivmod__rel ) ) ) ) )
=> ( ( ( C
!= ( E @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( E @ c_Polynomial_Odegree ) @ ( A @ ( E @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( A
= ( E @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) )
& ( ( C
= ( E @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( B
= ( E @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) )
& ( D
= ( A @ ( C @ ( B @ ( E @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(467,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__left__commute) ).
thf(2623,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(1182,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__unique) ).
thf(5336,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182]) ).
thf(507,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Oadd__left) ).
thf(2779,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(296,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B != A )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE) ).
thf(2019,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B != A )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(997,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Osynthetic__div ) ) @ ( C @ c_Polynomial_Odegree ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__synthetic__div) ).
thf(4619,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Osynthetic__div ) ) @ ( C @ c_Polynomial_Odegree ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(259,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
thf(1908,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(437,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__neg__neg) ).
thf(2534,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(659,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__strict__right__mono) ).
thf(3291,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(568,axiom,
tc_Nat_Onat @ class_Groups_Omonoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).
thf(2983,plain,
tc_Nat_Onat @ class_Groups_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(768,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_Opcompose ) ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( C @ ( D @ c_Polynomial_Opoly ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__pcompose) ).
thf(3733,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_Opcompose ) ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( C @ ( D @ c_Polynomial_Opoly ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(356,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__0 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Osemiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring) ).
thf(2233,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__0 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Osemiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(813,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Odivision__ring )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__minus__divide__divide) ).
thf(3892,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Odivision__ring )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(127,axiom,
tc_HOL_Obool @ class_Orderings_Opreorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
thf(1546,plain,
tc_HOL_Obool @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(1028,axiom,
! [A: $i] :
( ( A @ class_Groups_Oab__group__add )
=> ( ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__poly__code_I1_J) ).
thf(4719,plain,
! [A: $i] :
( ( A @ class_Groups_Oab__group__add )
=> ( ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(556,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ ( D @ c_Nat_Onat_Onat__case ) ) @ hAPP ) )
= ( A @ ( B @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__case__Suc) ).
thf(2951,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ ( D @ c_Nat_Onat_Onat__case ) ) @ hAPP ) )
= ( A @ ( B @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(496,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant ) ) )
<=> ! [D: $i,E: $i] :
( ( D @ ( A @ hAPP ) )
= ( E @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_constant__def) ).
thf(2736,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] :
( ( D @ ( A @ hAPP ) )
= ( E @ ( A @ hAPP ) ) )
=> ( A @ ( B @ ( C @ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant ) ) ) )
& ( ( A @ ( B @ ( C @ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant ) ) )
=> ! [D: $i,E: $i] :
( ( D @ ( A @ hAPP ) )
= ( E @ ( A @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(933,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ozero )
=> ( ( A
!= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Polynomial_Odegree ) @ ( A @ ( B @ c_Polynomial_Ocoeff ) @ hAPP ) )
!= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leading__coeff__neq__0) ).
thf(4357,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ozero )
=> ( ( A
!= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Polynomial_Odegree ) @ ( A @ ( B @ c_Polynomial_Ocoeff ) @ hAPP ) )
!= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(1156,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl3) ).
thf(5247,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).
thf(632,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc1) ).
thf(3203,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(623,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
=> ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Ole__neq__trans) ).
thf(3164,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
=> ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(749,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__commute) ).
thf(3658,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(873,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(4125,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(433,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__0) ).
thf(2517,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(1050,axiom,
! [A: $i,B: $i] :
( B
= ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zdiv__equality) ).
thf(4794,plain,
! [A: $i,B: $i] :
( B
= ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).
thf(483,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_COMBI @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBI__1) ).
thf(2683,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_COMBI @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(761,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ( ( A @ ( B @ ( C @ c_Polynomial_Omonom ) ) )
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
<=> ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_monom__eq__0__iff) ).
thf(3705,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ( ( B
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Omonom ) ) )
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( C @ c_Polynomial_Omonom ) ) )
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult2) ).
thf(1280,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(841,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).
thf(4014,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(274,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( C @ ( D @ ( E @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__dvd__mono) ).
thf(1957,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( C @ ( D @ ( E @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(1130,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
thf(5129,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).
thf(938,axiom,
tc_Nat_Onat @ class_Rings_Ocomm__semiring__0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__0) ).
thf(4399,plain,
tc_Nat_Onat @ class_Rings_Ocomm__semiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(396,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring__inverse__zero )
=> ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__inverse__eq) ).
thf(2385,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring__inverse__zero )
=> ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(1014,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__zadd__distrib) ).
thf(4670,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(782,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__is__0) ).
thf(3785,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(714,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( B @ ( D @ c_Divides_Odiv__class_Odiv ) ) ) ) )
& ( ( C
= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Odiv ) ) )
= ( D @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__mult1__if) ).
thf(3511,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( B @ ( D @ c_Divides_Odiv__class_Odiv ) ) ) ) )
& ( ( C
= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Odiv ) ) )
= ( D @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(809,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__comm__semiring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__mult__strict__left__mono) ).
