%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW272+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n008.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 09:09:47 AM UTC 2026
% Result : Theorem 50.30s 12.04s
% Output : Refutation 53.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1065
% Syntax : Number of formulae : 2132 ( 504 unt; 0 typ; 0 def)
% Number of atoms : 5594 (1798 equ; 0 cnn)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 31067 ( 384 ~; 144 |; 448 &;27221 @)
% ( 190 <=>;2680 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 111 ( 109 usr; 13 con; 0-5 aty)
% Number of variables : 5071 ( 0 ^;5040 !; 31 ?;5071 :)
% Comments :
%------------------------------------------------------------------------------
thf(v_s_____decl,type,
v_s____: $i ).
thf(c_Groups_Ozero__class_Ozero_decl,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
thf(tc_Polynomial_Opoly_decl,type,
tc_Polynomial_Opoly: $i > $i ).
thf(tc_Complex_Ocomplex_decl,type,
tc_Complex_Ocomplex: $i ).
thf(class_Rings_Olinordered__semidom_decl,type,
class_Rings_Olinordered__semidom: $i > $o ).
thf(c_Orderings_Oord__class_Oless__eq_decl,type,
c_Orderings_Oord__class_Oless__eq: $i > $i > $i > $o ).
thf(c_Groups_Oone__class_Oone_decl,type,
c_Groups_Oone__class_Oone: $i > $i ).
thf(tc_Nat_Onat_decl,type,
tc_Nat_Onat: $i ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i ).
thf(c_Power_Opower__class_Opower_decl,type,
c_Power_Opower__class_Opower: $i > $i ).
thf(c_Orderings_Oord__class_Oless_decl,type,
c_Orderings_Oord__class_Oless: $i > $i > $i > $o ).
thf(c_Groups_Otimes__class_Otimes_decl,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
thf(class_Fields_Olinordered__field__inverse__zero_decl,type,
class_Fields_Olinordered__field__inverse__zero: $i > $o ).
thf(c_Rings_Oinverse__class_Oinverse_decl,type,
c_Rings_Oinverse__class_Oinverse: $i > $i > $i ).
thf(c_Groups_Oplus__class_Oplus_decl,type,
c_Groups_Oplus__class_Oplus: $i > $i > $i > $i ).
thf(c_Nat_OSuc_decl,type,
c_Nat_OSuc: $i > $i ).
thf(tc_Int_Oint_decl,type,
tc_Int_Oint: $i ).
thf(class_Rings_Olinordered__idom_decl,type,
class_Rings_Olinordered__idom: $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(c_Divides_Odiv__class_Omod_decl,type,
c_Divides_Odiv__class_Omod: $i > $i > $i > $i ).
thf(c_Groups_Ouminus__class_Ouminus_decl,type,
c_Groups_Ouminus__class_Ouminus: $i > $i > $i ).
thf(class_Power_Opower_decl,type,
class_Power_Opower: $i > $o ).
thf(c_Power_Opower_Opower_decl,type,
c_Power_Opower_Opower: $i > $i > $i > $i ).
thf(class_Orderings_Oord_decl,type,
class_Orderings_Oord: $i > $o ).
thf(tc_fun_decl,type,
tc_fun: $i > $i > $i ).
thf(class_Groups_Oordered__ab__semigroup__add__imp__le_decl,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
thf(c_Groups_Ominus__class_Ominus_decl,type,
c_Groups_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(class_Rings_Oordered__cancel__semiring_decl,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
thf(c_fequal_decl,type,
c_fequal: $i > $i > $i ).
thf(class_Rings_Ocomm__semiring__1_decl,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
thf(class_Groups_Oordered__ab__semigroup__add_decl,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
thf(class_Groups_Oordered__cancel__ab__semigroup__add_decl,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
thf(class_Groups_Ogroup__add_decl,type,
class_Groups_Ogroup__add: $i > $o ).
thf(class_Groups_Ouminus_decl,type,
class_Groups_Ouminus: $i > $o ).
thf(class_Rings_Oordered__semiring_decl,type,
class_Rings_Oordered__semiring: $i > $o ).
thf(class_Rings_Ocomm__semiring_decl,type,
class_Rings_Ocomm__semiring: $i > $o ).
thf(class_Divides_Osemiring__div_decl,type,
class_Divides_Osemiring__div: $i > $o ).
thf(class_Groups_Oab__semigroup__add_decl,type,
class_Groups_Oab__semigroup__add: $i > $o ).
thf(class_Rings_Olinordered__semiring__1_decl,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
thf(class_Rings_Omult__zero_decl,type,
class_Rings_Omult__zero: $i > $o ).
thf(class_Rings_Olinordered__semiring__1__strict_decl,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
thf(class_Rings_Ocomm__semiring__0_decl,type,
class_Rings_Ocomm__semiring__0: $i > $o ).
thf(class_Rings_Oordered__ring_decl,type,
class_Rings_Oordered__ring: $i > $o ).
thf(class_Rings_Oidom_decl,type,
class_Rings_Oidom: $i > $o ).
thf(class_Rings_Ocomm__ring__1_decl,type,
class_Rings_Ocomm__ring__1: $i > $o ).
thf(class_Rings_Olinordered__ring_decl,type,
class_Rings_Olinordered__ring: $i > $o ).
thf(class_Groups_Ocancel__comm__monoid__add_decl,type,
class_Groups_Ocancel__comm__monoid__add: $i > $o ).
thf(c_Polynomial_Osmult_decl,type,
c_Polynomial_Osmult: $i > $i > $i > $i ).
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_Olinordered__ring__strict_decl,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
thf(class_Groups_Omonoid__mult_decl,type,
class_Groups_Omonoid__mult: $i > $o ).
thf(class_Rings_Oordered__comm__semiring_decl,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
thf(class_Fields_Ofield_decl,type,
class_Fields_Ofield: $i > $o ).
thf(c_Polynomial_Opoly__gcd_decl,type,
c_Polynomial_Opoly__gcd: $i > $i > $i > $i ).
thf(c_Polynomial_Odegree_decl,type,
c_Polynomial_Odegree: $i > $i > $i ).
thf(class_Groups_Ominus_decl,type,
class_Groups_Ominus: $i > $o ).
thf(class_Groups_Oab__group__add_decl,type,
class_Groups_Oab__group__add: $i > $o ).
thf(c_Nat_Onat_Onat__case_decl,type,
c_Nat_Onat_Onat__case: $i > $i > $i > $i ).
thf(class_Rings_Odvd_decl,type,
class_Rings_Odvd: $i > $o ).
thf(class_Rings_Olinordered__semiring_decl,type,
class_Rings_Olinordered__semiring: $i > $o ).
thf(class_Rings_Osemiring_decl,type,
class_Rings_Osemiring: $i > $o ).
thf(class_Groups_Ocomm__monoid__mult_decl,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
thf(class_Groups_Ozero_decl,type,
class_Groups_Ozero: $i > $o ).
thf(c_Polynomial_OpCons_decl,type,
c_Polynomial_OpCons: $i > $i > $i > $i ).
thf(c_Polynomial_Oorder_decl,type,
c_Polynomial_Oorder: $i > $i > $i > $i ).
thf(class_Rings_Ozero__neq__one_decl,type,
class_Rings_Ozero__neq__one: $i > $o ).
thf(class_Groups_Omonoid__add_decl,type,
class_Groups_Omonoid__add: $i > $o ).
thf(class_Rings_Osemiring__0_decl,type,
class_Rings_Osemiring__0: $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_Rings_Oring__1_decl,type,
class_Rings_Oring__1: $i > $o ).
thf(class_Groups_Oone_decl,type,
class_Groups_Oone: $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_Oring__1__no__zero__divisors_decl,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
thf(class_Rings_Oring__no__zero__divisors_decl,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
thf(class_Divides_Oring__div_decl,type,
class_Divides_Oring__div: $i > $o ).
thf(class_Rings_Ono__zero__divisors_decl,type,
class_Rings_Ono__zero__divisors: $i > $o ).
thf(v_na_____decl,type,
v_na____: $i ).
thf(c_Polynomial_Opoly_decl,type,
c_Polynomial_Opoly: $i > $i > $i ).
thf(class_Groups_Oab__semigroup__mult_decl,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
thf(class_Groups_Ocancel__semigroup__add_decl,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
thf(class_Rings_Oring_decl,type,
class_Rings_Oring: $i > $o ).
thf(class_Rings_Ocomm__ring_decl,type,
class_Rings_Ocomm__ring: $i > $o ).
thf(class_Groups_Ocancel__ab__semigroup__add_decl,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
thf(c_Polynomial_Opdivmod__rel_decl,type,
c_Polynomial_Opdivmod__rel: $i > $i > $i > $i > $i > $o ).
thf(class_RealVector_Oreal__normed__algebra_decl,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
thf(c_Polynomial_Ocoeff_decl,type,
c_Polynomial_Ocoeff: $i > $i > $i ).
thf(class_Rings_Odivision__ring_decl,type,
class_Rings_Odivision__ring: $i > $o ).
thf(c_Polynomial_Omonom_decl,type,
c_Polynomial_Omonom: $i > $i > $i > $i ).
thf(class_Fields_Ofield__inverse__zero_decl,type,
class_Fields_Ofield__inverse__zero: $i > $o ).
thf(class_Rings_Odivision__ring__inverse__zero_decl,type,
class_Rings_Odivision__ring__inverse__zero: $i > $o ).
thf(c_Polynomial_Opcompose_decl,type,
c_Polynomial_Opcompose: $i > $i > $i > $i ).
thf(v_a_____decl,type,
v_a____: $i ).
thf(v_qa_____decl,type,
v_qa____: $i ).
thf(c_Polynomial_Osynthetic__div_decl,type,
c_Polynomial_Osynthetic__div: $i > $i > $i > $i ).
thf(v_pa_____decl,type,
v_pa____: $i ).
thf(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly_decl,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly: $i > $i > $i > $i ).
thf(class_Lattices_Oab__semigroup__idem__mult_decl,type,
class_Lattices_Oab__semigroup__idem__mult: $i > $o ).
thf(c_Polynomial_OAbs__poly_decl,type,
c_Polynomial_OAbs__poly: $i > $i > $i ).
thf(c_Polynomial_Opos__poly_decl,type,
c_Polynomial_Opos__poly: $i > $i > $o ).
thf(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize_decl,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize: $i > $i > $i ).
thf(v_p_decl,type,
v_p: $i ).
thf(v_n_decl,type,
v_n: $i ).
thf(v_r_____decl,type,
v_r____: $i ).
thf(c_Polynomial_Opoly__rec_decl,type,
c_Polynomial_Opoly__rec: $i > $i > $i > $i > $i > $i ).
thf(v_q_decl,type,
v_q: $i ).
thf(c_If_decl,type,
c_If: $i > $i > $i > $i > $i ).
thf(575,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/sandbox2/benchmark/theBenchmark.p',fact_mult__poly__0__left) ).
thf(3021,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)],[575]) ).
thf(805,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__ring )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Polynomial_Osmult ) ) )
= ( A @ ( B @ ( D @ c_Polynomial_Osmult ) ) @ ( A @ ( C @ ( D @ c_Polynomial_Osmult ) ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__diff__left) ).
thf(3873,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__ring )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Polynomial_Osmult ) ) )
= ( A @ ( B @ ( D @ c_Polynomial_Osmult ) ) @ ( A @ ( C @ ( D @ c_Polynomial_Osmult ) ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(249,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__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__imp__le__exp) ).
thf(1879,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__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(230,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 ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__simps_I2_J) ).
thf(1823,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 ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(573,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 ) ) )
| ( A
= ( B @ c_Groups_Oone__class_Oone ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_square__eq__1__iff) ).
thf(3008,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 ) ) )
| ( 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 ) ) )
| ( A
= ( B @ c_Groups_Oone__class_Oone ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(744,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( 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/sandbox2/benchmark/theBenchmark.p',fact_add__is__0) ).
thf(3661,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 ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( 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)],[744]) ).
thf(840,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(4022,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(418,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__one__le__power) ).
thf(2463,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(274,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 @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__mult__iff) ).
thf(1956,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(191,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__mult )
=> ( ( A @ c_Nat_OSuc @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_power__Suc2) ).
thf(1686,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__mult )
=> ( ( A @ c_Nat_OSuc @ ( 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)],[191]) ).
thf(369,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__1) ).
thf(2295,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(861,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/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__def) ).
thf(4101,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)],[861]) ).
thf(968,axiom,
tc_Complex_Ocomplex @ class_Groups_Oab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__add) ).
thf(4450,plain,
tc_Complex_Ocomplex @ class_Groups_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(362,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/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel__disj) ).
thf(2263,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)],[362]) ).
thf(818,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 ) ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_combine__common__factor) ).
thf(3930,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 ) ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(681,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 ) ) @ ( C @ ( A @ ( F @ c_Polynomial_Osmult ) ) @ ( D @ ( E @ ( A @ ( F @ c_Polynomial_Osmult ) ) @ ( F @ c_Polynomial_Opdivmod__rel ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__smult__left) ).
thf(3434,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 ) ) @ ( C @ ( A @ ( F @ c_Polynomial_Osmult ) ) @ ( D @ ( E @ ( A @ ( F @ c_Polynomial_Osmult ) ) @ ( F @ c_Polynomial_Opdivmod__rel ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(610,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/sandbox2/benchmark/theBenchmark.p',fact_power__eq__0__iff) ).
thf(3167,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)],[610]) ).
thf(537,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_zmod__zminus2__not__zero) ).
thf(2876,plain,
! [A: $i,B: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( 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)],[537]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ~ ( B @ ( A @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__fun__def) ).
thf(1237,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( ( ~ ( B @ ( A @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
=> ( ~ ( B @ ( A @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(885,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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(4183,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)],[885]) ).
thf(697,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ozero )
=> ( ( A @ ( B @ c_Polynomial_Ocoeff ) @ ( B @ c_Polynomial_OAbs__poly ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__inverse) ).
thf(3477,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)],[697]) ).
thf(83,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B = A )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__add1__eq) ).
thf(1315,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 ) ) @ ( 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 ) ) @ ( 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)],[83]) ).
thf(509,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/sandbox2/benchmark/theBenchmark.p',fact_divisors__zero) ).
thf(2787,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)],[509]) ).
thf(281,axiom,
tc_Int_Oint @ class_Rings_Ozero__neq__one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).
thf(1982,plain,
tc_Int_Oint @ class_Rings_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(408,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__Suc__eq__Suc__mod) ).
thf(2427,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(424,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/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__dvd2) ).
thf(2480,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)],[424]) ).
thf(365,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/sandbox2/benchmark/theBenchmark.p',fact_mod__0) ).
thf(2280,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)],[365]) ).
thf(153,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__self) ).
thf(1554,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(113,axiom,
tc_Int_Oint @ class_Rings_Ocomm__semiring__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__0) ).
thf(1406,plain,
tc_Int_Oint @ class_Rings_Ocomm__semiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(798,axiom,
tc_Nat_Onat @ class_Rings_Oordered__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).
thf(3858,plain,
tc_Nat_Onat @ class_Rings_Oordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(786,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/sandbox2/benchmark/theBenchmark.p',fact_power__0) ).
thf(3813,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)],[786]) ).
thf(642,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( E @ c_Polynomial_OpCons ) ) @ ( C @ ( D @ ( E @ c_Polynomial_OpCons ) ) @ ( E @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( C @ ( E @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Polynomial_OpCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__pCons) ).
thf(3285,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( E @ c_Polynomial_OpCons ) ) @ ( C @ ( D @ ( E @ c_Polynomial_OpCons ) ) @ ( E @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( C @ ( E @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Polynomial_OpCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(593,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/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel2) ).
thf(3098,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)],[593]) ).
thf(203,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__eq) ).
thf(1728,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(49,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__one__le__iff__zero__less) ).
thf(1205,plain,
! [A: $i] :
( ( ( A @ ( 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__eq ) ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( 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)],[49]) ).
thf(168,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( B @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__right) ).
thf(1591,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( B @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(949,axiom,
! [A: $i] :
( ( ( A @ ( v_pa____ @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) )
= ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( v_qa____ @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) )
= ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pq0) ).
thf(4408,plain,
! [A: $i] :
( ( ( A @ ( v_pa____ @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) )
= ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( v_qa____ @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) )
= ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(985,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring) ).
thf(4487,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(666,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 ) ) @ ( C @ c_Polynomial_Odegree ) )
= ( A @ ( C @ c_Polynomial_Odegree ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__add__eq__left) ).