thf(3882,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__comm__semiring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ class_Fields_Ofield )
=> ( ( C @ ( D @ ( E @ ( F @ ( G @ c_Polynomial_Opdivmod__rel ) ) ) ) )
=> ( ( A @ ( B @ ( E @ ( F @ ( G @ c_Polynomial_Opdivmod__rel ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pdivmod__rel__unique) ).
thf(1395,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ class_Fields_Ofield )
=> ( ( C @ ( D @ ( E @ ( F @ ( G @ c_Polynomial_Opdivmod__rel ) ) ) ) )
=> ( ( A @ ( B @ ( E @ ( F @ ( G @ c_Polynomial_Opdivmod__rel ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(1150,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Ominus) ).
thf(5232,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).
thf(798,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oantisym__conv) ).
thf(3837,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A = B )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(64,axiom,
tc_Int_Oint @ class_Groups_Ocomm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).
thf(1380,plain,
tc_Int_Oint @ class_Groups_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(460,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Ocoeff ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Polynomial_Ocoeff ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_coeff__add) ).
thf(2604,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Ocoeff ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Polynomial_Ocoeff ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(1061,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_coeff__eq__0) ).
thf(4843,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).
thf(716,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__inject__exp) ).
thf(3521,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B = A )
=> ( ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(615,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__1) ).
thf(3132,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( c_Nat_OSuc @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__relations_I1_J) ).
thf(1248,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) ) ) )
& ( ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(307,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_RealVector_Oreal__normed__field )
=> ( ( C @ ( D @ ( E @ ( F @ c_Deriv_Oderiv ) ) ) )
=> ( ( A @ ( D @ ( B @ ( F @ c_Deriv_Oderiv ) ) ) )
=> ( A @ ( C @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( E @ ( F @ c_Groups_Oplus__class_Oplus @ ( F @ ( F @ ( F @ tc_fun ) @ ( F @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ ( F @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( F @ c_Deriv_Oderiv ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DERIV__add) ).
thf(2050,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_RealVector_Oreal__normed__field )
=> ( ( C @ ( D @ ( E @ ( F @ c_Deriv_Oderiv ) ) ) )
=> ( ( A @ ( D @ ( B @ ( F @ c_Deriv_Oderiv ) ) ) )
=> ( A @ ( C @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( E @ ( F @ c_Groups_Oplus__class_Oplus @ ( F @ ( F @ ( F @ tc_fun ) @ ( F @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ ( F @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( F @ c_Deriv_Oderiv ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(505,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( A @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__simps_I2_J) ).
thf(2768,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( A @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(102,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) ) @ ( c_fNot @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oorder_Ostrict__mono ) ) ) )
=> ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oorder_Omono ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Ostrict__mono__mono) ).
thf(1480,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_COMBC ) ) ) @ ( c_fNot @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( c_fconj @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ c_COMBS ) ) @ ( tc_Nat_Onat @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_Nat_Onat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oorder_Ostrict__mono ) ) ) )
=> ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oorder_Omono ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(581,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(3015,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(880,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oord__eq__le__trans) ).
thf(4146,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(499,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring )
=> ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__inverse) ).
thf(2751,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring )
=> ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__neg__pos__less0) ).
thf(1363,plain,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(168,axiom,
tc_Int_Oint @ class_Rings_Ozero__neq__one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).
thf(1657,plain,
tc_Int_Oint @ class_Rings_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(897,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__left__disj) ).
thf(4210,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( ( ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(1124,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__right) ).
thf(5105,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).
thf(1183,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Osemiring__1 )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__add) ).
thf(5339,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Osemiring__1 )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183]) ).
thf(29,axiom,
tc_Int_Oint @ class_Groups_Oab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).
thf(1288,plain,
tc_Int_Oint @ class_Groups_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(669,axiom,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__Suc0__eq__1) ).
thf(3323,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(384,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__0 )
=> ( ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__poly__0__right) ).
thf(2340,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__0 )
=> ( ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(1138,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( B
!= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
!= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Odegree ) )
= ( A @ ( C @ c_Polynomial_Odegree ) @ ( B @ ( C @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__mult__eq) ).
thf(5176,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( B
!= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
!= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Odegree ) )
= ( A @ ( C @ c_Polynomial_Odegree ) @ ( B @ ( C @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).
thf(924,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ ( tc_Nat_Onat @ ( C @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Transcendental_Odiffs ) ) )
= ( A @ ( B @ ( C @ c_Transcendental_Odiffs ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diffs__minus) ).
thf(4318,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ ( tc_Nat_Onat @ ( C @ ( C @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Transcendental_Odiffs ) ) )
= ( A @ ( B @ ( C @ c_Transcendental_Odiffs ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(1134,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc0) ).
thf(5159,plain,
! [A: $i] :
( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).
thf(108,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__div__cancel) ).
thf(1495,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(1073,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1 )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__squared__diff__one__factored) ).