thf(3382,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 ) ) @ ( C @ c_Polynomial_Odegree ) )
= ( A @ ( C @ c_Polynomial_Odegree ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(241,axiom,
tc_Int_Oint @ class_Groups_Ozero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).
thf(1855,plain,
tc_Int_Oint @ class_Groups_Ozero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(748,axiom,
tc_Nat_Onat @ class_Rings_Ono__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).
thf(3680,plain,
tc_Nat_Onat @ class_Rings_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(210,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( C @ ( D @ c_Nat_Onat_Onat__case ) ) @ hAPP ) )
= ( A @ ( B @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__case__Suc) ).
thf(1750,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( C @ ( D @ c_Nat_Onat_Onat__case ) ) @ hAPP ) )
= ( A @ ( B @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(614,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 ) ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Polynomial_Omonom ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__monom) ).
thf(3185,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 ) ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Polynomial_Omonom ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(749,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 ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__inverse) ).
thf(3681,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 ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(50,axiom,
tc_Int_Oint @ class_Rings_Oordered__cancel__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).
thf(1211,plain,
tc_Int_Oint @ class_Rings_Oordered__cancel__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(34,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/sandbox2/benchmark/theBenchmark.p',fact_power__gt1__lemma) ).
thf(1158,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)],[34]) ).
thf(566,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/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__cong) ).
thf(2976,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)],[566]) ).
thf(517,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 ) )
= ( A @ ( C @ c_Rings_Oinverse__class_Oinverse ) @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__mult__distrib) ).
thf(2808,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 ) )
= ( A @ ( C @ c_Rings_Oinverse__class_Oinverse ) @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(473,axiom,
! [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] :
( ( D @ ( B @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ! [D: $i] :
( ( D @ ( B @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_incr__mult__lemma) ).
thf(2644,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] :
( ( D @ ( B @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ! [D: $i] :
( ( D @ ( B @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(398,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zminus) ).
thf(2395,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(547,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__pCons) ).
thf(2908,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(716,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_power__add) ).
thf(3549,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( 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)],[716]) ).
thf(434,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 @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) ).
thf(2527,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 @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(580,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 ) ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(3040,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 ) ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(944,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__ring )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring) ).
thf(4391,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__ring )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(605,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__0 )
=> ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( B @ ( C @ c_Polynomial_Osmult ) ) @ ( C @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__smult__le) ).
thf(3153,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__0 )
=> ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( B @ ( C @ c_Polynomial_Osmult ) ) @ ( C @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(691,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( D @ c_Polynomial_Osmult ) ) @ ( C @ ( D @ c_Polynomial_Osmult ) ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Osmult ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__smult) ).
thf(3460,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( D @ c_Polynomial_Osmult ) ) @ ( C @ ( D @ c_Polynomial_Osmult ) ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Osmult ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(356,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__assoc) ).
thf(2248,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(920,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/sandbox2/benchmark/theBenchmark.p',fact_order__root) ).
thf(4326,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)],[920]) ).
thf(894,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 ) @ ( B @ c_Polynomial_Osmult ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd_Osimps_I1_J) ).
thf(4215,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 ) @ ( B @ c_Polynomial_Osmult ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(529,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_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Polynomial_Opcompose ) ) @ ( C @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__pcompose__le) ).
thf(2854,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_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Polynomial_Opcompose ) ) @ ( C @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(1039,axiom,
! [A: $i] :
( ( A @ class_Groups_Oab__group__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ogroup__add) ).
thf(4614,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)],[1039]) ).
thf(670,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__minus__cancel) ).
thf(3402,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(1006,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring) ).
thf(4532,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(862,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/sandbox2/benchmark/theBenchmark.p',fact_monom__eq__iff) ).
thf(4105,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)],[862]) ).
thf(796,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(3848,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(623,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( 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 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib) ).
thf(3217,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( 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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(859,axiom,
tc_Nat_Onat @ class_Rings_Olinordered__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).
thf(4090,plain,
tc_Nat_Onat @ class_Rings_Olinordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(1051,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ tc_Polynomial_Opoly @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(4647,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)],[1051]) ).
thf(205,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__imp__mod__0) ).
thf(1735,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)],[205]) ).
thf(1004,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring) ).
thf(4528,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__antisym__nonneg) ).
thf(1164,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(963,axiom,
! [A: $i] :
( ( A @ class_Groups_Ocancel__comm__monoid__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ocancel__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add) ).
thf(4440,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)],[963]) ).
thf(1018,axiom,
tc_Complex_Ocomplex @ class_Groups_Omonoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__mult) ).
thf(4564,plain,
tc_Complex_Ocomplex @ class_Groups_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(273,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oorder__trans) ).
thf(1954,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)],[273]) ).
thf(94,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc2) ).
thf(1354,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(126,axiom,
tc_Int_Oint @ class_Rings_Olinordered__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).
thf(1458,plain,
tc_Int_Oint @ class_Rings_Olinordered__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(639,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/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd_Oleft__commute) ).
thf(3276,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)],[639]) ).
thf(784,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( A @ ( A @ ( B @ ( C @ c_Polynomial_Omonom ) ) @ ( C @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__monom__le) ).
thf(3794,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( A @ ( A @ ( B @ ( C @ c_Polynomial_Omonom ) ) @ ( C @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(1046,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oone ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oone) ).
thf(4633,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).
thf(683,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__ring )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonpos) ).
thf(3439,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__ring )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(583,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/sandbox2/benchmark/theBenchmark.p',fact_poly__eq__iff) ).
thf(3049,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)],[583]) ).
thf(768,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 ) ) @ ( 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 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__diff) ).
thf(3745,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 ) ) @ ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(598,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( B
!= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( B @ ( C @ c_Polynomial_Odegree ) @ ( B @ ( A @ ( C @ c_Polynomial_Oorder ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__degree) ).
thf(3135,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( B
!= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( B @ ( C @ c_Polynomial_Odegree ) @ ( B @ ( A @ ( C @ c_Polynomial_Oorder ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(741,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 ) ) ) )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__zero__sym) ).
thf(3649,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 ) ) ) ) )
& ( ( ( B @ c_Groups_Ozero__class_Ozero )
= ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(68,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__asym) ).
thf(1275,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)],[68]) ).
thf(325,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( A @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__self2) ).
thf(2141,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( A @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(1050,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ( ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) )
= ( 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/sandbox2/benchmark/theBenchmark.p',fact_pCons__eq__0__iff) ).
thf(4638,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 ) ) )
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) )
= ( 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)],[1050]) ).
thf(247,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/sandbox2/benchmark/theBenchmark.p',fact_zpower__zmod) ).
thf(1872,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)],[247]) ).
thf(422,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 ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__inverse) ).
thf(2476,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 ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(467,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl3) ).
thf(2627,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)],[467]) ).
thf(849,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/sandbox2/benchmark/theBenchmark.p',fact_coeff__inject) ).
thf(4058,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)],[849]) ).
thf(633,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__poly__code_I2_J) ).
thf(3253,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(791,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
= A )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__zero) ).
thf(3826,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 ) )
= A ) )
& ( ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
= A )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(674,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/sandbox2/benchmark/theBenchmark.p',fact_mod__less__divisor) ).
thf(3414,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)],[674]) ).
thf(214,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oantisym) ).
thf(1761,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)],[214]) ).
thf(903,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 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__def) ).
thf(4247,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 ) ) ) ) )
=> ( 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 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(720,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 ) ) ) )
<=> ( A
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__iff) ).
thf(3562,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 ) ) ) ) )
& ( ( B
= ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( A
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(451,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 ) ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__strict__right__mono) ).
thf(2580,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 ) ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(140,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/sandbox2/benchmark/theBenchmark.p',fact_nat__less__cases) ).
thf(1507,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)],[140]) ).
thf(387,axiom,
! [A: $i,B: $i] :
( ( B = A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__imp__le) ).
thf(2360,plain,
! [A: $i,B: $i] :
( ( B = A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(235,axiom,
tc_Int_Oint @ class_Groups_Ocomm__monoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).
thf(1835,plain,
tc_Int_Oint @ class_Groups_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(793,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__cancel1) ).
thf(3836,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B = A )
=> ( ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(492,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( 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__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono2) ).
thf(2723,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( 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__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(937,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring) ).
thf(4371,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(1041,axiom,
tc_Complex_Ocomplex @ class_Groups_Ominus,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ominus) ).
thf(4618,plain,
tc_Complex_Ocomplex @ class_Groups_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(867,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/sandbox2/benchmark/theBenchmark.p',fact_degree__1) ).
thf(4124,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)],[867]) ).
thf(96,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__cancel) ).
thf(1359,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(171,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( 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 ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__imp__le) ).
thf(1601,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( 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 ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(843,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 ) ) @ ( C @ c_Polynomial_Odegree ) )
= ( A @ ( C @ c_Polynomial_Odegree ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__add__eq__right) ).
thf(4030,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 ) ) @ ( C @ c_Polynomial_Odegree ) )
= ( A @ ( C @ c_Polynomial_Odegree ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(400,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/sandbox2/benchmark/theBenchmark.p',fact_mod__less) ).
thf(2400,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)],[400]) ).
thf(751,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__1) ).
thf(3688,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( 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)],[751]) ).
thf(942,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 ) ) )
= ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__0__0) ).
thf(4386,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 ) ) )
= ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(874,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(4142,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(300,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( B @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__conv2) ).
thf(2046,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( B @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(564,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/sandbox2/benchmark/theBenchmark.p',fact_poly__mult) ).
thf(2972,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)],[564]) ).
thf(736,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/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__1__left) ).
thf(3634,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)],[736]) ).
thf(428,axiom,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__1__left) ).
thf(2491,plain,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(815,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/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__1__right) ).
thf(3915,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)],[815]) ).
thf(569,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( 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 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Odiff__left) ).
thf(2985,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(990,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Ono__zero__divisors ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ono__zero__divisors) ).
thf(4496,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Ono__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(107,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C = A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__imp__eq__base) ).
thf(1391,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(183,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/sandbox2/benchmark/theBenchmark.p',fact_gcd__lcm__complete__lattice__nat_Otop__greatest) ).
thf(1650,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)],[183]) ).
thf(764,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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(3730,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)],[764]) ).
thf(181,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/sandbox2/benchmark/theBenchmark.p',fact_pow__divides__pow__int) ).
thf(1645,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)],[181]) ).
thf(334,axiom,
tc_Int_Oint @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(2173,plain,
tc_Int_Oint @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(1036,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ocomm__monoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult) ).
thf(4607,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)],[1036]) ).
thf(99,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_n__less__n__mult__m) ).
thf(1366,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( 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)],[99]) ).
thf(521,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_add__gr__0) ).
thf(2819,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 ) ) @ ( 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 ) ) @ ( 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)],[521]) ).
thf(223,axiom,
tc_Int_Oint @ class_Orderings_Oord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).
thf(1803,plain,
tc_Int_Oint @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(1055,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oring__no__zero__divisors ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors) ).
thf(4665,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)],[1055]) ).
thf(918,axiom,
~ ( v_pa____ @ ( v_pa____ @ ( v_a____ @ ( tc_Complex_Ocomplex @ c_Polynomial_Oorder ) ) @ c_Nat_OSuc @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( tc_Complex_Ocomplex @ c_Groups_Oone__class_Oone @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( v_a____ @ ( tc_Complex_Ocomplex @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ap_I2_J) ).
thf(4322,plain,
~ ( v_pa____ @ ( v_pa____ @ ( v_a____ @ ( tc_Complex_Ocomplex @ c_Polynomial_Oorder ) ) @ c_Nat_OSuc @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( tc_Complex_Ocomplex @ c_Groups_Oone__class_Oone @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( v_a____ @ ( tc_Complex_Ocomplex @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(807,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/sandbox2/benchmark/theBenchmark.p',fact_coeff__1) ).
thf(3878,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)],[807]) ).
thf(322,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/sandbox2/benchmark/theBenchmark.p',fact_zdvd__zmod) ).
thf(2136,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)],[322]) ).
thf(141,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__less__eq__dividend) ).
thf(1518,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(63,axiom,
tc_Int_Oint @ class_Groups_Oordered__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).
thf(1265,plain,
tc_Int_Oint @ class_Groups_Oordered__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(436,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__dvd__iff) ).
thf(2531,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 ) @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( 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)],[436]) ).
thf(977,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 ) )
= ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__poly__code_I1_J) ).
thf(4467,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 ) )
= ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(199,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/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__disj) ).
thf(1709,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)],[199]) ).
thf(1002,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__semiring) ).
thf(4524,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(924,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring )
=> ( ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Polynomial_Osmult ) ) )
= ( A @ ( B @ ( C @ c_Polynomial_Osmult ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__minus__right) ).
thf(4348,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring )
=> ( ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Polynomial_Osmult ) ) )
= ( A @ ( B @ ( C @ c_Polynomial_Osmult ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(678,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_Osmult ) ) @ ( 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 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__smult__left) ).
thf(3425,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_Osmult ) ) @ ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(297,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leI) ).
thf(2039,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(582,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Polynomial_Osmult ) ) )
= ( A @ ( B @ ( D @ c_Polynomial_Osmult ) ) @ ( A @ ( C @ ( D @ c_Polynomial_Osmult ) ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__add__left) ).
thf(3046,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Polynomial_Osmult ) ) )
= ( A @ ( B @ ( D @ c_Polynomial_Osmult ) ) @ ( A @ ( C @ ( D @ c_Polynomial_Osmult ) ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(952,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(4415,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)],[952]) ).
thf(487,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__trans) ).
thf(2708,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(260,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__shift) ).
thf(1907,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(776,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( 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 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Odiff) ).
thf(3776,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(70,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Ominus__class_Ominus ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__self) ).
thf(1279,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Ominus__class_Ominus ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(45,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 ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).
thf(1191,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 ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(501,axiom,
tc_Nat_Onat @ class_Rings_Olinordered__comm__semiring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).
thf(2745,plain,
tc_Nat_Onat @ class_Rings_Olinordered__comm__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(789,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/sandbox2/benchmark/theBenchmark.p',fact_mult__1) ).
thf(3820,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)],[789]) ).
thf(1049,axiom,
tc_Complex_Ocomplex @ class_Rings_Ocomm__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring) ).
thf(4637,plain,
tc_Complex_Ocomplex @ class_Rings_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).
thf(1009,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1) ).
thf(4539,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(685,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 ) ) @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__pCons__0) ).
thf(3442,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 ) ) @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(962,axiom,
tc_Complex_Ocomplex @ class_Fields_Ofield,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield) ).
thf(4439,plain,
tc_Complex_Ocomplex @ class_Fields_Ofield,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(73,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__power) ).
thf(1287,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)],[73]) ).
thf(1013,axiom,
tc_Complex_Ocomplex @ class_Fields_Ofield__inverse__zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield__inverse__zero) ).
thf(4546,plain,
tc_Complex_Ocomplex @ class_Fields_Ofield__inverse__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(497,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/sandbox2/benchmark/theBenchmark.p',fact_mod__poly__eq) ).
thf(2735,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)],[497]) ).
thf(519,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( D @ c_Polynomial_OpCons ) ) @ ( C @ ( D @ c_Polynomial_Osmult ) ) )
= ( A @ ( C @ ( D @ c_Polynomial_Osmult ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_OpCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__pCons) ).
thf(2814,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( D @ c_Polynomial_OpCons ) ) @ ( C @ ( D @ c_Polynomial_Osmult ) ) )
= ( A @ ( C @ ( D @ c_Polynomial_Osmult ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_OpCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(486,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
thf(2698,plain,
! [A: $i,B: $i] :
( ( ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(76,axiom,
tc_Int_Oint @ class_Rings_Oordered__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).
thf(1298,plain,
tc_Int_Oint @ class_Rings_Oordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(481,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_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__pos__lemma) ).
thf(2682,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_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(231,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 ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).
thf(1826,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 ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(339,axiom,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less0) ).
thf(2185,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)],[339]) ).
thf(162,axiom,
tc_Int_Oint @ class_Groups_Omonoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).
thf(1577,plain,
tc_Int_Oint @ class_Groups_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(795,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
thf(3845,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(427,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__mod__geq) ).
thf(2488,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(129,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/sandbox2/benchmark/theBenchmark.p',fact_pos__zmult__eq__1__iff) ).
thf(1462,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)],[129]) ).
thf(26,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/sandbox2/benchmark/theBenchmark.p',fact_not__one__less__zero) ).
thf(1132,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)],[26]) ).
thf(581,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 ) )
= ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_Omonom ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__monom) ).