thf(4895,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1 )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).
thf(343,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__mod__minus__right) ).
thf(2186,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(47,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Power_Opower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Power_Opower) ).
thf(1335,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Power_Opower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(185,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Divides_Oring__div )
=> ( ( ( D @ ( E @ ( F @ c_Divides_Odiv__class_Omod ) ) )
= ( D @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
=> ( ( ( D @ ( B @ ( F @ c_Divides_Odiv__class_Omod ) ) )
= ( D @ ( A @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
=> ( ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ c_Divides_Odiv__class_Omod ) ) )
= ( D @ ( A @ ( C @ ( F @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ c_Divides_Odiv__class_Omod ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__diff__cong) ).
thf(1693,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Divides_Oring__div )
=> ( ( ( D @ ( E @ ( F @ c_Divides_Odiv__class_Omod ) ) )
= ( D @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
=> ( ( ( D @ ( B @ ( F @ c_Divides_Odiv__class_Omod ) ) )
= ( D @ ( A @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
=> ( ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ c_Divides_Odiv__class_Omod ) ) )
= ( D @ ( A @ ( C @ ( F @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( F @ c_Divides_Odiv__class_Omod ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(764,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Oinject) ).
thf(3716,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( B @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(704,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring )
=> ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__inverse__eq__divide) ).
thf(3479,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring )
=> ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(403,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( B @ c_Polynomial_Ocoeff ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ ( tc_Nat_Onat @ ( B @ ( B @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Polynomial_OAbs__poly ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_uminus__poly__def) ).
thf(2417,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( B @ c_Polynomial_Ocoeff ) @ ( B @ c_Groups_Ouminus__class_Ouminus @ ( tc_Nat_Onat @ ( B @ ( B @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Polynomial_OAbs__poly ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(631,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Oidom )
& ( B @ class_Int_Oring__char__0 ) )
=> ( ( ( A @ ( B @ c_Polynomial_Opoly ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Opoly ) ) )
<=> ( A
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__zero) ).
thf(3196,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Oidom )
& ( B @ class_Int_Oring__char__0 ) )
=> ( ( ( A
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Polynomial_Opoly ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Opoly ) ) ) )
& ( ( ( A @ ( B @ c_Polynomial_Opoly ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Opoly ) ) )
=> ( A
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(1157,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__1__left) ).
thf(5251,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).
thf(1106,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__divide__less__eq) ).
thf(5036,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).
thf(952,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Odivision__ring__inverse__zero )
=> ( ( ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( A @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__eq__imp__eq) ).
thf(4442,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Odivision__ring__inverse__zero )
=> ( ( ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( A @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(847,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) ) )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negative__eq__positive) ).
thf(4034,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) ) ) )
& ( ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(778,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Ozero )
=> ( ( A @ ( B @ ( F @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( F @ ( E @ c_Polynomial_Opoly__rec ) ) ) ) )
= ( A @ ( C @ ( D @ ( F @ ( E @ c_Polynomial_Opoly__rec ) ) ) ) @ ( D @ ( F @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_fequal @ hAPP ) @ ( E @ c_If @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__rec_Osimps) ).
thf(3765,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Ozero )
=> ( ( A @ ( B @ ( F @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( F @ ( E @ c_Polynomial_Opoly__rec ) ) ) ) )
= ( A @ ( C @ ( D @ ( F @ ( E @ c_Polynomial_Opoly__rec ) ) ) ) @ ( D @ ( F @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_fequal @ hAPP ) @ ( E @ c_If @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(354,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).
thf(2223,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(512,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__0 )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__semigroup__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__mult) ).
thf(2795,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__0 )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__semigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(1166,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__power) ).
thf(5283,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166]) ).
thf(1178,axiom,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
thf(5322,plain,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178]) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ozero )
=> ( ( A @ ( B @ c_Polynomial_Ocoeff ) @ ( B @ c_Polynomial_OAbs__poly ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_coeff__inverse) ).
thf(1346,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ozero )
=> ( ( A @ ( B @ c_Polynomial_Ocoeff ) @ ( B @ c_Polynomial_OAbs__poly ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(1080,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( ( A @ ( B @ ( C @ c_Polynomial_Opoly ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
<=> ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__eq__0__iff__dvd) ).
thf(4923,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Opoly ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( C @ c_Polynomial_Opoly ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__not__zless) ).
thf(1261,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(804,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_RealVector_Oreal__normed__field )
=> ( ( B @ ( C @ ( D @ hAPP ) @ ( E @ ( F @ c_Deriv_Oderiv ) ) ) )
=> ( ( A @ ( C @ ( D @ ( F @ c_Deriv_Oderiv ) ) ) )
=> ( A @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ ( F @ ( F @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ c_Deriv_Oderiv ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DERIV__chain2) ).