thf(3043,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 ) )
= ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_Omonom ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(406,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__0__left) ).
thf(2420,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)],[406]) ).
thf(264,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/sandbox2/benchmark/theBenchmark.p',fact_dvdI) ).
thf(1922,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)],[264]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( B @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Rings_Oinverse__class_Oinverse ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__le__1__iff) ).
thf(1147,plain,
! [A: $i,B: $i] :
( ( B @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Rings_Oinverse__class_Oinverse ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Rings_Oinverse__class_Oinverse ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(197,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__left__eq) ).
thf(1704,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(935,axiom,
tc_Complex_Ocomplex @ class_Rings_Oring__1__no__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors) ).
thf(4368,plain,
tc_Complex_Ocomplex @ class_Rings_Oring__1__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(757,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/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(3708,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)],[757]) ).
thf(974,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/sandbox2/benchmark/theBenchmark.p',fact_poly__0) ).
thf(4460,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)],[974]) ).
thf(248,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/sandbox2/benchmark/theBenchmark.p',fact_ord__eq__less__trans) ).
thf(1875,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)],[248]) ).
thf(914,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__0__iff__equal) ).
thf(4302,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(17,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/sandbox2/benchmark/theBenchmark.p',fact_power__strict__increasing__iff) ).
thf(1100,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)],[17]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__lessD1) ).
thf(1232,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( 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)],[54]) ).
thf(709,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( 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 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__mult__distrib2) ).
thf(3517,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( 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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(834,axiom,
~ ! [A: $i] :
( v_qa____
!= ( A @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( tc_Complex_Ocomplex @ c_Groups_Oone__class_Oone @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( v_a____ @ ( tc_Complex_Ocomplex @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Br_O_Aq_A_061_A_091_058_N_Aa_M_A1_058_093_A_K_Ar_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(3998,plain,
~ ! [A: $i] :
( v_qa____
!= ( A @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( tc_Complex_Ocomplex @ c_Groups_Oone__class_Oone @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( v_a____ @ ( tc_Complex_Ocomplex @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(254,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__mono2) ).
thf(1892,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(667,axiom,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_One__nat__def) ).
thf(3385,plain,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(692,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__ring )
=> ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__square) ).
thf(3463,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__ring )
=> ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__mono) ).
thf(1379,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(333,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oord__eq__le__trans) ).
thf(2169,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)],[333]) ).
thf(401,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 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
thf(2403,plain,
! [A: $i] :
( ( ? [B: $i] :
( A
= ( B @ c_Nat_OSuc ) )
=> ( 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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__mono) ).
thf(1347,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(160,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__trans) ).
thf(1572,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)],[160]) ).
thf(110,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__diff__iff) ).
thf(1398,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( 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)],[110]) ).
thf(591,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/sandbox2/benchmark/theBenchmark.p',fact_mult__is__0) ).
thf(3084,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)],[591]) ).
thf(551,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 ) )
= ( A @ ( B @ hAPP ) @ ( D @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__apply) ).
thf(2929,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 ) )
= ( A @ ( B @ hAPP ) @ ( D @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(1059,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/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__by__0) ).
thf(4675,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)],[1059]) ).
thf(650,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= A )
<=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__equation__iff) ).
thf(3312,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= B )
=> ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= A ) )
& ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= A )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(159,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ c_Nat_OSuc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
thf(1568,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ c_Nat_OSuc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(97,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 ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__mono) ).
thf(1362,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 ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(275,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff__inverse) ).
thf(1963,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(612,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/sandbox2/benchmark/theBenchmark.p',fact_power__one__right) ).
thf(3180,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)],[612]) ).
thf(979,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/sandbox2/benchmark/theBenchmark.p',fact_psize__eq__0__iff) ).
thf(4471,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)],[979]) ).
thf(523,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 ) ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__eq__0__iff__dvd) ).
thf(2829,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 ) ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( 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 ) ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(780,axiom,
tc_Nat_Onat @ class_Rings_Odvd,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Odvd) ).
thf(3788,plain,
tc_Nat_Onat @ class_Rings_Odvd,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(1031,axiom,
! [A: $i] :
( ( A @ class_Groups_Ocomm__monoid__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__add) ).
thf(4595,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)],[1031]) ).
thf(1065,axiom,
! [A: $i] :
( ( A @ class_Groups_Ocomm__monoid__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Omonoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__add) ).
thf(4696,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)],[1065]) ).
thf(680,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/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__eq) ).
thf(3431,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)],[680]) ).
thf(313,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( D @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma__neg) ).
thf(2090,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( D @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(762,axiom,
! [A: $i] :
( ( A @ c_Nat_OSuc )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
thf(3724,plain,
! [A: $i] :
( ( A @ c_Nat_OSuc )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(541,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos) ).
thf(2893,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(360,axiom,
tc_Int_Oint @ class_Rings_Oidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).
thf(2259,plain,
tc_Int_Oint @ class_Rings_Oidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(475,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).
thf(2650,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
thf(1334,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(189,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD1) ).
thf(1682,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(243,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 @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux2) ).
thf(1858,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 @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(721,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 ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self2) ).
thf(3569,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 ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(1061,axiom,
tc_Complex_Ocomplex @ class_Rings_Ocomm__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring) ).
thf(4686,plain,
tc_Complex_Ocomplex @ class_Rings_Ocomm__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).
thf(506,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 ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__right) ).
thf(2777,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 ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(797,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 ) ) )
= ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( C
= ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__add__iff2) ).
thf(3851,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 ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( C
= ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(337,axiom,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
!= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0__neq__1) ).
thf(2178,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)],[337]) ).
thf(950,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__ring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring__1) ).
thf(4411,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)],[950]) ).
thf(464,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__ex__iff) ).
thf(2616,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(271,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono1) ).
thf(1946,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(946,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/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__0) ).
thf(4396,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)],[946]) ).
thf(186,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessD) ).
thf(1664,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( 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)],[186]) ).
thf(512,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 ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__unique) ).
thf(2794,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 ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(809,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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(3887,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)],[809]) ).
thf(379,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 ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__dvd__conv_I1_J) ).
thf(2324,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( 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 ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(882,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/sandbox2/benchmark/theBenchmark.p',fact_poly__1) ).
thf(4173,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)],[882]) ).
thf(820,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/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).
thf(3934,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)],[820]) ).
thf(1022,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/sandbox2/benchmark/theBenchmark.p',fact_monom__eq__0) ).
thf(4578,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)],[1022]) ).
thf(316,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff) ).
thf(2105,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(970,axiom,
tc_Complex_Ocomplex @ class_Groups_Oab__group__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__group__add) ).
thf(4454,plain,
tc_Complex_Ocomplex @ class_Groups_Oab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(1033,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(4600,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)],[1033]) ).
thf(414,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0__eq__0) ).
thf(2451,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(351,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__power__dvd) ).
thf(2236,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( 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)],[351]) ).
thf(232,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_Osmult ) ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_smult__dvd__cancel) ).
thf(1828,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_Osmult ) ) @ ( 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)],[232]) ).
thf(279,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/sandbox2/benchmark/theBenchmark.p',fact_zless__linear) ).
thf(1978,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)],[279]) ).
thf(367,axiom,
! [A: $i] : ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
thf(2291,plain,
! [A: $i] : ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(660,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/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__right__eq) ).
thf(3357,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)],[660]) ).
thf(358,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 ) ) )
= ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
thf(2254,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 ) ) )
= ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(443,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zmod) ).
thf(2555,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(645,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( 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 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib2) ).
thf(3300,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( 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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ! [E: $i] : ( E @ ( A @ hAPP ) @ ( E @ ( B @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__fun__def) ).
thf(1183,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( ! [E: $i] : ( E @ ( A @ hAPP ) @ ( E @ ( B @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ! [E: $i] : ( E @ ( A @ hAPP ) @ ( E @ ( B @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(307,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel1) ).
thf(2073,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)],[307]) ).
thf(303,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__eq ) ) )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__Suc__le__self) ).
thf(2058,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__eq ) ) )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(39,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/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
thf(1169,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)],[39]) ).
thf(844,axiom,
tc_Nat_Onat @ class_Rings_Ocomm__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).
thf(4033,plain,
tc_Nat_Onat @ class_Rings_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(256,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__right) ).
thf(1896,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)],[256]) ).
thf(108,axiom,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__zeroE) ).
thf(1394,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)],[108]) ).
thf(145,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/sandbox2/benchmark/theBenchmark.p',fact_zdvd__mono) ).
thf(1526,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)],[145]) ).
thf(93,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/sandbox2/benchmark/theBenchmark.p',fact_mod__mod__trivial) ).
thf(1351,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)],[93]) ).
thf(120,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Odiff__diff__eq) ).
thf(1433,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(626,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 ) ) @ ( C @ c_Polynomial_Odegree ) )
= ( B @ ( C @ c_Polynomial_Odegree ) @ c_Nat_OSuc ) ) )
& ( ( B
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ c_Polynomial_Odegree ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__pCons__eq__if) ).
thf(3226,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 ) ) @ ( C @ c_Polynomial_Odegree ) )
= ( B @ ( C @ c_Polynomial_Odegree ) @ c_Nat_OSuc ) ) )
& ( ( B
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ c_Polynomial_Odegree ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(803,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonneg) ).
thf(3870,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(893,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/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__less__cancel1) ).
thf(4211,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)],[893]) ).
thf(344,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__add1__eq__le) ).
thf(2205,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( 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 ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(568,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Oring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( 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 ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__diff__eq) ).
thf(2982,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Oring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( 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 ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(390,axiom,
! [A: $i,B: $i] :
( ( ( B @ c_Nat_OSuc )
= ( A @ c_Nat_OSuc ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__inject) ).
thf(2367,plain,
! [A: $i,B: $i] :
( ( ( B @ c_Nat_OSuc )
= ( A @ c_Nat_OSuc ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(266,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 ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__add) ).
thf(1928,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 ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(848,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__mod__minus__right) ).
thf(4055,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) @ ( 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)],[848]) ).
thf(587,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add__cancel) ).
thf(3068,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(898,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/sandbox2/benchmark/theBenchmark.p',fact_mult_Ozero__right) ).
thf(4230,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)],[898]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( 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__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing) ).
thf(1072,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( 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__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(435,axiom,
tc_Int_Oint @ class_Groups_Ocancel__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).
thf(2530,plain,
tc_Int_Oint @ class_Groups_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(178,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/sandbox2/benchmark/theBenchmark.p',fact_ord__less__eq__trans) ).
thf(1622,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)],[178]) ).
thf(858,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring )
=> ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__inverse) ).
thf(4087,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring )
=> ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(567,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__ring__1 )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).
thf(2979,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__ring__1 )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(288,axiom,
tc_Int_Oint @ class_Groups_Omonoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).
thf(2002,plain,
tc_Int_Oint @ class_Groups_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(1008,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/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__0) ).
thf(4536,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)],[1008]) ).
thf(825,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/sandbox2/benchmark/theBenchmark.p',fact_zmult__1__right) ).
thf(3955,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)],[825]) ).
thf(90,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/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__less) ).
thf(1345,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)],[90]) ).
thf(514,axiom,
! [A: $i] :
( ( A @ class_Rings_Odivision__ring )
=> ( ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Rings_Oinverse__class_Oinverse ) )
= ( A @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__1) ).
thf(2799,plain,
! [A: $i] :
( ( A @ class_Rings_Odivision__ring )
=> ( ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Rings_Oinverse__class_Oinverse ) )
= ( A @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(725,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 ) ) @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__dvd) ).
thf(3588,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 ) ) @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(194,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A
!= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( C @ c_Polynomial_Odegree ) @ ( B @ ( C @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__imp__degree__le) ).
thf(1697,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A
!= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( C @ c_Polynomial_Odegree ) @ ( B @ ( C @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(57,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel2) ).
thf(1242,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)],[57]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( B @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_inverse__positive__iff__positive) ).
thf(1104,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 ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse ) @ ( 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)],[18]) ).
thf(941,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/sandbox2/benchmark/theBenchmark.p',fact_poly__zero) ).
thf(4379,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)],[941]) ).
thf(327,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zless__mono) ).
thf(2154,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(143,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff__inverse2) ).
thf(1521,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(850,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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(4065,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)],[850]) ).
thf(157,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/sandbox2/benchmark/theBenchmark.p',fact_one__dvd) ).
thf(1564,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)],[157]) ).
thf(245,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 ) ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_zdvd__reduce) ).
thf(1863,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 ) ) @ ( 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 ) ) @ ( 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)],[245]) ).
thf(557,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 ) ) @ ( D @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__add__less) ).
thf(2954,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 ) ) @ ( D @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(290,axiom,
tc_Int_Oint @ class_Rings_Oordered__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).
thf(2011,plain,
tc_Int_Oint @ class_Rings_Oordered__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(703,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( 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 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oadd__left) ).
thf(3503,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(726,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 ) @ ( C @ c_Polynomial_Osmult ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__code) ).
thf(3591,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 ) @ ( C @ c_Polynomial_Osmult ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(646,axiom,
tc_Nat_Onat @ class_Rings_Ocomm__semiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
thf(3303,plain,
tc_Nat_Onat @ class_Rings_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(981,axiom,
! [A: $i] :
( ( A @ class_Groups_Ozero )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ozero) ).
thf(4480,plain,
! [A: $i] :
( ( A @ class_Groups_Ozero )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(80,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).
thf(1306,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(373,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__0) ).
thf(2307,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(472,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ c_Nat_OSuc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__le) ).
thf(2641,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ c_Nat_OSuc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(579,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Polynomial_Osmult ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__1__left) ).
thf(3037,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Polynomial_Osmult ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(5,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/sandbox2/benchmark/theBenchmark.p',fact_less__1__mult) ).
thf(1074,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)],[5]) ).
thf(173,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/sandbox2/benchmark/theBenchmark.p',fact_pow__divides__eq__int) ).
thf(1604,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)],[173]) ).
thf(550,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).
thf(2922,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 ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(1027,axiom,
tc_Complex_Ocomplex @ class_Rings_Ono__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ono__zero__divisors) ).
thf(4589,plain,
tc_Complex_Ocomplex @ class_Rings_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).
thf(1044,axiom,
tc_Complex_Ocomplex @ class_Rings_Ocomm__semiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
thf(4629,plain,
tc_Complex_Ocomplex @ class_Rings_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).
thf(388,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/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__greatest) ).
thf(2364,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)],[388]) ).
thf(331,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ominus )
=> ( B @ ( A @ tc_fun ) @ class_Groups_Ominus ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ominus) ).
thf(2164,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ominus )
=> ( B @ ( A @ tc_fun ) @ class_Groups_Ominus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(1,conjecture,
( v_s____
!= ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ( v_s____
!= ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(1067,plain,
~ ( ( v_s____
!= ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(916,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 ) ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(4312,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 ) ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(510,axiom,
tc_Nat_Onat @ class_Groups_Ominus,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).
thf(2790,plain,
tc_Nat_Onat @ class_Groups_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(216,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/sandbox2/benchmark/theBenchmark.p',fact_nat__dvd__1__iff__1) ).
thf(1768,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)],[216]) ).
thf(546,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 ) ) @ ( C @ ( D @ c_Polynomial_Osmult ) ) )
= ( A @ ( C @ ( D @ c_Polynomial_Osmult ) ) @ ( B @ ( C @ ( D @ c_Polynomial_Osmult ) ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__add__right) ).
thf(2905,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 ) ) @ ( C @ ( D @ c_Polynomial_Osmult ) ) )
= ( A @ ( C @ ( D @ c_Polynomial_Osmult ) ) @ ( B @ ( C @ ( D @ c_Polynomial_Osmult ) ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(395,axiom,
! [A: $i] :
~ ( A @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
thf(2382,plain,
! [A: $i] :
~ ( A @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(305,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc0) ).
thf(2061,plain,
! [A: $i] :
( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( 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)],[305]) ).
thf(287,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/sandbox2/benchmark/theBenchmark.p',fact_one__less__power) ).
thf(2000,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)],[287]) ).
thf(412,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__triv__left) ).
thf(2441,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)],[412]) ).
thf(458,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 ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).
thf(2596,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__eq ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(939,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oord) ).
thf(4375,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( B @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__inverse__iff) ).
thf(1123,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__eq ) ) )
& ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ c_Rings_Oinverse__class_Oinverse ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(1037,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__semiring__1__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict) ).
thf(4609,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__semiring__1__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(138,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ c_Nat_OSuc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
thf(1502,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ c_Nat_OSuc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(187,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ole__neq__trans) ).
thf(1666,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)],[187]) ).
thf(134,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__lt__two__imp__zero__or__one) ).
thf(1487,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(989,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 ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__poly__code_I1_J) ).
thf(4493,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 ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(632,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Oring__div )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__minus__eq) ).
thf(3250,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Oring__div )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(708,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_Osmult ) ) )
= ( A @ ( B @ ( C @ c_Polynomial_Osmult ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__minus__left) ).
thf(3514,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_Osmult ) ) )
= ( A @ ( B @ ( C @ c_Polynomial_Osmult ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(758,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_OpCons ) ) @ ( D @ c_Polynomial_Osynthetic__div ) ) )
= ( A @ ( B @ ( D @ c_Polynomial_Osynthetic__div ) ) @ ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( D @ c_Polynomial_OpCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__pCons) ).
thf(3711,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_OpCons ) ) @ ( D @ c_Polynomial_Osynthetic__div ) ) )
= ( A @ ( B @ ( D @ c_Polynomial_Osynthetic__div ) ) @ ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( D @ c_Polynomial_OpCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(89,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult2) ).
thf(1343,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)],[89]) ).
thf(838,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/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__unique__div) ).
thf(4016,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)],[838]) ).
thf(445,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__mod__iff) ).
thf(2560,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)],[445]) ).
thf(516,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 ) ) @ ( 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 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__add) ).
thf(2805,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 ) ) @ ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(563,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/sandbox2/benchmark/theBenchmark.p',fact_zmod__simps_I3_J) ).
thf(2969,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)],[563]) ).
thf(860,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 ) ) )
= ( 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 ) ) ) )
<=> ( ( C = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__eq) ).
thf(4091,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 ) ) )
= ( 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 ) ) ) ) )
& ( ( ( 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 ) ) )
= ( 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 ) ) ) )
=> ( ( C = A )
| ( D = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(627,axiom,
tc_Nat_Onat @ class_Rings_Omult__zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).
thf(3233,plain,
tc_Nat_Onat @ class_Rings_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(554,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 ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__eq__zero__iff) ).
thf(2937,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 ) ) )
= ( 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 ) ) )
= ( 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)],[554]) ).
thf(992,axiom,
! [A: $i] :
( ( A @ class_Groups_Ocomm__monoid__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__add) ).
thf(4499,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)],[992]) ).
thf(460,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc) ).
thf(2606,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(787,axiom,
tc_Nat_Onat @ class_Rings_Ozero__neq__one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).
thf(3816,plain,
tc_Nat_Onat @ class_Rings_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(177,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD2) ).
thf(1619,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(847,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/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).
thf(4044,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)],[847]) ).
thf(251,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SucI) ).
thf(1883,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(826,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add__distrib) ).
thf(3958,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(833,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_Osmult ) ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_smult__dvd__iff) ).
thf(3980,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 ) ) @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_Osmult ) ) @ ( 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)],[833]) ).
thf(873,axiom,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__square) ).
thf(4140,plain,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(263,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring__strict) ).
thf(1920,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)],[263]) ).
thf(277,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B = A )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__le__eq__trans) ).
thf(1968,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B = A )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(878,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__pCons) ).
thf(4155,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 ) ) @ ( C @ c_Polynomial_Opos__poly ) ) )
& ( ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) @ ( 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)],[878]) ).
thf(75,axiom,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__0) ).
thf(1296,plain,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(461,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 ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).
thf(2609,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 ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(715,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Polynomial_Omonom ) ) )
= ( A @ ( B @ ( C @ c_Polynomial_Omonom ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Polynomial_OpCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monom__Suc) ).
thf(3546,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Polynomial_Omonom ) ) )
= ( A @ ( B @ ( C @ c_Polynomial_Omonom ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Polynomial_OpCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(953,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__0 )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__semigroup__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__mult) ).
thf(4417,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)],[953]) ).
thf(855,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 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__mult__eq) ).
thf(4080,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 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(476,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__mono) ).
thf(2653,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(641,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/sandbox2/benchmark/theBenchmark.p',fact_mod__poly__less) ).
thf(3282,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)],[641]) ).
thf(116,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SucI) ).
thf(1423,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(824,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__cancel) ).
thf(3948,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 ) ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(616,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
thf(3191,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(906,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/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Ozero) ).
thf(4280,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)],[906]) ).
thf(504,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/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__unique) ).
thf(2758,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)],[504]) ).
thf(536,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__eq ) ) )
=> ( ( ( A @ ( B @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( B
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__zero__or__degree__less) ).
thf(2873,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__eq ) ) )
=> ( ( ( A @ ( B @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( B
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(1025,axiom,
tc_Complex_Ocomplex @ class_Rings_Oidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).
thf(4585,plain,
tc_Complex_Ocomplex @ class_Rings_Oidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(411,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 ) ) )
= ( A @ ( B @ ( E @ c_Groups_Ominus__class_Ominus ) ) ) )
=> ( ( D = C )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__eq) ).
thf(2433,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 ) ) )
= ( A @ ( B @ ( E @ c_Groups_Ominus__class_Ominus ) ) ) )
=> ( ( ( B = A )
=> ( D = C ) )
& ( ( D = C )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(644,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring )
=> ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse ) )
!= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__imp__inverse__nonzero) ).
thf(3297,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring )
=> ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse ) )
!= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(657,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/sandbox2/benchmark/theBenchmark.p',fact_degree__offset__poly) ).
thf(3349,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)],[657]) ).
thf(236,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__add) ).
thf(1836,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(338,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ c_Nat_OSuc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).
thf(2181,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ c_Nat_OSuc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).
thf(1195,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(345,axiom,
tc_Int_Oint @ class_Rings_Oring__no__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).
thf(2211,plain,
tc_Int_Oint @ class_Rings_Oring__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(114,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__diff__conv) ).
thf(1407,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(438,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/sandbox2/benchmark/theBenchmark.p',fact_mult__dvd__mono) ).
thf(2547,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)],[438]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__semidom )
=> ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__one) ).
thf(1128,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__semidom )
=> ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(763,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/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__right) ).
thf(3727,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)],[763]) ).
thf(499,axiom,
tc_Nat_Onat @ class_Rings_Oordered__cancel__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).
thf(2741,plain,
tc_Nat_Onat @ class_Rings_Oordered__cancel__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(672,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 ) @ ( F @ c_Polynomial_Osmult ) ) @ ( C @ ( E @ ( F @ c_Polynomial_Osmult ) ) @ ( D @ ( F @ c_Polynomial_Opdivmod__rel ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__smult__right) ).
thf(3408,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 ) @ ( F @ c_Polynomial_Osmult ) ) @ ( C @ ( E @ ( F @ c_Polynomial_Osmult ) ) @ ( D @ ( F @ c_Polynomial_Opdivmod__rel ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(261,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__eq ) ) )
<=> ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel2) ).
thf(1910,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( 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__eq ) ) ) )
& ( ( 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__eq ) ) )
=> ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(686,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/sandbox2/benchmark/theBenchmark.p',fact_times_Oidem) ).
thf(3445,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)],[686]) ).
thf(842,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__commute) ).
thf(4027,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(111,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oord )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
thf(1402,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oord )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(282,axiom,
tc_Int_Oint @ class_Groups_Oordered__ab__semigroup__add__imp__le,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(1983,plain,
tc_Int_Oint @ class_Groups_Oordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(393,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add2) ).
thf(2377,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(542,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/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__distrib2) ).
thf(2895,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)],[542]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Nat_OSuc @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__less__cancel1) ).
thf(1328,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Nat_OSuc @ ( 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)],[86]) ).
thf(449,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc1) ).
thf(2577,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(242,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( A @ ( C @ c_Polynomial_Odegree ) @ c_Nat_OSuc @ ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__pCons__le) ).
thf(1856,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( A @ ( C @ c_Polynomial_Odegree ) @ c_Nat_OSuc @ ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(117,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 ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__iff2) ).
thf(1425,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 ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(149,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/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono__neg) ).
thf(1540,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)],[149]) ).
thf(468,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0) ).
thf(2631,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(595,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) @ ( 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 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__mod__minus__left) ).
thf(3119,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) @ ( 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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(589,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/sandbox2/benchmark/theBenchmark.p',fact_power__commutes) ).
thf(3078,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)],[589]) ).
thf(837,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 ) ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).
thf(4012,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__eq ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(212,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/sandbox2/benchmark/theBenchmark.p',fact_zdvd__mult__cancel) ).
thf(1755,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)],[212]) ).
thf(621,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/sandbox2/benchmark/theBenchmark.p',fact_field__power__not__zero) ).
thf(3205,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)],[621]) ).
thf(778,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(3782,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(732,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
<=> ( A
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__0__iff) ).
thf(3615,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( A
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(55,axiom,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).
thf(1234,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)],[55]) ).
thf(596,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 ) )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__1__iff) ).
thf(3122,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(555,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ! [D: $i] :
( ( D @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ ( A @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
=> ( B @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__le) ).
thf(2946,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ! [D: $i] :
( ( D @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ ( A @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
=> ( B @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(221,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( B = A )
<=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__iff__diff__eq__0) ).
thf(1794,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(483,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
thf(2685,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(224,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( 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 @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__mult) ).
thf(1804,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( 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 @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(800,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__minus) ).
thf(3862,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(22,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/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__exp) ).
thf(1121,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)],[22]) ).
thf(984,axiom,
tc_Complex_Ocomplex @ class_Rings_Ocomm__ring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring__1) ).
thf(4486,plain,
tc_Complex_Ocomplex @ class_Rings_Ocomm__ring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(1048,axiom,
tc_Complex_Ocomplex @ class_Groups_Ozero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).
thf(4636,plain,
tc_Complex_Ocomplex @ class_Groups_Ozero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).
thf(136,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ouminus )
=> ( B @ ( A @ tc_fun ) @ class_Groups_Ouminus ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ouminus) ).
thf(1498,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ouminus )
=> ( B @ ( A @ tc_fun ) @ class_Groups_Ouminus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(166,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__asym_H) ).
thf(1587,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)],[166]) ).
thf(15,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__eq ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__power) ).
thf(1096,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__eq ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(899,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( D @ c_Polynomial_Osmult ) ) @ ( 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 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__smult__right) ).
thf(4233,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( D @ c_Polynomial_Osmult ) ) @ ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(188,axiom,
! [A: $i,B: $i] :
( ( ( B @ c_Nat_OSuc )
= ( A @ c_Nat_OSuc ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Oinject) ).
thf(1672,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( B @ c_Nat_OSuc )
= ( A @ c_Nat_OSuc ) ) )
& ( ( ( B @ c_Nat_OSuc )
= ( A @ c_Nat_OSuc ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(756,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__minus__self__iff) ).
thf(3704,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__eq ) ) )
=> ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(471,axiom,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
thf(2638,plain,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( ( B @ c_Nat_OSuc @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Nat_OSuc @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inject__base) ).
thf(1118,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( ( B @ c_Nat_OSuc @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Nat_OSuc @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(574,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 ) ) @ ( B @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Odegree ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__linear__power) ).
thf(3018,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 ) ) @ ( B @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Odegree ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(109,axiom,
tc_Int_Oint @ class_Rings_Olinordered__semiring__1__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).
thf(1397,plain,
tc_Int_Oint @ class_Rings_Olinordered__semiring__1__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(8,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__eq ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__power) ).
thf(1082,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__eq ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(601,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 ) ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Omonom ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__monom) ).
thf(3143,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 ) ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Omonom ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(733,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__eq ) ) )
=> ( ( B @ ( A @ ( D @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__add__le) ).
thf(3622,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__eq ) ) )
=> ( ( B @ ( A @ ( D @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(759,axiom,
tc_Nat_Onat @ class_Groups_Ozero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
thf(3714,plain,
tc_Nat_Onat @ class_Groups_Ozero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(948,axiom,
( ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Odegree ) )
= v_n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_assms_I2_J) ).
thf(4406,plain,
( ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Odegree ) )
= v_n ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(195,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__imp__not__less) ).
thf(1700,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)],[195]) ).
thf(617,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/sandbox2/benchmark/theBenchmark.p',fact_nat__case__0) ).
thf(3194,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)],[617]) ).
thf(965,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__0 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Omult__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Omult__zero) ).
thf(4444,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)],[965]) ).
thf(207,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__eq ) ) )
<=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__neg) ).
thf(1744,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__eq ) ) )
=> ( 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__eq ) ) ) )
& ( ( 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__eq ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(1005,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Odvd ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Odvd) ).
thf(4530,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Odvd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(35,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semidom) ).
thf(1160,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(600,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__ring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( 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__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono__neg) ).
thf(3141,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__ring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( 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__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(880,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/sandbox2/benchmark/theBenchmark.p',fact_zmod__zmult1__eq) ).
thf(4167,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)],[880]) ).
thf(128,axiom,
tc_Int_Oint @ class_Groups_Ocancel__comm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__comm__monoid__add) ).
thf(1461,plain,
tc_Int_Oint @ class_Groups_Ocancel__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(957,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__ring )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring) ).
thf(4425,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__ring )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(534,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 ) ) @ ( B @ ( C @ ( F @ ( H @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( G @ ( H @ c_Polynomial_Opdivmod__rel ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__mult) ).
thf(2868,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 ) ) @ ( 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)],[534]) ).
thf(943,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oring__1__no__zero__divisors ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors) ).
thf(4389,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)],[943]) ).
thf(955,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 ) ) @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Divides_Odiv__class_Omod ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__smult__right) ).
thf(4421,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 ) ) @ ( 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)],[955]) ).
thf(917,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 ) ) )
& ( ( 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/sandbox2/benchmark/theBenchmark.p',fact_psize__def) ).
thf(4315,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 ) ) )
& ( ( 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)],[917]) ).
thf(684,axiom,
tc_Nat_Onat @ class_Groups_Omonoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
thf(3441,plain,
tc_Nat_Onat @ class_Groups_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(376,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__mod) ).
thf(2312,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)],[376]) ).
thf(1012,axiom,
tc_Complex_Ocomplex @ class_Groups_Ocomm__monoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) ).
thf(4545,plain,
tc_Complex_Ocomplex @ class_Groups_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(308,axiom,
tc_Int_Oint @ class_Int_Oring__char__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).
thf(2080,plain,
tc_Int_Oint @ class_Int_Oring__char__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(679,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_Osmult ) ) @ ( 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 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__smult__left) ).
thf(3428,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_Osmult ) ) @ ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(226,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring )
=> ( ( 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 @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__less__imp__less) ).
thf(1810,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring )
=> ( ( 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 @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(220,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/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
thf(1791,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)],[220]) ).
thf(440,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_n__less__m__mult__n) ).
thf(2551,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( 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)],[440]) ).
thf(745,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 ) @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ c_Rings_Oinverse__class_Oinverse ) @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_division__ring__inverse__add) ).
thf(3671,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 ) @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ c_Rings_Oinverse__class_Oinverse ) @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(253,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/sandbox2/benchmark/theBenchmark.p',fact_zmod__zero) ).
thf(1889,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)],[253]) ).
thf(718,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 ) ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__add__mult__distrib) ).
thf(3555,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 ) ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(175,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/sandbox2/benchmark/theBenchmark.p',fact_power__strict__decreasing) ).
thf(1612,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)],[175]) ).
thf(884,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/sandbox2/benchmark/theBenchmark.p',fact_mult__1__left) ).
thf(4180,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)],[884]) ).
thf(755,axiom,
tc_Nat_Onat @ class_Groups_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
thf(3703,plain,
tc_Nat_Onat @ class_Groups_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(552,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Oordered__semiring )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono) ).
thf(2932,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Oordered__semiring )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(419,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).
thf(2465,plain,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(430,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/sandbox2/benchmark/theBenchmark.p',fact_pos__mod__bound) ).
thf(2505,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)],[430]) ).
thf(821,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Oring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__diff__right__eq) ).
thf(3937,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Oring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(866,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).
thf(4120,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__eq ) ) )
=> ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(283,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oantisym__conv) ).
thf(1984,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)],[283]) ).
thf(877,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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(4152,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)],[877]) ).
thf(817,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 ) ) )
| ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_square__eq__iff) ).
thf(3920,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( ( ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
| ( 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 ) ) )
| ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(897,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/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel1) ).
thf(4223,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)],[897]) ).
thf(931,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/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__0) ).
thf(4361,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)],[931]) ).
thf(217,axiom,
tc_Int_Oint @ class_Rings_Odvd,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Odvd) ).