thf(3869,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_RealVector_Oreal__normed__field )
=> ( ( B @ ( C @ ( D @ hAPP ) @ ( E @ ( F @ c_Deriv_Oderiv ) ) ) )
=> ( ( A @ ( C @ ( D @ ( F @ c_Deriv_Oderiv ) ) ) )
=> ( A @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ ( F @ ( F @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ c_Deriv_Oderiv ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(417,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Ocoeff ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_coeff__smult) ).
thf(2467,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_Osmult @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Ocoeff ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(707,axiom,
! [A: $i] :
( ( A @ class_Groups_Ocancel__comm__monoid__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ocancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add) ).
thf(3489,plain,
! [A: $i] :
( ( A @ class_Groups_Ocancel__comm__monoid__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ocancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(904,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__assoc) ).
thf(4239,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(902,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel2) ).
thf(4229,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(1010,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( B @ ( A @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Divides_Odiv__class_Odiv ) ) )
= ( C @ c_Groups_Oone__class_Oone @ ( B @ ( A @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__add__self2) ).
thf(4659,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( B @ ( A @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Divides_Odiv__class_Odiv ) ) )
= ( C @ c_Groups_Oone__class_Oone @ ( B @ ( A @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(811,axiom,
! [A: $i,B: $i] :
( ( B @ class_Fields_Ofield )
=> ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_field__class_Onormalizing__field__rules_I2_J) ).
thf(3886,plain,
! [A: $i,B: $i] :
( ( B @ class_Fields_Ofield )
=> ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) )
= ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(439,axiom,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__zeroE) ).
thf(2539,plain,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zminus1__not__zero) ).
thf(1299,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(789,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ono__zero__divisors )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_no__zero__divisors) ).
thf(3812,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ono__zero__divisors )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(931,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Opos__poly ) )
<=> ( ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ( A
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) )
| ( A @ ( C @ c_Polynomial_Opos__poly ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__poly__pCons) ).
thf(4345,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( ( ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ( A
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) )
| ( A @ ( C @ c_Polynomial_Opos__poly ) ) )
=> ( A @ ( B @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Opos__poly ) ) )
& ( ( A @ ( B @ ( C @ c_Polynomial_OpCons @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Opos__poly ) )
=> ( ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ( A
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) )
| ( A @ ( C @ c_Polynomial_Opos__poly ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(899,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__self) ).
thf(4221,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(673,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__mult) ).
thf(3341,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(266,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Opos__poly ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__poly__def) ).
thf(1930,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( ( B @ ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Opos__poly ) )
=> ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Opos__poly ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(387,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__int) ).
thf(2353,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(1164,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__0 )
=> ( ( ( A @ ( B @ ( C @ c_Polynomial_Osynthetic__div ) ) )
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( B @ ( C @ c_Polynomial_Odegree ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_synthetic__div__eq__0__iff) ).
thf(5275,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__0 )
=> ( ( ( ( B @ ( C @ c_Polynomial_Odegree ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Osynthetic__div ) ) )
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( C @ c_Polynomial_Osynthetic__div ) ) )
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( C @ c_Polynomial_Odegree ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164]) ).
thf(359,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ono__zero__divisors )
=> ( ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divisors__zero) ).
thf(2241,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ono__zero__divisors )
=> ( ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(327,axiom,
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__numerals_I2_J) ).
thf(2127,plain,
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(1063,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_field__divide__inverse) ).
thf(4848,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).
thf(515,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__imp__neq) ).
thf(2810,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(53,axiom,
tc_Int_Oint @ class_Nat_Osemiring__char__0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Nat_Osemiring__char__0) ).
thf(1352,plain,
tc_Int_Oint @ class_Nat_Osemiring__char__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(905,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( A
!= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ~ ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ tc_Polynomial_Opoly @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Osgn__class_Osgn ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) )
& ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ tc_Polynomial_Opoly @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Osgn__class_Osgn ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone ) ) ) ) )
& ( ( A
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Osgn__class_Osgn ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__poly__def) ).
thf(4242,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( A
!= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ~ ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ tc_Polynomial_Opoly @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Osgn__class_Osgn ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) )
& ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ tc_Polynomial_Opoly @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Osgn__class_Osgn ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone ) ) ) ) )
& ( ( A
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Osgn__class_Osgn ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(122,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__relations_I2_J) ).
thf(1532,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(540,axiom,
tc_Nat_Onat @ class_Orderings_Opreorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
thf(2898,plain,
tc_Nat_Onat @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(66,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Osemiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring__1) ).
thf(1384,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(689,axiom,
! [A: $i,B: $i] :
( ( B != A )
<=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
thf(3411,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( B != A ) )
& ( ( B != A )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(422,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__antisym) ).
thf(2485,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(282,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Groups_Ocomm__monoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Ocomm__monoid__mult) ).
thf(1976,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Groups_Ocomm__monoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(130,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Oring__div )
=> ( ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_Divides_Odiv__class_Odiv ) ) )
= ( B @ ( A @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__div__neg) ).
thf(1550,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Oring__div )
=> ( ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_Divides_Odiv__class_Odiv ) ) )
= ( B @ ( A @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(969,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ozero )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Omonom ) ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_monom__eq__0) ).