thf(1776,plain,
tc_Int_Oint @ class_Rings_Odvd,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(742,axiom,
( ( v_pa____ @ ( tc_Complex_Ocomplex @ c_Polynomial_Odegree ) )
= v_na____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dpn) ).
thf(3656,plain,
( ( v_pa____ @ ( tc_Complex_Ocomplex @ c_Polynomial_Odegree ) )
= v_na____ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(58,axiom,
! [A: $i] :
( ( A @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).
thf(1249,plain,
! [A: $i] :
( ( A @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(433,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oord__eq__less__trans) ).
thf(2519,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)],[433]) ).
thf(125,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 ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__diff) ).
thf(1456,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 ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(997,axiom,
( v_qa____
= ( v_r____ @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( tc_Complex_Ocomplex @ c_Groups_Oone__class_Oone @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( v_a____ @ ( tc_Complex_Ocomplex @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_r) ).
thf(4508,plain,
( v_qa____
= ( v_r____ @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( tc_Complex_Ocomplex @ c_Groups_Oone__class_Oone @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( v_a____ @ ( tc_Complex_Ocomplex @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(105,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq) ).
thf(1382,plain,
! [A: $i,B: $i] :
( ( ( B @ c_Nat_OSuc @ ( 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 @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(526,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( 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 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Suc) ).
thf(2845,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( 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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(585,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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(3059,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)],[585]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__mono) ).
thf(1266,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(659,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Polynomial_Opoly__gcd ) ) )
= ( A @ ( B @ ( C @ c_Polynomial_Opoly__gcd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__minus__right) ).
thf(3354,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Polynomial_Opoly__gcd ) ) )
= ( A @ ( B @ ( C @ c_Polynomial_Opoly__gcd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(851,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_OpCons ) ) @ ( D @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) )
= ( A @ ( B @ ( D @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) @ ( C @ ( D @ c_Polynomial_OpCons ) ) @ ( A @ ( B @ ( D @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) @ ( A @ ( D @ c_Polynomial_Osmult ) ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__pCons) ).
thf(4068,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_OpCons ) ) @ ( D @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) )
= ( A @ ( B @ ( D @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) @ ( C @ ( D @ c_Polynomial_OpCons ) ) @ ( A @ ( B @ ( D @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) @ ( A @ ( D @ c_Polynomial_Osmult ) ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(528,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Odivision__ring__inverse__zero )
=> ( ( ( B @ ( C @ c_Rings_Oinverse__class_Oinverse ) )
= ( A @ ( C @ c_Rings_Oinverse__class_Oinverse ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__eq__imp__eq) ).
thf(2851,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Odivision__ring__inverse__zero )
=> ( ( ( B @ ( C @ c_Rings_Oinverse__class_Oinverse ) )
= ( A @ ( C @ c_Rings_Oinverse__class_Oinverse ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(354,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 ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__apply) ).
thf(2243,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 ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(385,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).
thf(2355,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(982,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__left) ).
thf(4482,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(773,axiom,
~ ! [A: $i] :
( v_pa____
!= ( A @ ( v_pa____ @ ( v_a____ @ ( tc_Complex_Ocomplex @ c_Polynomial_Oorder ) ) @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( tc_Complex_Ocomplex @ c_Groups_Oone__class_Oone @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( v_a____ @ ( tc_Complex_Ocomplex @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bs_O_Ap_A_061_A_091_058_N_Aa_M_A1_058_093_A_094_Aorder_Aa_Ap_A_K_As_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(3760,plain,
~ ! [A: $i] :
( v_pa____
!= ( A @ ( v_pa____ @ ( v_a____ @ ( tc_Complex_Ocomplex @ c_Polynomial_Oorder ) ) @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( tc_Complex_Ocomplex @ c_Groups_Oone__class_Oone @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( v_a____ @ ( tc_Complex_Ocomplex @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(118,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__0__less) ).
thf(1429,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(829,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/sandbox2/benchmark/theBenchmark.p',fact_power_Opower_Opower__0) ).
thf(3967,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)],[829]) ).
thf(631,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 ) ) )
= ( A @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__diff__mult) ).
thf(3247,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 ) ) )
= ( A @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(532,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Olinordered__semiring__1 )
=> ( ( D @ ( E @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( D @ ( C @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( A @ ( B @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= ( F @ c_Groups_Oone__class_Oone ) )
=> ( D @ ( C @ ( A @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__le) ).
thf(2862,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Olinordered__semiring__1 )
=> ( ( D @ ( E @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( D @ ( C @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( A @ ( B @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= ( F @ c_Groups_Oone__class_Oone ) )
=> ( D @ ( C @ ( A @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(871,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ozero )
=> ( ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Polynomial_OpCons ) ) @ ( B @ c_Polynomial_Odegree ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__pCons__0) ).
thf(4135,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ozero )
=> ( ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Polynomial_OpCons ) ) @ ( B @ c_Polynomial_Odegree ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(302,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 ) @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__dvd__conv_I2_J) ).
thf(2052,plain,
! [A: $i,B: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( 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 ) @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(425,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( 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 ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__eq) ).
thf(2482,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( 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 ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(594,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 ) ) )
!= ( 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 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__noteq) ).
thf(3109,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 ) ) )
!= ( 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 ) ) ) )
=> ( ( 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 ) ) )
!= ( 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 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(572,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 ) ) @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ c_Polynomial_Osynthetic__div ) ) @ ( A @ ( B @ ( C @ c_Polynomial_Opoly ) @ hAPP ) @ ( C @ c_Polynomial_OpCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__correct) ).
thf(3005,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 ) ) @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ c_Polynomial_Osynthetic__div ) ) @ ( A @ ( B @ ( C @ c_Polynomial_Opoly ) @ hAPP ) @ ( C @ c_Polynomial_OpCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(284,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 ) ) @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__diff__nat) ).
thf(1991,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 ) ) @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(343,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/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__neg) ).
thf(2203,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)],[343]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mono) ).
thf(1086,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(734,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( ( B @ ( A @ ( D @ c_Polynomial_OpCons ) ) @ ( B @ ( C @ ( D @ c_Polynomial_Osmult ) ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) )
= ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( B
= ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__eq__0__lemma) ).
thf(3624,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( ( B @ ( A @ ( D @ c_Polynomial_OpCons ) ) @ ( B @ ( C @ ( D @ c_Polynomial_Osmult ) ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) )
= ( 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)],[734]) ).
thf(193,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
thf(1695,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(312,axiom,
tc_Int_Oint @ class_Rings_Oring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).
thf(2089,plain,
tc_Int_Oint @ class_Rings_Oring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(341,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__antisym) ).
thf(2189,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(407,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 ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).
thf(2423,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__eq ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(1015,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/sandbox2/benchmark/theBenchmark.p',fact_zero__reorient) ).
thf(4550,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)],[1015]) ).
thf(603,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/sandbox2/benchmark/theBenchmark.p',fact_poly__replicate__append) ).
thf(3147,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)],[603]) ).
thf(689,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( 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 ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__minus) ).
thf(3454,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( 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 ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(876,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 ) ) )
!= ( A @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__scale__eq__noteq) ).
thf(4148,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 ) ) )
!= ( A @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(469,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 @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__less__one) ).
thf(2634,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 @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(813,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/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).
thf(3903,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)],[813]) ).
thf(640,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( 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 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__class_Odistrib) ).
thf(3279,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(613,axiom,
( v_pa____
= ( v_s____ @ ( v_pa____ @ ( v_a____ @ ( tc_Complex_Ocomplex @ c_Polynomial_Oorder ) ) @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( tc_Complex_Ocomplex @ c_Groups_Oone__class_Oone @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( v_a____ @ ( tc_Complex_Ocomplex @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_s) ).
thf(3183,plain,
( v_pa____
= ( v_s____ @ ( v_pa____ @ ( v_a____ @ ( tc_Complex_Ocomplex @ c_Polynomial_Oorder ) ) @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( tc_Complex_Ocomplex @ c_Groups_Oone__class_Oone @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( v_a____ @ ( tc_Complex_Ocomplex @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(648,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 ) ) )
= ( A @ ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(3306,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 ) ) )
= ( A @ ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(238,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/sandbox2/benchmark/theBenchmark.p',fact_zmult__zless__mono2) ).
thf(1846,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)],[238]) ).
thf(561,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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(2963,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)],[561]) ).
thf(72,axiom,
tc_Int_Oint @ class_Groups_Ouminus,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ouminus) ).
thf(1286,plain,
tc_Int_Oint @ class_Groups_Ouminus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(44,axiom,
! [A: $i] :
( A
!= ( A @ c_Nat_OSuc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
thf(1187,plain,
! [A: $i] :
( A
!= ( A @ c_Nat_OSuc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(967,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Ozero__neq__one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ozero__neq__one) ).
thf(4448,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)],[967]) ).
thf(706,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring__inverse__zero )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Rings_Oinverse__class_Oinverse ) )
= ( A @ ( B @ c_Rings_Oinverse__class_Oinverse ) @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__minus__eq) ).
thf(3508,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring__inverse__zero )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Rings_Oinverse__class_Oinverse ) )
= ( A @ ( B @ c_Rings_Oinverse__class_Oinverse ) @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).
thf(1167,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(381,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 ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).
thf(2338,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 ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(286,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring__1 )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__minus__iff) ).
thf(1996,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 ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( 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)],[286]) ).
thf(326,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/sandbox2/benchmark/theBenchmark.p',fact_nat__zero__less__power__iff) ).
thf(2144,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)],[326]) ).
thf(336,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
thf(2176,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(296,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_zero__less__diff) ).
thf(2033,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 ) ) @ ( 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 ) ) @ ( 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)],[296]) ).
thf(453,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__le__nonneg__dividend) ).
thf(2585,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(810,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__cancel) ).
thf(3890,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 ) ) )
= ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(67,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 ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less) ).
thf(1273,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 ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(151,axiom,
! [A: $i,B: $i] :
( ( B = A )
| ~ ( A @ ( B @ c_fequal ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__1) ).
thf(1548,plain,
! [A: $i,B: $i] :
( ( B = A )
| ~ ( A @ ( B @ c_fequal ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(945,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 ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__poly__code_I2_J) ).
thf(4393,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 ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(929,axiom,
tc_Complex_Ocomplex @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(4359,plain,
tc_Complex_Ocomplex @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(933,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__comm__semiring) ).
thf(4365,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(28,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 ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__nonpositive__iff__nonpositive) ).
thf(1135,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__eq ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Rings_Oinverse__class_Oinverse ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Rings_Oinverse__class_Oinverse ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(182,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/sandbox2/benchmark/theBenchmark.p',fact_gcd__lcm__complete__lattice__nat_Obot__least) ).
thf(1648,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)],[182]) ).
thf(215,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oord__le__eq__trans) ).
thf(1764,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)],[215]) ).
thf(403,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/sandbox2/benchmark/theBenchmark.p',fact_nat__power__less__imp__less) ).
thf(2413,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)],[403]) ).
thf(978,axiom,
tc_Complex_Ocomplex @ class_Groups_Oab__semigroup__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) ).
thf(4470,plain,
tc_Complex_Ocomplex @ class_Groups_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(30,axiom,
tc_Nat_Onat @ class_Rings_Olinordered__semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
thf(1146,plain,
tc_Nat_Onat @ class_Rings_Olinordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(864,axiom,
tc_Nat_Onat @ class_Power_Opower,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Power_Opower) ).
thf(4116,plain,
tc_Nat_Onat @ class_Power_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(926,axiom,
tc_Complex_Ocomplex @ class_Groups_Oone,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oone) ).
thf(4354,plain,
tc_Complex_Ocomplex @ class_Groups_Oone,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(1030,axiom,
tc_Complex_Ocomplex @ class_Groups_Ocancel__comm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add) ).
thf(4594,plain,
tc_Complex_Ocomplex @ class_Groups_Ocancel__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(730,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__0 )
=> ( ( ( B @ ( C @ ( E @ c_Polynomial_Osmult ) ) @ ( D @ ( E @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( E @ c_Polynomial_OpCons ) ) ) )
=> ( ( B
= ( C @ ( D @ ( E @ c_Polynomial_Osynthetic__div ) ) ) )
& ( A
= ( C @ ( D @ ( E @ c_Polynomial_Opoly ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__unique) ).
thf(3607,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__0 )
=> ( ( ( B @ ( C @ ( E @ c_Polynomial_Osmult ) ) @ ( D @ ( E @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( E @ c_Polynomial_OpCons ) ) ) )
=> ( ( B
= ( C @ ( D @ ( E @ c_Polynomial_Osynthetic__div ) ) ) )
& ( A
= ( C @ ( D @ ( E @ c_Polynomial_Opoly ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(767,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( A
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equal__neg__zero) ).
thf(3738,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 ) ) ) )
& ( ( A
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(78,axiom,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl) ).
thf(1301,plain,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(711,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/sandbox2/benchmark/theBenchmark.p',fact_poly__pcompose) ).
thf(3523,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)],[711]) ).
thf(754,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
<=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__neg__iff__add__eq__0) ).
thf(3696,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) )
& ( ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(986,axiom,
tc_Complex_Ocomplex @ class_Rings_Osemiring__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring__0) ).
thf(4489,plain,
tc_Complex_Ocomplex @ class_Rings_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(654,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring )
=> ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse ) @ ( B @ c_Rings_Oinverse__class_Oinverse ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__inverse__eq) ).
thf(3343,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring )
=> ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse ) @ ( B @ c_Rings_Oinverse__class_Oinverse ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(607,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__unique) ).
thf(3158,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(361,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/sandbox2/benchmark/theBenchmark.p',fact_mod__mod__cancel) ).
thf(2260,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)],[361]) ).
thf(33,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 ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__negative__iff__negative) ).
thf(1154,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 ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Rings_Oinverse__class_Oinverse ) @ ( 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)],[33]) ).
thf(846,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ozero )
=> ( ( A @ c_Nat_OSuc @ ( B @ ( C @ ( D @ c_Polynomial_OpCons ) ) @ ( D @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Ocoeff ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__pCons__Suc) ).
thf(4041,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ozero )
=> ( ( A @ c_Nat_OSuc @ ( B @ ( C @ ( D @ c_Polynomial_OpCons ) ) @ ( D @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Ocoeff ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(668,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
thf(3387,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B = A )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(234,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add1) ).
thf(1833,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(511,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( 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 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__mult__distrib) ).
thf(2791,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( 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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(695,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/sandbox2/benchmark/theBenchmark.p',fact_not__square__less__zero) ).
thf(3472,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)],[695]) ).
thf(1060,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/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__by__0__iff) ).
thf(4677,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)],[1060]) ).
thf(106,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ c_Nat_OSuc @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) ).
thf(1388,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ c_Nat_OSuc @ ( 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)],[106]) ).
thf(399,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel) ).
thf(2398,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)],[399]) ).
thf(60,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__left) ).
thf(1256,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)],[60]) ).
thf(559,axiom,
! [A: $i] :
( ( A @ c_Nat_OSuc )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
thf(2959,plain,
! [A: $i] :
( ( A @ c_Nat_OSuc )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(628,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 ) ) )
= ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__add__iff1) ).
thf(3234,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 ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= A )
=> ( ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(531,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring__inverse__zero )
=> ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse ) @ ( B @ c_Rings_Oinverse__class_Oinverse ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__inverse__eq) ).
thf(2859,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring__inverse__zero )
=> ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse ) @ ( B @ c_Rings_Oinverse__class_Oinverse ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(907,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( 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 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Oadd) ).
thf(4283,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(854,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( 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 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zminus) ).
thf(4077,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( 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 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(340,axiom,
tc_Int_Oint @ class_Rings_Oring__1__no__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).
thf(2188,plain,
tc_Int_Oint @ class_Rings_Oring__1__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(915,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( D @ c_Polynomial_OpCons ) ) @ ( 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 ) ) @ ( C @ ( B @ ( D @ c_Polynomial_Osmult ) ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pCons__right) ).
thf(4309,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( D @ c_Polynomial_OpCons ) ) @ ( 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 ) ) @ ( C @ ( B @ ( D @ c_Polynomial_Osmult ) ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(184,axiom,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
thf(1652,plain,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(766,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__one__le) ).
thf(3736,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__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(590,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/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__self__implies__10) ).
thf(3081,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)],[590]) ).
thf(976,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__idom) ).
thf(4465,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(812,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 ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Polynomial_Omonom ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__monom) ).
thf(3900,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 ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Polynomial_Omonom ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(1035,axiom,
! [A: $i] :
( ( A @ class_Groups_Ocancel__comm__monoid__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ocancel__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add) ).
thf(4605,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)],[1035]) ).
thf(147,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 ) ) @ ( F @ c_Divides_Odiv__class_Omod ) ) )
= ( D @ ( A @ ( C @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Divides_Odiv__class_Omod ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__cong) ).
thf(1535,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 ) ) @ ( F @ c_Divides_Odiv__class_Omod ) ) )
= ( D @ ( A @ ( C @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Divides_Odiv__class_Omod ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(490,axiom,
! [A: $i] :
( ( A @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).
thf(2716,plain,
! [A: $i] :
( ( A @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(729,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Odivision__ring )
=> ( ( ( B @ ( C @ c_Rings_Oinverse__class_Oinverse ) )
= ( A @ ( C @ c_Rings_Oinverse__class_Oinverse ) ) )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__eq__imp__eq) ).
thf(3604,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Odivision__ring )
=> ( ( ( B @ ( C @ c_Rings_Oinverse__class_Oinverse ) )
= ( A @ ( C @ c_Rings_Oinverse__class_Oinverse ) ) )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(1028,axiom,
tc_Complex_Ocomplex @ class_Rings_Oring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1) ).
thf(4590,plain,
tc_Complex_Ocomplex @ class_Rings_Oring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(142,axiom,
tc_Int_Oint @ class_Groups_Olinordered__ab__group__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).
thf(1520,plain,
tc_Int_Oint @ class_Groups_Olinordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(802,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Oordered__semiring )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono_H) ).
thf(3868,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Oordered__semiring )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(520,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__semiring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( 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__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono) ).
thf(2817,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__semiring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( 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__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(522,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__ring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( 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__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono__neg) ).
thf(2827,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__ring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( 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__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(995,axiom,
tc_Complex_Ocomplex @ class_Rings_Ocomm__semiring__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
thf(4505,plain,
tc_Complex_Ocomplex @ class_Rings_Ocomm__semiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(983,axiom,
tc_Complex_Ocomplex @ class_Groups_Ocomm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__add) ).
thf(4485,plain,
tc_Complex_Ocomplex @ class_Groups_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(1016,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/sandbox2/benchmark/theBenchmark.p',fact_coeff__0) ).
thf(4558,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)],[1016]) ).
thf(775,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ominus) ).
thf(3773,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(498,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/sandbox2/benchmark/theBenchmark.p',fact_mult_Ozero__left) ).
thf(2738,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)],[498]) ).
thf(951,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Power_Opower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Power_Opower) ).
thf(4413,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Power_Opower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(653,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(3340,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(682,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
thf(3436,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(416,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl2) ).
thf(2457,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)],[416]) ).
thf(675,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__le__self__iff) ).
thf(3416,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__eq ) ) )
=> ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__commute) ).
thf(1258,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(647,axiom,
! [A: $i] : ( v_na____ @ ( v_pa____ @ ( A @ ( tc_Complex_Ocomplex @ c_Polynomial_Oorder ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_oop) ).
thf(3304,plain,
! [A: $i] : ( v_na____ @ ( v_pa____ @ ( A @ ( tc_Complex_Ocomplex @ c_Polynomial_Oorder ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(902,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 ) ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_order__1) ).
thf(4245,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 ) ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( 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)],[902]) ).
thf(625,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/sandbox2/benchmark/theBenchmark.p',fact_mod__by__1) ).
thf(3223,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)],[625]) ).
thf(330,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 @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) ).
thf(2161,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 @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(1003,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Int_Oring__char__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Int_Oring__char__0) ).
thf(4526,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)],[1003]) ).
thf(29,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/sandbox2/benchmark/theBenchmark.p',fact_power__inject__exp) ).
thf(1139,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)],[29]) ).
thf(785,axiom,
! [A: $i,B: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
& ( 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 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__is__add) ).
thf(3796,plain,
! [A: $i,B: $i] :
( ( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
& ( 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 ) ) ) )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
& ( 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 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(770,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 ) ) @ ( 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 ) ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__correct_H) ).
thf(3751,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 ) ) @ ( 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 ) ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(868,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__comm__semiring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( 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__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__left__mono) ).
thf(4127,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__comm__semiring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( 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__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(347,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__diff) ).
thf(2220,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(828,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).
thf(3964,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(295,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 ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).
thf(2029,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 ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(886,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Polynomial_Odegree ) )
= ( A @ ( B @ c_Polynomial_Odegree ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__minus) ).
thf(4186,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Polynomial_Odegree ) )
= ( A @ ( B @ c_Polynomial_Odegree ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(198,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add1) ).
thf(1707,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(368,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring )
=> ( ( 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 ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__less__imp__less) ).
thf(2293,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring )
=> ( ( 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 ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(66,axiom,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__refl) ).
thf(1271,plain,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(101,axiom,
tc_Int_Oint @ class_Rings_Olinordered__semiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).
thf(1371,plain,
tc_Int_Oint @ class_Rings_Olinordered__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(740,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(3646,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(863,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__ring )
=> ( ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__pos__le) ).
thf(4112,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__ring )
=> ( ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(622,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/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__monic) ).
thf(3208,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)],[622]) ).
thf(900,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( 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 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Oadd) ).
thf(4236,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(895,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/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__distrib) ).
thf(4218,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)],[895]) ).
thf(700,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/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__1__iff) ).
thf(3487,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)],[700]) ).
thf(13,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 ) ) @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__two) ).
thf(1092,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 ) ) @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(332,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 ) ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_realpow__minus__mult) ).
thf(2166,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 ) ) @ ( 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)],[332]) ).
thf(12,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/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power) ).
thf(1090,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)],[12]) ).
thf(448,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__eq ) ) )
<=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__pos) ).
thf(2573,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__eq ) ) )
=> ( 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__eq ) ) ) )
& ( ( 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__eq ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(960,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( ( B @ ( C @ ( D @ c_Polynomial_Osmult ) ) )
= ( B @ ( A @ ( D @ c_Polynomial_OpCons ) ) ) )
=> ( B
= ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__unique__lemma) ).
thf(4433,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( ( B @ ( C @ ( D @ c_Polynomial_Osmult ) ) )
= ( B @ ( A @ ( D @ c_Polynomial_OpCons ) ) ) )
=> ( B
= ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(95,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( B @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( C @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__self1) ).
thf(1356,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( B @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( C @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(375,axiom,
tc_Int_Oint @ class_Rings_Ono__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).
thf(2311,plain,
tc_Int_Oint @ class_Rings_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(658,axiom,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__cube) ).
thf(3352,plain,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(606,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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(3155,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)],[606]) ).
thf(777,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 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monom__0) ).
thf(3779,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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(150,axiom,
! [A: $i,B: $i] :
( ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
thf(1542,plain,
! [A: $i,B: $i] :
( ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(201,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/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel1) ).
thf(1722,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)],[201]) ).
thf(1026,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/sandbox2/benchmark/theBenchmark.p',fact_poly__rec__0) ).
thf(4586,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)],[1026]) ).
thf(724,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 ) ) @ ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__mult__le) ).
thf(3586,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 ) ) @ ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(122,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__mono) ).
thf(1439,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(41,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/sandbox2/benchmark/theBenchmark.p',fact_gr__implies__not0) ).
thf(1175,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)],[41]) ).
thf(991,axiom,
tc_Complex_Ocomplex @ class_Groups_Ogroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ogroup__add) ).
thf(4498,plain,
tc_Complex_Ocomplex @ class_Groups_Ogroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(71,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 ) ) @ ( 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 ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__period) ).
thf(1282,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 ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( 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 ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(936,axiom,
! [A: $i] :
( ( A @ class_Fields_Ofield )
=> ( A @ tc_Polynomial_Opoly @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Divides_Oring__div) ).
thf(4369,plain,
! [A: $i] :
( ( A @ class_Fields_Ofield )
=> ( A @ tc_Polynomial_Opoly @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(310,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/sandbox2/benchmark/theBenchmark.p',fact_pow__divides__pow__nat) ).
thf(2084,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)],[310]) ).
thf(465,axiom,
tc_Int_Oint @ class_Groups_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).
thf(2624,plain,
tc_Int_Oint @ class_Groups_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(404,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 ) ) @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).
thf(2415,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 ) ) @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(255,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/sandbox2/benchmark/theBenchmark.p',fact_nat__dvd__not__less) ).
thf(1894,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)],[255]) ).
thf(429,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ole__less) ).
thf(2493,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)],[429]) ).
thf(1043,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/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__0__iff) ).
thf(4620,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)],[1043]) ).
thf(161,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/sandbox2/benchmark/theBenchmark.p',fact_mod__self) ).
thf(1574,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)],[161]) ).
thf(225,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 ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__iff1) ).
thf(1806,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 ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(505,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add) ).
thf(2774,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(144,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__linear) ).
thf(1524,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__mono) ).
thf(1349,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(315,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/sandbox2/benchmark/theBenchmark.p',fact_neq0__conv) ).
thf(2097,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)],[315]) ).
thf(637,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
thf(3270,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(268,axiom,
tc_Nat_Onat @ class_Divides_Osemiring__div,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Divides_Osemiring__div) ).
thf(1933,plain,
tc_Nat_Onat @ class_Divides_Osemiring__div,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(359,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).
thf(2257,plain,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( 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)],[359]) ).
thf(167,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 @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__trans__Suc) ).
thf(1589,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 @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(355,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add2) ).
thf(2246,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(172,axiom,
tc_Int_Oint @ class_Rings_Ocomm__ring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).
thf(1603,plain,
tc_Int_Oint @ class_Rings_Ocomm__ring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(1040,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__0 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring) ).
thf(4616,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)],[1040]) ).
thf(618,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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(3197,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)],[618]) ).
thf(222,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/sandbox2/benchmark/theBenchmark.p',fact_neg__mod__bound) ).
thf(1801,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)],[222]) ).
thf(530,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ ( E @ c_Polynomial_OpCons ) ) @ ( C @ ( D @ ( E @ c_Polynomial_OpCons ) ) @ ( E @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( E @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Polynomial_OpCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pCons) ).
thf(2856,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ ( E @ c_Polynomial_OpCons ) ) @ ( C @ ( D @ ( E @ c_Polynomial_OpCons ) ) @ ( E @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( E @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Polynomial_OpCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(883,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_even__less__0__iff) ).
thf(4176,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 ) ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( 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)],[883]) ).
thf(702,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/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__commute) ).
thf(3500,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)],[702]) ).
thf(599,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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(3138,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)],[599]) ).
thf(1056,axiom,
! [A: $i] :
( ( A @ class_Rings_Odivision__ring__inverse__zero )
=> ( ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Rings_Oinverse__class_Oinverse ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__zero) ).
thf(4667,plain,
! [A: $i] :
( ( A @ class_Rings_Odivision__ring__inverse__zero )
=> ( ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Rings_Oinverse__class_Oinverse ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).
thf(515,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/sandbox2/benchmark/theBenchmark.p',fact_degree__monom__eq) ).
thf(2802,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)],[515]) ).
thf(891,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/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel2) ).
thf(4203,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)],[891]) ).
thf(1047,axiom,
tc_Complex_Ocomplex @ class_Rings_Oring__no__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors) ).
thf(4635,plain,
tc_Complex_Ocomplex @ class_Rings_Oring__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).
thf(959,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/sandbox2/benchmark/theBenchmark.p',fact_degree__0) ).
thf(4430,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)],[959]) ).
thf(130,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 ) ) @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__smult) ).
thf(1471,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 ) ) @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(836,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/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd_Ocommute) ).
thf(4009,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)],[836]) ).
thf(1021,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/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__zero__iff) ).
thf(4569,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)],[1021]) ).
thf(285,axiom,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0__right) ).
thf(1993,plain,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(507,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__neg__le) ).
thf(2780,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(1053,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Ozero )
=> ( ( A @ ( B @ ( F @ c_Polynomial_OpCons ) ) @ ( 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 ) @ ( E @ c_If ) ) ) @ ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__rec_Osimps) ).
thf(4652,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Ozero )
=> ( ( A @ ( B @ ( F @ c_Polynomial_OpCons ) ) @ ( 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 ) @ ( E @ c_If ) ) ) @ ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(912,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( C @ ( B @ hAPP ) )
= ( C @ ( A @ hAPP ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).
thf(4296,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( C @ ( B @ hAPP ) )
= ( C @ ( A @ hAPP ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(154,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).
thf(1556,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(104,axiom,
tc_Int_Oint @ class_Rings_Omult__zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).
thf(1381,plain,
tc_Int_Oint @ class_Rings_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(417,axiom,
! [A: $i] : ( A @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__refl) ).
thf(2461,plain,
! [A: $i] : ( A @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(294,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__imp__not__eq2) ).
thf(2025,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)],[294]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( A @ ( 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 @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__base) ).
thf(1080,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( A @ ( 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 @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1010,axiom,
tc_Complex_Ocomplex @ class_Rings_Omult__zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Omult__zero) ).
thf(4541,plain,
tc_Complex_Ocomplex @ class_Rings_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(500,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 ) ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_coeff__mult__degree__sum) ).
thf(2742,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 ) ) @ ( 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)],[500]) ).
thf(377,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__mult__iff) ).
thf(2314,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(466,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 ) ) @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__mono2) ).
thf(2625,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 ) ) @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(722,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
<=> ( A
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equation__minus__iff) ).
thf(3572,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( A
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
=> ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) )
& ( ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
=> ( A
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(36,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 @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__gt1) ).
thf(1162,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 @ ( 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)],[36]) ).
thf(905,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/sandbox2/benchmark/theBenchmark.p',fact_poly__power) ).
thf(4277,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)],[905]) ).
thf(503,axiom,
tc_Nat_Onat @ class_Orderings_Oord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
thf(2757,plain,
tc_Nat_Onat @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(578,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( 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 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(3034,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(832,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/sandbox2/benchmark/theBenchmark.p',fact_mult__0__right) ).
thf(3977,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)],[832]) ).
thf(84,axiom,
tc_Int_Oint @ class_Groups_Oab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).
thf(1325,plain,
tc_Int_Oint @ class_Groups_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(456,axiom,
tc_Int_Oint @ class_Rings_Ocomm__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring) ).
thf(2593,plain,
tc_Int_Oint @ class_Rings_Ocomm__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(688,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/sandbox2/benchmark/theBenchmark.p',fact_poly__monom) ).
thf(3451,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)],[688]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_zpower__zadd__distrib) ).
thf(1293,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( 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)],[74]) ).
thf(441,axiom,
tc_Int_Oint @ class_Rings_Oring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring) ).
thf(2553,plain,
tc_Int_Oint @ class_Rings_Oring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(604,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( 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 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(3150,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(525,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/sandbox2/benchmark/theBenchmark.p',fact_zmod__simps_I4_J) ).
thf(2842,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)],[525]) ).
thf(488,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__eq ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__le__cancel1) ).
thf(2710,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__eq ) ) )
=> ( 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__eq ) ) ) )
& ( ( 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__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(548,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 ) ) )
= ( B @ ( C @ c_Groups_Oone__class_Oone @ ( A @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(2911,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 ) ) )
= ( B @ ( C @ c_Groups_Oone__class_Oone @ ( A @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(698,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__nonneg) ).
thf(3480,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 ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( 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)],[698]) ).
thf(714,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/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel1) ).
thf(3539,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)],[714]) ).
thf(383,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/sandbox2/benchmark/theBenchmark.p',fact_gr0I) ).
thf(2350,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)],[383]) ).
thf(524,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/sandbox2/benchmark/theBenchmark.p',fact_expand__poly__eq) ).
thf(2835,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)],[524]) ).
thf(677,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/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono1) ).
thf(3423,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)],[677]) ).
thf(123,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel__left) ).
thf(1445,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)],[123]) ).
thf(324,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono) ).
thf(2139,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(746,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/sandbox2/benchmark/theBenchmark.p',fact_power__mult) ).
thf(3674,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)],[746]) ).
thf(662,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
<=> ( ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
| ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__two__disj) ).
thf(3363,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( ( ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
| ( B = A ) )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
=> ( ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
| ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(132,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).
thf(1477,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( A = B )
=> ( B @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(437,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oeq__iff) ).
thf(2535,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)],[437]) ).
thf(888,axiom,
tc_Nat_Onat @ class_Groups_Oordered__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
thf(4196,plain,
tc_Nat_Onat @ class_Groups_Oordered__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(806,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 ) ) @ ( C @ c_Polynomial_Opos__poly ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__add) ).
thf(3876,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 ) ) @ ( C @ c_Polynomial_Opos__poly ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(306,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leE) ).