thf(4506,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ozero )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Omonom ) ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(853,axiom,
tc_Nat_Onat @ class_Groups_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
thf(4066,plain,
tc_Nat_Onat @ class_Groups_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(110,axiom,
tc_Int_Oint @ class_Groups_Ominus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ominus) ).
thf(1500,plain,
tc_Int_Oint @ class_Groups_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(1110,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Power_Opower_Opower ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ ( E @ c_Power_Opower_Opower ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power_Opower_Opower__Suc) ).
thf(5060,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Power_Opower_Opower ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ ( E @ c_Power_Opower_Opower ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).
thf(940,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__power__divide) ).
thf(4410,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(147,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__triv__right) ).
thf(1597,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(485,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_RealVector_Oreal__normed__field )
=> ( ( C @ ( D @ ( E @ ( F @ c_Deriv_Oderiv ) ) ) )
=> ( ( A @ ( D @ ( B @ ( F @ c_Deriv_Oderiv ) ) ) )
=> ( D @ ( E @ hAPP ) @ ( A @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ hAPP ) @ ( C @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ ( F @ ( F @ ( F @ tc_fun ) @ ( F @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ ( F @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( F @ c_Deriv_Oderiv ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DERIV__mult) ).
thf(2687,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_RealVector_Oreal__normed__field )
=> ( ( C @ ( D @ ( E @ ( F @ c_Deriv_Oderiv ) ) ) )
=> ( ( A @ ( D @ ( B @ ( F @ c_Deriv_Oderiv ) ) ) )
=> ( D @ ( E @ hAPP ) @ ( A @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ hAPP ) @ ( C @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ ( F @ ( F @ ( F @ tc_fun ) @ ( F @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ ( F @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( F @ c_Deriv_Oderiv ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(251,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__dvd__iff) ).
thf(1880,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring__1 )
=> ( ( ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(113,axiom,
tc_Int_Oint @ class_Rings_Olinordered__idom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).
thf(1505,plain,
tc_Int_Oint @ class_Rings_Olinordered__idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(820,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__less__power) ).
thf(3918,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(860,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring) ).
thf(4088,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(166,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
| ( B = A )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__linear) ).
thf(1653,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
| ( B = A )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(276,axiom,
tc_Int_Oint @ class_Power_Opower,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Power_Opower) ).
thf(1962,plain,
tc_Int_Oint @ class_Power_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(137,axiom,
! [A: $i,B: $i] :
( ( B @ class_Divides_Osemiring__div )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__by__0) ).
thf(1565,plain,
! [A: $i,B: $i] :
( ( B @ class_Divides_Osemiring__div )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(239,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mod) ).
thf(1848,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(77,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__dvd) ).
thf(1416,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(694,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__idom) ).
thf(3432,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(1078,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(4908,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).
thf(668,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( A
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equal__neg__zero) ).
thf(3316,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) ) )
& ( ( A
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus @ hAPP ) ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(661,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Odiv ) ) )
= ( C @ ( B @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self1) ).
thf(3296,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Odiv ) ) )
= ( C @ ( B @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(339,axiom,
! [A: $i,B: $i] :
( ( B @ class_Fields_Olinordered__field )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_positive__imp__inverse__positive) ).
thf(2177,plain,
! [A: $i,B: $i] :
( ( B @ class_Fields_Olinordered__field )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(506,axiom,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( c_Nat_OSuc @ hAPP ) )
!= A )
=> ( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( c_Nat_OSuc @ hAPP ) )
= A )
=> ( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__Suc) ).
thf(2771,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( c_Nat_OSuc @ hAPP ) )
!= A )
=> ( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( c_Nat_OSuc @ hAPP ) )
= A )
=> ( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(775,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pow__divides__eq__int) ).
thf(3753,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C @ ( A @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(816,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
thf(3901,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(580,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ c_Groups_Oone__class_Oone @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__decreasing) ).
thf(3013,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ c_Groups_Oone__class_Oone @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(150,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Rings_Osemiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Osemiring) ).
thf(1606,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Rings_Osemiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(702,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Osemiring__1 )
=> ( ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus @ ( B @ ( B @ ( B @ c_COMBC ) ) ) @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat__aux ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__1__class_Oof__nat__code) ).
thf(3474,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Osemiring__1 )
=> ( ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus @ ( B @ ( B @ ( B @ c_COMBC ) ) ) @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat__aux ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(929,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Rings_Odvd )
& ( D @ class_Rings_Ocomm__ring ) )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [E: $i,F: $i] :
( ( A @ ( E @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( F @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__period_I3_J) ).
thf(4335,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Rings_Odvd )
& ( D @ class_Rings_Ocomm__ring ) )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [E: $i,F: $i] :
( ( ( A @ ( B @ ( F @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( E @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( F @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(1137,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__less__divide__eq) ).
thf(5172,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).
thf(1056,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).
thf(4826,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).
thf(717,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__one) ).
thf(3528,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(500,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__add) ).