thf(2069,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(265,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( C @ ( D @ ( E @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ ( E @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__dvd) ).
thf(1926,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( C @ ( D @ ( E @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ ( E @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(560,axiom,
tc_Nat_Onat @ class_Groups_Oab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
thf(2962,plain,
tc_Nat_Onat @ class_Groups_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(493,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__minus) ).
thf(2725,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(169,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( C = B )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__eq__le__trans) ).
thf(1594,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( C = B )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(346,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel__right) ).
thf(2212,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)],[346]) ).
thf(735,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/sandbox2/benchmark/theBenchmark.p',fact_power__0__left) ).
thf(3627,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)],[735]) ).
thf(994,axiom,
! [A: $i] :
( ( A @ class_Rings_Ozero__neq__one )
=> ( ( A @ c_Groups_Ozero__class_Ozero )
!= ( A @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__neq__one) ).
thf(4502,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)],[994]) ).
thf(938,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).
thf(4373,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)],[938]) ).
thf(629,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( 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 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib) ).
thf(3241,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( 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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( B @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Rings_Oinverse__class_Oinverse ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Orderings_Oord__class_Oless ) ) )
| ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__less__1__iff) ).
thf(1113,plain,
! [A: $i,B: $i] :
( ( B @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Orderings_Oord__class_Oless ) ) )
| ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Rings_Oinverse__class_Oinverse ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Rings_Oinverse__class_Oinverse ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Orderings_Oord__class_Oless ) ) )
| ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(513,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__semiring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( 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__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono) ).
thf(2797,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__semiring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( 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__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(202,axiom,
! [A: $i] :
( ( A @ class_Fields_Ofield )
=> ( A @ tc_Polynomial_Opoly @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Divides_Osemiring__div) ).
thf(1726,plain,
! [A: $i] :
( ( A @ class_Fields_Ofield )
=> ( A @ tc_Polynomial_Opoly @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(98,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
thf(1364,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(656,axiom,
tc_Nat_Onat @ class_Rings_Osemiring__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).
thf(3348,plain,
tc_Nat_Onat @ class_Rings_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(328,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diffs0__imp__equal) ).
thf(2156,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(156,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__power__same) ).
thf(1562,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)],[156]) ).
thf(857,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( 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 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Odiff) ).
thf(4084,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(179,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 ) )
<=> ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__power__eq__Suc__0__iff) ).
thf(1626,plain,
! [A: $i,B: $i] :
( ( ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( 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 ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
=> ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(272,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).
thf(1948,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(463,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__imp__le) ).
thf(2614,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)],[463]) ).
thf(79,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 ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add1) ).
thf(1304,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 ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(190,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__not__sym) ).
thf(1684,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)],[190]) ).
thf(910,axiom,
tc_Nat_Onat @ class_Groups_Oordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(4292,plain,
tc_Nat_Onat @ class_Groups_Oordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(88,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__antisym) ).
thf(1340,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)],[88]) ).
thf(1023,axiom,
( v_qa____
!= ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q0) ).
thf(4581,plain,
( v_qa____
!= ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(927,axiom,
! [A: $i] :
( ( A @ class_Groups_Oab__group__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__group__add) ).
thf(4355,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)],[927]) ).
thf(544,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/sandbox2/benchmark/theBenchmark.p',fact_mult__0) ).
thf(2899,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)],[544]) ).
thf(152,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__antisym) ).
thf(1551,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(452,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less1) ).
thf(2582,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(115,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq) ).
thf(1413,plain,
! [A: $i,B: $i] :
( ( ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ c_Nat_OSuc @ ( 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)],[115]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__nonnegative__iff__nonnegative) ).
thf(1076,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__eq ) ) )
=> ( A @ ( B @ c_Rings_Oinverse__class_Oinverse ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(549,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
thf(2914,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C = A )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(577,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 ) ) @ ( F @ c_Divides_Odiv__class_Omod ) ) )
= ( D @ ( A @ ( C @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Divides_Odiv__class_Omod ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__diff__cong) ).
thf(3031,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 ) ) @ ( F @ c_Divides_Odiv__class_Omod ) ) )
= ( D @ ( A @ ( C @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Divides_Odiv__class_Omod ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(213,axiom,
! [A: $i] :
( ( A @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__self) ).
thf(1758,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)],[213]) ).
thf(317,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__is__0__eq_H) ).
thf(2107,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(972,axiom,
tc_Complex_Ocomplex @ class_Groups_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add) ).
thf(4458,plain,
tc_Complex_Ocomplex @ class_Groups_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(478,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).
thf(2665,plain,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B = A )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(669,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Odivision__ring__inverse__zero )
=> ( ( ( B @ ( C @ c_Rings_Oinverse__class_Oinverse ) )
= ( A @ ( C @ c_Rings_Oinverse__class_Oinverse ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__eq__iff__eq) ).
thf(3395,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Odivision__ring__inverse__zero )
=> ( ( ( B = A )
=> ( ( B @ ( C @ c_Rings_Oinverse__class_Oinverse ) )
= ( A @ ( C @ c_Rings_Oinverse__class_Oinverse ) ) ) )
& ( ( ( B @ ( C @ c_Rings_Oinverse__class_Oinverse ) )
= ( A @ ( C @ c_Rings_Oinverse__class_Oinverse ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(508,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/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self2__is__0) ).
thf(2784,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)],[508]) ).
thf(608,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_Osmult ) ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__smult) ).
thf(3161,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_Osmult ) ) @ ( 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)],[608]) ).
thf(259,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__mono) ).
thf(1905,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(69,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__eq ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__le__mono) ).
thf(1277,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__eq ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(320,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__eq) ).
thf(2124,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( 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)],[320]) ).
thf(27,axiom,
tc_Int_Oint @ class_Rings_Olinordered__semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).
thf(1134,plain,
tc_Int_Oint @ class_Rings_Olinordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(602,axiom,
tc_Nat_Onat @ class_Groups_Omonoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).
thf(3146,plain,
tc_Nat_Onat @ class_Groups_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(1020,axiom,
( v_n
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_assms_I3_J) ).
thf(4566,plain,
( v_n
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).
thf(482,axiom,
tc_Int_Oint @ class_Groups_Oordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(2684,plain,
tc_Int_Oint @ class_Groups_Oordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(1063,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/sandbox2/benchmark/theBenchmark.p',fact_monom__eq__0__iff) ).
thf(4688,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)],[1063]) ).
thf(446,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/sandbox2/benchmark/theBenchmark.p',fact_mod__by__0) ).
thf(2564,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)],[446]) ).
thf(447,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/sandbox2/benchmark/theBenchmark.p',fact_pow__divides__eq__nat) ).
thf(2567,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)],[447]) ).
thf(208,axiom,
tc_Int_Oint @ class_Groups_Oab__group__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).
thf(1748,plain,
tc_Int_Oint @ class_Groups_Oab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(370,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__trans) ).
thf(2298,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)],[370]) ).
thf(664,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/sandbox2/benchmark/theBenchmark.p',fact_mult__1__right) ).
thf(3376,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)],[664]) ).
thf(814,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Omonoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__mult) ).
thf(3913,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)],[814]) ).
thf(392,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult) ).
thf(2375,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)],[392]) ).
thf(771,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 ) @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ c_Rings_Oinverse__class_Oinverse ) @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse ) @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__add) ).
thf(3754,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 ) @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ c_Rings_Oinverse__class_Oinverse ) @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse ) @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(211,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 ) ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono) ).
thf(1753,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 ) ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(133,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__Suc) ).
thf(1484,plain,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(16,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/sandbox2/benchmark/theBenchmark.p',fact_power__less__power__Suc) ).
thf(1098,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)],[16]) ).
thf(539,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/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__mult2) ).
thf(2882,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)],[539]) ).
thf(738,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring )
=> ( 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 ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__ge__zero) ).
thf(3640,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring )
=> ( 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 ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(170,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 ) ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__geq) ).
thf(1598,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 ) ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(930,axiom,
tc_Complex_Ocomplex @ class_Rings_Odvd,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odvd) ).
thf(4360,plain,
tc_Complex_Ocomplex @ class_Rings_Odvd,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(705,axiom,
tc_Nat_Onat @ class_Rings_Oordered__comm__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).
thf(3507,plain,
tc_Nat_Onat @ class_Rings_Oordered__comm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(3,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__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__le__zero) ).
thf(1070,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__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(987,axiom,
tc_Complex_Ocomplex @ class_Rings_Oring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring) ).
thf(4490,plain,
tc_Complex_Ocomplex @ class_Rings_Oring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_fequal ) @ hBOOL )
| ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__2) ).
thf(1225,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_fequal ) @ hBOOL )
| ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(304,axiom,
tc_Int_Oint @ class_Rings_Olinordered__comm__semiring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).
thf(2060,plain,
tc_Int_Oint @ class_Rings_Olinordered__comm__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(342,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/sandbox2/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
thf(2192,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)],[342]) ).
thf(1058,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/sandbox2/benchmark/theBenchmark.p',fact_not__pos__poly__0) ).
thf(4673,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)],[1058]) ).
thf(158,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/sandbox2/benchmark/theBenchmark.p',fact_zdvd__zmod__imp__zdvd) ).
thf(1566,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)],[158]) ).
thf(291,axiom,
tc_Int_Oint @ class_Rings_Osemiring__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).
thf(2012,plain,
tc_Int_Oint @ class_Rings_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(792,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).
thf(3833,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(1007,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Olinordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add) ).
thf(4534,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)],[1007]) ).
thf(496,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/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__left) ).
thf(2732,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)],[496]) ).
thf(890,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_OpCons ) ) @ ( 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 ) ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pcompose__pCons) ).
thf(4200,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_OpCons ) ) @ ( 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 ) ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(100,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ c_Nat_OSuc )
!= A )
=> ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessI) ).
thf(1368,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ c_Nat_OSuc )
!= A )
=> ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(999,axiom,
( ( v_pa____ @ ( v_a____ @ ( tc_Complex_Ocomplex @ c_Polynomial_Oorder ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_oa) ).
thf(4517,plain,
( ( v_pa____ @ ( v_a____ @ ( tc_Complex_Ocomplex @ c_Polynomial_Oorder ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(491,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Osemiring__0 )
& ( B @ class_Power_Opower ) )
=> ( ( A @ c_Nat_OSuc @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__Suc) ).
thf(2720,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Osemiring__0 )
& ( B @ class_Power_Opower ) )
=> ( ( A @ c_Nat_OSuc @ ( 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)],[491]) ).
thf(804,axiom,
tc_Nat_Onat @ class_Groups_Oab__semigroup__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
thf(3872,plain,
tc_Nat_Onat @ class_Groups_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(940,axiom,
( ( v_a____ @ ( v_pa____ @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) )
= ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_a) ).
thf(4377,plain,
( ( v_a____ @ ( v_pa____ @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) )
= ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(919,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__one__le) ).
thf(4324,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__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(1045,axiom,
! [A: $i] :
( ( ( A @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) )
= ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( v_q @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) )
= ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_assms_I1_J) ).
thf(4630,plain,
! [A: $i] :
( ( ( A @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) )
= ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( v_q @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) )
= ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(687,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/sandbox2/benchmark/theBenchmark.p',fact_power__one) ).
thf(3448,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)],[687]) ).
thf(314,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__poly__gcd__iff) ).
thf(2092,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)],[314]) ).
thf(808,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( A @ ( B @ ( C @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__power__le) ).
thf(3885,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( A @ ( B @ ( C @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Odegree ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(835,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/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__eq__0__iff) ).
thf(4003,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)],[835]) ).
thf(364,axiom,
! [A: $i,B: $i] :
( ( B = A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oeq__refl) ).
thf(2276,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)],[364]) ).
thf(233,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SucE) ).
thf(1830,plain,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( 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)],[233]) ).
thf(925,axiom,
( ( v_qa____
= ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( v_na____ @ ( v_qa____ @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( v_pa____ @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_calculation) ).
thf(4351,plain,
( ( v_qa____
= ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( v_na____ @ ( v_qa____ @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( v_pa____ @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(148,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funD) ).
thf(1538,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(299,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( E @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( E @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma) ).
thf(2044,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( E @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( E @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(420,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 @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__power__le) ).
thf(2468,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 @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(739,axiom,
! [A: $i] :
( ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__nonzero) ).
thf(3642,plain,
! [A: $i] :
( ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(1017,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 ) ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__0__right) ).
thf(4561,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 ) ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(219,axiom,
tc_Int_Oint @ class_Groups_Ogroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).
thf(1790,plain,
tc_Int_Oint @ class_Groups_Ogroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(822,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 ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( D @ c_Groups_Ouminus__class_Ouminus ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__minus__cong) ).
thf(3940,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 ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( D @ c_Groups_Ouminus__class_Ouminus ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(349,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( 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__eq ) ) )
=> ( ( C @ ( 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 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__neg__lemma) ).
thf(2224,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( 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__eq ) ) )
=> ( ( C @ ( 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 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(415,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__commute) ).
thf(2454,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(228,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ole__less__trans) ).
thf(1813,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)],[228]) ).
thf(752,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/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self1__is__0) ).
thf(3691,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)],[752]) ).
thf(180,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__0__iff) ).
thf(1637,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(638,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/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__mult1) ).
thf(3273,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)],[638]) ).
thf(620,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 ) )
= ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__power__inverse) ).
thf(3202,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 ) )
= ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(246,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Ominus__class_Ominus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0__right) ).
thf(1869,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Ominus__class_Ominus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(875,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring )
=> ( ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__zero__imp__zero) ).
thf(4145,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring )
=> ( ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(790,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( 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 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oadd__right) ).
thf(3823,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(870,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(4132,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(378,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 ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add2) ).
thf(2322,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 ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ c_Nat_OSuc @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ c_Nat_OSuc @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__imp__le__base) ).
thf(1130,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ c_Nat_OSuc @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ c_Nat_OSuc @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(865,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( 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 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Suc__right) ).
thf(4117,plain,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( 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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(164,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add1__zle__eq) ).
thf(1579,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(206,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oneq__le__trans) ).
thf(1738,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)],[206]) ).
thf(592,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/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__unique__mod) ).
thf(3095,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)],[592]) ).
thf(879,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__ab__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__imp__eq) ).
thf(4164,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__ab__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(760,axiom,
v_pa____ @ ( v_pa____ @ ( v_a____ @ ( tc_Complex_Ocomplex @ c_Polynomial_Oorder ) ) @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( tc_Complex_Ocomplex @ c_Groups_Oone__class_Oone @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( v_a____ @ ( tc_Complex_Ocomplex @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ap_I1_J) ).
thf(3715,plain,
v_pa____ @ ( v_pa____ @ ( v_a____ @ ( tc_Complex_Ocomplex @ c_Polynomial_Oorder ) ) @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( tc_Complex_Ocomplex @ c_Groups_Oone__class_Oone @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( v_a____ @ ( tc_Complex_Ocomplex @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(269,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 ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_odd__less__0) ).
thf(1934,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 ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( 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 ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( 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)],[269]) ).
thf(402,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 ) ) @ ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).
thf(2411,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 ) ) @ ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(257,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__imp__not__eq) ).
thf(1898,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)],[257]) ).
thf(280,axiom,
tc_Int_Oint @ class_Divides_Osemiring__div,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Osemiring__div) ).
thf(1981,plain,
tc_Int_Oint @ class_Divides_Osemiring__div,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(1038,axiom,
( v_na____
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n0) ).
thf(4611,plain,
( v_na____
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(961,axiom,
( v_pa____
!= ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pne) ).
thf(4436,plain,
( v_pa____
!= ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(565,axiom,
v_qa____ @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( tc_Complex_Ocomplex @ c_Groups_Oone__class_Oone @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( v_a____ @ ( tc_Complex_Ocomplex @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_091_058_N_Aa_M_A1_058_093_Advd_Aq_096) ).
thf(2975,plain,
v_qa____ @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( tc_Complex_Ocomplex @ c_Groups_Oone__class_Oone @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( v_a____ @ ( tc_Complex_Ocomplex @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(450,axiom,
tc_Int_Oint @ class_Power_Opower,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Power_Opower) ).
thf(2579,plain,
tc_Int_Oint @ class_Power_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(209,axiom,
tc_Int_Oint @ class_Rings_Olinordered__idom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).
thf(1749,plain,
tc_Int_Oint @ class_Rings_Olinordered__idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(250,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__triv__right) ).
thf(1881,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)],[250]) ).
thf(480,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__minus__eq) ).
thf(2675,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( B = A )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(112,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__eq ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__less__mono) ).