thf(2754,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse @ hAPP ) @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(479,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__neg__pos) ).
thf(2672,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(473,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ~ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__less__zero) ).
thf(2640,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ~ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(448,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oring__1__no__zero__divisors ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors) ).
thf(2563,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oring__1__no__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(1174,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__algebra )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Ozero) ).
thf(5307,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__algebra )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).
thf(1176,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) )
= ( B @ ( C @ c_Polynomial_OpCons @ ( A @ ( C @ c_Polynomial_Osmult @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ ( C @ tc_Polynomial_Opoly @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ c_COMBS ) ) @ hAPP ) @ ( C @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ c_COMBK ) @ ( C @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ ( C @ tc_Polynomial_Opoly @ c_Polynomial_Opoly__rec ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_offset__poly__def) ).
thf(5312,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) )
= ( B @ ( C @ c_Polynomial_OpCons @ ( A @ ( C @ c_Polynomial_Osmult @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ ( C @ tc_Polynomial_Opoly @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ c_COMBS ) ) @ hAPP ) @ ( C @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ c_COMBK ) @ ( C @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ ( C @ tc_Polynomial_Opoly @ ( C @ tc_Polynomial_Opoly @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ ( C @ tc_Polynomial_Opoly @ c_Polynomial_Opoly__rec ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176]) ).
thf(269,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( A @ ( A @ ( B @ ( C @ c_Polynomial_Opoly__gcd ) ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__gcd__dvd2) ).
thf(1945,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( A @ ( A @ ( B @ ( C @ c_Polynomial_Opoly__gcd ) ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(662,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1__right) ).
thf(3299,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(981,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__class_Odistrib) ).
thf(4555,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(201,axiom,
tc_Int_Oint @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(1737,plain,
tc_Int_Oint @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(601,axiom,
! [A: $i] : ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gcd__lcm__complete__lattice__nat_Otop__greatest) ).
thf(3096,plain,
! [A: $i] : ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(349,axiom,
! [A: $i] : ( A @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessI) ).
thf(2206,plain,
! [A: $i] : ( A @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(179,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_RealVector_Oreal__normed__field )
=> ( ( B @ ( C @ ( D @ ( E @ c_Deriv_Oderiv ) ) ) )
=> ( A @ ( B @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ ( E @ c_Rings_Oinverse__class_Odivide @ ( E @ ( E @ ( E @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( E @ c_COMBC ) ) ) @ hAPP ) @ ( E @ c_Deriv_Oderiv ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DERIV__cdivide) ).
thf(1681,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_RealVector_Oreal__normed__field )
=> ( ( B @ ( C @ ( D @ ( E @ c_Deriv_Oderiv ) ) ) )
=> ( A @ ( B @ ( E @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ ( E @ c_Rings_Oinverse__class_Odivide @ ( E @ ( E @ ( E @ tc_fun ) @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( E @ c_COMBC ) ) ) @ hAPP ) @ ( E @ c_Deriv_Oderiv ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(537,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__left__mono__neg) ).
thf(2887,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(697,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Odiff) ).
thf(3443,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(409,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBS__1) ).
thf(2438,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(358,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( A @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Divides_Odiv__class_Omod ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self2__is__0) ).
thf(2238,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( A @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Divides_Odiv__class_Omod ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(850,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
thf(4056,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(744,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mult__distrib2) ).
thf(3637,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(573,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__left__eq) ).
thf(2993,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(345,axiom,
tc_Nat_Onat @ class_Orderings_Oord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
thf(2191,plain,
tc_Nat_Onat @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Groups_Omonoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Omonoid__add) ).
thf(1204,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ class_Groups_Omonoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(318,axiom,
! [A: $i,B: $i] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
thf(2087,plain,
! [A: $i,B: $i] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(958,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__0 )
=> ( ( ( A @ ( B @ ( C @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) )
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
<=> ( B
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_offset__poly__eq__0__iff) ).
thf(4459,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__0 )
=> ( ( ( B
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) )
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( C @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) )
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( B
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(588,axiom,
! [A: $i,B: $i] :
( ( B @ class_Divides_Osemiring__div )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__by__1) ).
thf(3047,plain,
! [A: $i,B: $i] :
( ( B @ class_Divides_Osemiring__div )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(418,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc__less) ).
thf(2470,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(260,axiom,
tc_Int_Oint @ class_Groups_Oab__semigroup__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).
thf(1912,plain,
tc_Int_Oint @ class_Groups_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(567,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring )
=> ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__self) ).
thf(2980,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring )
=> ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(5976,plain,
$false,
inference(e,[status(thm)],[2163,3021,3873,1411,1469,4169,4729,3434,1237,1840,3969,2559,3927,2331,5028,1818,1950,1586,1501,4447,1337,1718,5088,2744,2889,2295,3053,4450,4005,2336,3008,2131,3661,1767,2921,4290,3477,2595,1850,4166,2250,3534,2104,4226,4075,2659,5242,3377,1401,4960,4603,2282,5405,4973,5383,1437,4479,1486,3681,3990,3072,1924,3762,3905,1522,2495,5292,2062,3549,1422,4697,3959,3912,3098,4326,2380,1793,5237,2195,1788,1608,4090,4418,2933,1275,3616,1327,1988,1761,3313,4435,3895,1458,3276,2607,2686,1756,1310,3004,4647,3942,3135,4097,4884,4870,3044,1735,1867,3175,2316,3446,5257,4638,1872,4650,2168,5005,3562,4941,2723,2432,3502,5123,1645,1529,2531,4775,2957,2763,3915,2548,3249,1441,1601,1386,3898,2082,4137,1724,1475,3809,4607,1366,4665,5269,4610,1703,1228,1482,5352,5342,1887,1628,5429,2328,4692,3495,4224,4761,3821,3125,1455,2703,3263,4439,3029,4743,3425,1430,2814,1985,4422,1660,1760,4956,4415,2269,2444,1860,2217,3542,1313,4275,5182,4023,3089,2488,5289,4568,3803,5108,4766,4428,2571,2356,2420,4119,5214,5199,2049,1890,4622,2635,2301,5077,1232,1847,1922,2691,1892,3374,3385,4179,5193,4830,3084,4551,1568,4368,2520,4632,3835,2989,1963,5091,4471,5020,4400,4302,2388,5264,1465,4173,2090,5333,1418,3702,1858,4724,4134,1581,3152,2073,3851,1489,4205,4988,1302,1664,3966,2027,4903,3075,4072,4578,2105,4857,4258,2996,3724,4454,2782,1828,3973,1978,4751,3537,1377,1215,1896,3712,1622,4996,2286,1201,4707,3211,1696,2833,3739,3505,4504,2523,1796,1526,2137,2002,3955,3243,3327,1433,2965,4519,1697,3559,4082,1564,1863,2954,2011,4199,4323,4589,2574,3186,5167,1338,1915,1311,1730,3011,1206,4604,3984,3265,2646,1306,4531,5017,3531,3635,2047,5117,4031,4100,1768,2382,2061,5281,4999,2000,1636,2441,2409,1223,4466,3827,3603,4434,3742,4128,3884,2414,3664,5049,2589,1900,1723,4016,2560,3867,5002,4785,4499,4284,1619,4821,2986,3778,3889,3471,4044,1560,2445,4280,4140,1365,2477,1555,1951,2179,4942,1656,1407,3408,3799,4063,3282,3307,5302,1837,1968,3090,2565,4994,3137,3349,3556,1819,1624,3546,4746,4740,3050,2313,2492,4104,1634,1392,3667,4732,3731,1592,4957,2840,2973,1498,1672,2726,4840,4012,3237,4109,3001,3782,1234,1541,3482,1762,2515,1270,1772,1259,3122,2946,2990,2377,4668,1953,4512,5423,1804,5345,2895,2709,1970,3218,1856,3518,3963,4095,3119,3746,3440,3205,3087,3018,4898,4676,1683,1361,4772,2830,2868,4545,3032,3194,2038,3643,4457,2472,3935,4653,1329,2877,3952,4951,1942,4276,5080,1292,1739,1461,4425,3714,3728,4421,4315,1424,1414,2053,1842,1810,4861,4054,3428,2551,2085,3486,2536,1451,2836,2845,3743,1668,4482,2465,2497,3937,1947,1984,1852,2862,1720,2140,1825,2968,5063,1776,1263,4846,3611,2766,2052,1599,3333,4953,3109,4069,3920,2272,3215,1525,5245,3279,4966,3173,2076,2368,5417,3508,5126,2423,5170,4163,3147,1991,2788,3834,1318,3802,5310,5153,2926,4644,3225,5402,4625,2208,4782,3592,1846,1663,3190,2189,3422,5295,2617,3675,4308,2235,1278,2001,1510,1764,4131,2677,2904,2585,3491,3289,4797,1595,4503,4017,1374,2260,2936,2729,1754,2292,1959,2556,4354,3871,2275,2033,3257,3607,3079,1747,2941,1548,1927,1631,5043,4786,4662,2970,3768,1884,3240,5065,1752,4122,5099,5097,1965,2134,4341,3070,1784,1389,3736,3081,3945,2674,2568,2716,3604,1520,4612,4769,1256,1226,5022,2959,3213,2220,1707,4413,1332,4854,1258,2474,1356,3170,1675,1428,4251,4537,3796,5185,5427,4558,4186,4096,1271,4837,3646,4112,4171,4236,1865,4218,3594,1997,3700,4060,2706,3832,1765,3302,3568,5432,1638,4887,4716,3101,4929,2214,5103,3287,2257,1492,5222,4616,1690,3384,2065,2079,2311,1209,5071,3352,4704,5143,1282,4369,2642,3815,2637,5325,3551,4305,1349,3270,4601,3106,3468,1542,2856,4176,3138,1571,2871,1376,4509,1439,5267,2197,4477,1667,4694,4911,4818,5335,2757,4208,4332,2785,2874,4296,2974,1688,2182,4635,5114,5202,3747,2025,2632,4445,2610,4882,1557,2129,2343,4833,1731,4264,3572,4985,5286,5392,3614,2542,2289,4726,3861,2928,1381,3150,4684,3539,2350,3759,2620,3806,4085,2931,2797,2101,5299,4067,3876,2365,2962,5254,2401,1699,3627,2171,5197,1245,2592,2244,1435,2022,3363,3310,1477,3325,3178,4282,2999,2156,2984,1973,4473,1562,2614,1304,2107,5025,4529,4879,2629,1340,1472,2333,2899,5435,1626,2816,4690,2318,3206,3293,4598,3161,4735,1420,3981,2503,2449,1509,2597,4581,5133,4722,1547,3640,4360,3112,2661,2012,1647,4534,5074,3129,4641,2689,3988,2513,2298,3391,2977,1611,2375,4939,5399,2192,4673,4287,1780,3209,1230,2850,1484,3246,5235,4561,2700,4020,3554,3344,1869,2429,3655,1980,3544,1658,4800,1579,1711,2747,3448,4522,4092,4905,1790,5420,3305,1432,4190,2165,3691,3114,3273,1317,3127,1538,2545,3359,4737,1738,3041,3829,3493,2579,1670,2030,2939,4150,1617,1404,1358,2247,1934,3697,2411,2500,1543,1766,3356,5240,1353,4748,2843,4106,4991,1506,1749,4143,1427,4431,3388,1504,4202,1585,2511,4634,3117,2860,2949,2807,1272,5100,2848,3366,2865,2924,4548,4851,3565,1685,1553,1844,2611,1289,4678,2435,3284,2760,2626,1316,5179,3092,4945,2818,4763,2828,5386,1321,4656,1834,1913,1448,2490,3346,1390,1575,1734,5068,2792,5315,2273,2174,2098,1674,4681,1854,3235,1822,4823,4900,4710,3864,1721,2853,5272,3825,2554,4468,3104,2004,4261,2394,4182,3694,4293,5408,1308,2576,3993,2095,1614,2447,2944,1689,5304,4321,2041,4153,3879,3844,2648,3430,4591,3267,4299,2462,5040,3677,2362,2680,2183,1212,2902,2120,5211,2230,1893,2036,1444,5196,4372,2623,5336,2779,2019,4619,1908,2534,3291,2983,3733,2233,3892,1546,4719,2951,2736,4357,5247,3203,3164,3658,4125,2517,4794,2683,3705,1280,4014,1957,5129,4399,2385,4670,3785,3511,3882,1395,5232,3837,1380,2604,4843,3521,3132,1248,2050,2768,1480,3015,4146,2751,1363,1657,4210,5105,5339,1288,3323,2340,5176,4318,5159,1495,4895,2186,1335,1693,3716,3479,2417,3196,5251,5036,4442,4034,3765,2223,2795,5283,5322,1346,4923,1261,3869,2467,3489,4239,4229,4659,3886,2539,1299,3812,4345,4221,3341,1930,2353,5275,2241,2127,4848,2810,1352,4242,1532,2898,1384,3411,2485,1976,1550,4506,4066,1500,5060,4410,1597,2687,1880,1505,3918,4088,1653,1962,1565,1848,1416,3432,4908,3316,3296,2177,2771,3753,3901,3013,1606,3474,4335,5172,4826,3528,2754,2672,2640,2563,5307,5312,1945,3299,4555,1737,3096,2206,1681,2887,3443,2438,2238,4056,3637,2993,2191,1204,2087,4459,3047,2470,1912,2980]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW246+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/0.41 % Computer : n019.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 15:32:21 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.85/1.00 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.72/1.53 % [INFO] Parsing done (526ms).
% 2.72/1.55 % [INFO] Running in sequential loop mode.
% 3.65/1.94 % [INFO] eprover registered as external prover.
% 3.65/1.95 % [INFO] Scanning for conjecture ...
% 4.69/2.21 % [INFO] Found a conjecture (or negated_conjecture) and 1198 axioms. Running axiom selection ...
% 5.67/2.43 % [INFO] Axiom selection finished. Selected 1198 axioms (removed 0 axioms).
% 7.54/2.83 % [INFO] Problem is first-order (TPTP FOF).
% 7.54/2.87 % [INFO] Type checking passed.
% 7.54/2.88 % [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 ...
% 46.80/11.98 % External prover 'e' found a proof!
% 46.80/11.99 % [INFO] Killing All external provers ...
% 46.80/11.99 % Time passed: 11432ms (effective reasoning time: 10432ms)
% 46.80/11.99 % 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)>
% 46.80/12.00 % 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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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
% 46.80/12.00 % No. of inferences in proof: 2400
% 46.80/12.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 11432 ms resp. 10432 ms w/o parsing
% 50.91/12.79 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 50.91/12.81 % [INFO] Killing All external provers ...
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