thf(1404,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__eq ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(444,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 ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
thf(2558,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 ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(830,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 ) ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
thf(3970,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 ) ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( 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)],[830]) ).
thf(196,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/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono__neg) ).
thf(1702,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)],[196]) ).
thf(394,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( F @ ( D @ ( 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__eq ) ) )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( F @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( E @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).
thf(2379,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( F @ ( D @ ( 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__eq ) ) )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( F @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( E @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(998,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/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__eq__0__iff) ).
thf(4510,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)],[998]) ).
thf(386,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__right__eq) ).
thf(2357,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(278,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 @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( 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 ) ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_order) ).
thf(1972,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 @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( 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 ) ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( 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)],[278]) ).
thf(139,axiom,
tc_Int_Oint @ class_Groups_Ocomm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).
thf(1506,plain,
tc_Int_Oint @ class_Groups_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(165,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 ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).
thf(1585,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 ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(14,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/sandbox2/benchmark/theBenchmark.p',fact_zero__less__one) ).
thf(1094,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)],[14]) ).
thf(432,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/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__right__disj) ).
thf(2511,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)],[432]) ).
thf(1064,axiom,
tc_Complex_Ocomplex @ class_Rings_Osemiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring) ).
thf(4695,plain,
tc_Complex_Ocomplex @ class_Rings_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(576,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/sandbox2/benchmark/theBenchmark.p',fact_coeff__monom) ).
thf(3024,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)],[576]) ).
thf(494,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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(2728,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)],[494]) ).
thf(823,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ( A @ ( C @ c_Polynomial_Odegree ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ? [D: $i] :
( ( ( D @ ( A @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) )
!= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( D @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__degree__imp) ).
thf(3943,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ( A @ ( C @ c_Polynomial_Odegree ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ? [D: $i] :
( ( ( D @ ( A @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) )
!= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( D @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(200,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field__inverse__zero )
=> ( ! [D: $i] :
( ( D @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( D @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__le__mult__one__interval) ).
thf(1717,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field__inverse__zero )
=> ( ! [D: $i] :
( ( D @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( D @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(922,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).
thf(4342,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(827,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring )
=> ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Rings_Oinverse__class_Oinverse ) )
= ( A @ ( B @ c_Rings_Oinverse__class_Oinverse ) @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__minus__eq) ).
thf(3961,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring )
=> ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Rings_Oinverse__class_Oinverse ) )
= ( A @ ( B @ c_Rings_Oinverse__class_Oinverse ) @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(588,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/sandbox2/benchmark/theBenchmark.p',fact_nat__0__less__mult__iff) ).
thf(3071,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)],[588]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__diff__iff) ).
thf(1372,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( B = A )
=> ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) )
& ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(634,axiom,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ c_Nat_OSuc )
!= A )
=> ( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ c_Nat_OSuc ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ c_Nat_OSuc )
= A )
=> ( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__Suc) ).
thf(3256,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ c_Nat_OSuc )
!= A )
=> ( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ c_Nat_OSuc ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ c_Nat_OSuc )
= A )
=> ( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(710,axiom,
! [A: $i,B: $i] :
( ( B @ class_Fields_Ofield )
=> ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( A @ ( B @ c_Rings_Oinverse__class_Oinverse ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__inverse) ).
thf(3520,plain,
! [A: $i,B: $i] :
( ( B @ class_Fields_Ofield )
=> ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( A @ ( B @ c_Rings_Oinverse__class_Oinverse ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(527,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/sandbox2/benchmark/theBenchmark.p',fact_mult__poly__0__right) ).
thf(2848,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)],[527]) ).
thf(750,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= B )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
thf(3684,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= B )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(643,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ozero )
=> ( ( ( C @ ( D @ ( E @ c_Polynomial_OpCons ) ) )
= ( A @ ( B @ ( E @ c_Polynomial_OpCons ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__eq__iff) ).
thf(3288,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 ) ) )
= ( A @ ( B @ ( E @ c_Polynomial_OpCons ) ) ) ) )
& ( ( ( C @ ( D @ ( E @ c_Polynomial_OpCons ) ) )
= ( A @ ( B @ ( E @ c_Polynomial_OpCons ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(292,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__0__eq) ).
thf(2013,plain,
! [A: $i] :
( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(909,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_Osmult ) ) @ ( D @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Ocoeff ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__smult) ).
thf(4289,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_Osmult ) ) @ ( 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)],[909]) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__dvd__imp__le) ).
thf(1459,plain,
! [A: $i,B: $i,C: $i] :
( ( 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_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(42,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/sandbox2/benchmark/theBenchmark.p',fact_power__power__power) ).
thf(1180,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)],[42]) ).
thf(276,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 ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
thf(1966,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 ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(540,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/sandbox2/benchmark/theBenchmark.p',fact_zmod__eq__0__iff) ).
thf(2885,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)],[540]) ).
thf(485,axiom,
! [A: $i,B: $i] : ( B @ c_Nat_OSuc @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__Suc) ).
thf(2696,plain,
! [A: $i,B: $i] : ( B @ c_Nat_OSuc @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(535,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oab__semigroup__add )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(2870,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oab__semigroup__add )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(229,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__conv) ).
thf(1817,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(954,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__0 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__0) ).
thf(4419,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)],[954]) ).
thf(713,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 ) ) @ ( A @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unity__coeff__ex) ).
thf(3533,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 ) ) @ ( 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 ) ) @ ( A @ ( C @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(615,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/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ozero) ).
thf(3188,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)],[615]) ).
thf(185,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B != A )
& ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__le) ).
thf(1654,plain,
! [A: $i,B: $i] :
( ( ( ( B != A )
& ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B != A )
& ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(462,axiom,
! [A: $i,B: $i] :
~ ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less2) ).
thf(2611,plain,
! [A: $i,B: $i] :
~ ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(655,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonneg) ).
thf(3346,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(204,axiom,
tc_Int_Oint @ class_Groups_Ominus,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ominus) ).
thf(1734,plain,
tc_Int_Oint @ class_Groups_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( B @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_one__less__inverse__iff) ).
thf(1108,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 ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse ) @ ( 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)],[19]) ).
thf(533,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ominus__left) ).
thf(2865,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(270,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( B @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).
thf(1940,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(262,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__refl) ).
thf(1918,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)],[262]) ).
thf(690,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/sandbox2/benchmark/theBenchmark.p',fact_poly__dvd__antisym) ).
thf(3457,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)],[690]) ).
thf(1066,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__ring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1) ).
thf(4698,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)],[1066]) ).
thf(9,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 ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__add__strict) ).
thf(1084,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 ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(956,axiom,
tc_Complex_Ocomplex @ class_Groups_Ocancel__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) ).
thf(4424,plain,
tc_Complex_Ocomplex @ class_Groups_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(872,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/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono2) ).
thf(4138,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)],[872]) ).
thf(772,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/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__assoc) ).
thf(3757,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)],[772]) ).
thf(423,axiom,
tc_Int_Oint @ class_Rings_Olinordered__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).
thf(2479,plain,
tc_Int_Oint @ class_Rings_Olinordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(374,axiom,
tc_Int_Oint @ class_Divides_Oring__div,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Oring__div) ).
thf(2310,plain,
tc_Int_Oint @ class_Divides_Oring__div,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(237,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__pos__nat) ).
thf(1844,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)],[237]) ).
thf(318,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/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power__nat__eq) ).
thf(2110,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)],[318]) ).
thf(651,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
<=> ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
& ( 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 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__1) ).
thf(3320,plain,
! [A: $i,B: $i] :
( ( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
& ( 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 ) ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
=> ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
& ( 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 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(372,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__mod__imp__dvd) ).
thf(2305,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)],[372]) ).
thf(975,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oidom) ).
thf(4463,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(881,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( 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 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib2) ).
thf(4170,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( 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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(382,axiom,
! [A: $i] :
( ( v_na____ @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ! [B: $i,C: $i] :
( ! [D: $i] :
( ( ( D @ ( B @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) )
= ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) )
=> ( ( D @ ( C @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) )
= ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( ( B @ ( tc_Complex_Ocomplex @ c_Polynomial_Odegree ) )
= A )
=> ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( C @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IH) ).
thf(2342,plain,
! [A: $i] :
( ( v_na____ @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ! [B: $i,C: $i] :
( ! [D: $i] :
( ( ( D @ ( B @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) )
= ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) )
=> ( ( D @ ( C @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) )
= ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( ( B @ ( tc_Complex_Ocomplex @ c_Polynomial_Odegree ) )
= A )
=> ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( C @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(584,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( 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 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Ominus) ).
thf(3056,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( 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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(350,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( B
= ( A @ c_Nat_OSuc ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__eq) ).
thf(2226,plain,
! [A: $i,B: $i] :
( ( ( ( B
= ( A @ c_Nat_OSuc ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B
= ( A @ c_Nat_OSuc ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(124,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zminus2) ).
thf(1453,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(413,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oord__less__eq__trans) ).
thf(2443,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)],[413]) ).
thf(85,axiom,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oorder__refl) ).
thf(1326,plain,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(363,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ c_Nat_OSuc @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_power_Opower_Opower__Suc) ).
thf(2273,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ c_Nat_OSuc @ ( 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)],[363]) ).
thf(699,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 ) ) @ ( 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 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__add) ).
thf(3484,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 ) ) @ ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(781,axiom,
tc_Nat_Onat @ class_Groups_Ocomm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
thf(3789,plain,
tc_Nat_Onat @ class_Groups_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(357,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 @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( C @ ( B @ ( 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__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux1) ).
thf(2251,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 @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( C @ ( B @ ( 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__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(442,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/sandbox2/benchmark/theBenchmark.p',fact_int__0__less__1) ).
thf(2554,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)],[442]) ).
thf(518,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 ) ) @ ( 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 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__poly__add__left) ).
thf(2811,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 ) ) @ ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(769,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 ) ) @ ( B @ ( C @ c_Polynomial_OpCons ) ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_coeff__linear__power) ).
thf(3748,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 ) ) @ ( B @ ( C @ c_Polynomial_OpCons ) ) @ ( 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)],[769]) ).
thf(240,axiom,
tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
thf(1854,plain,
tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(410,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__imp__add1__zle) ).
thf(2431,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(693,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
thf(3465,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 ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( 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)],[693]) ).
thf(455,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__trans) ).
thf(2591,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(731,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/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__strict__left__mono) ).
thf(3613,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)],[731]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Power_Opower )
=> ( ( A @ c_Nat_OSuc @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_power__Suc) ).
thf(1253,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Power_Opower )
=> ( ( A @ c_Nat_OSuc @ ( 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)],[59]) ).
thf(570,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/sandbox2/benchmark/theBenchmark.p',fact_nat__1__eq__mult__iff) ).
thf(2988,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)],[570]) ).
thf(457,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 ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).
thf(2594,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 ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(335,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 ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono1) ).
thf(2174,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 ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(366,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__1__iff__1) ).
thf(2283,plain,
! [A: $i] :
( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(624,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oab__group__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__left__minus) ).
thf(3220,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oab__group__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(1011,axiom,
! [A: $i] :
( ( A @ class_Rings_Ozero__neq__one )
=> ( ( A @ c_Groups_Oone__class_Oone )
!= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__neq__zero) ).
thf(4542,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)],[1011]) ).
thf(321,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_dvd__reduce) ).
thf(2130,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 ) ) @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( 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)],[321]) ).
thf(799,axiom,
! [A: $i] :
( ( A @ class_Groups_Ogroup__add )
=> ( ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__zero) ).
thf(3859,plain,
! [A: $i] :
( ( A @ class_Groups_Ogroup__add )
=> ( ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(155,axiom,
! [A: $i] :
( ( A @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).
thf(1558,plain,
! [A: $i] :
( ( A @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(553,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
thf(2934,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(969,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Osmult ) ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__0__left) ).
thf(4451,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Osmult ) ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(397,axiom,
tc_Int_Oint @ class_Rings_Olinordered__ring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).
thf(2394,plain,
tc_Int_Oint @ class_Rings_Olinordered__ring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(244,axiom,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le0) ).
thf(1861,plain,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(558,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ c_Polynomial_Ocoeff ) )
= ( A @ ( C @ c_Polynomial_Ocoeff ) @ ( B @ ( C @ c_Nat_Onat_Onat__case ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__pCons) ).
thf(2956,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ c_Polynomial_Ocoeff ) )
= ( A @ ( C @ c_Polynomial_Ocoeff ) @ ( B @ ( C @ c_Nat_Onat_Onat__case ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(911,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_OpCons ) ) @ ( 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 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__pCons) ).
thf(4293,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_OpCons ) ) @ ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(298,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__antisym) ).
thf(2041,plain,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(701,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) )
= ( A @ ( C @ c_Polynomial_Ocoeff ) @ ( B @ ( C @ c_Nat_Onat_Onat__case ) ) @ ( C @ c_Polynomial_OAbs__poly ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__def) ).
thf(3497,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) )
= ( 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)],[701]) ).
thf(380,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__is__0__eq) ).
thf(2330,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(81,axiom,
tc_Int_Oint @ class_Rings_Ocomm__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).
thf(1308,plain,
tc_Int_Oint @ class_Rings_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(980,axiom,
! [A: $i] :
( ( A @ class_Groups_Ocancel__comm__monoid__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ocancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add) ).
thf(4478,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)],[980]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( 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 )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__diffD) ).
thf(1193,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( 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 )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(747,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 ) ) @ ( 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 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__diff) ).
thf(3677,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 ) ) @ ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(82,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__eq__mod__eq__0) ).
thf(1309,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)],[82]) ).
thf(717,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/sandbox2/benchmark/theBenchmark.p',fact_no__zero__divisors) ).
thf(3552,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)],[717]) ).
thf(192,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).
thf(1689,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(309,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__commute) ).
thf(2081,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(753,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( 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__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono1) ).
thf(3694,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( 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__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(1034,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/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd_Osimps_I2_J) ).
thf(4602,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)],[1034]) ).
thf(889,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/sandbox2/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).
thf(4197,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)],[889]) ).
thf(1052,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 ) ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_poly__rec__pCons) ).
thf(4649,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 ) ) @ ( 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)],[1052]) ).
thf(794,axiom,
tc_Nat_Onat @ class_Groups_Oone,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
thf(3844,plain,
tc_Nat_Onat @ class_Groups_Oone,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(474,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__linear) ).
thf(2648,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(218,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( 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 ) ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).
thf(1777,plain,
! [A: $i,B: $i] :
( ( ( ? [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B
= ( C @ c_Nat_OSuc ) ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ c_Nat_OSuc @ ( 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 ) ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(1029,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 ) ) @ ( C @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) )
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Polynomial_OpCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__single) ).
thf(4591,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 ) ) @ ( C @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) )
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Polynomial_OpCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(636,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Oring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__diff__left__eq) ).
thf(3267,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Oring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(913,axiom,
! [A: $i] :
( ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zminus__inverse2) ).
thf(4299,plain,
! [A: $i] :
( ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(727,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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(3598,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)],[727]) ).
thf(783,axiom,
tc_Nat_Onat @ class_Rings_Ocomm__semiring__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__0) ).
thf(3793,plain,
tc_Nat_Onat @ class_Rings_Ocomm__semiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(51,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__le) ).
thf(1212,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)],[51]) ).
thf(545,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 ) ) @ ( C @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(2902,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 ) ) @ ( C @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(319,axiom,
! [A: $i] :
( ( A @ c_Nat_OSuc )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
thf(2120,plain,
! [A: $i] :
( ( A @ c_Nat_OSuc )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(853,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/sandbox2/benchmark/theBenchmark.p',fact_coeff__eq__0) ).
thf(4074,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)],[853]) ).
thf(966,axiom,
! [A: $i] :
( ( A @ class_Groups_Oab__group__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ouminus ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ouminus) ).
thf(4446,plain,
! [A: $i] :
( ( A @ class_Groups_Oab__group__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ouminus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(841,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/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__mult) ).
thf(4025,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)],[841]) ).
thf(1042,axiom,
tc_Complex_Ocomplex @ class_Groups_Omonoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__add) ).
thf(4619,plain,
tc_Complex_Ocomplex @ class_Groups_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(676,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/sandbox2/benchmark/theBenchmark.p',fact_mult__idem) ).
thf(3420,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)],[676]) ).
thf(176,axiom,
! [A: $i,B: $i] :
( ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ hAPP ) @ hBOOL )
=> ? [C: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ hAPP ) @ hBOOL )
& ! [D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( D @ ( B @ hAPP ) @ hBOOL ) )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__least__nat__less) ).
thf(1614,plain,
! [A: $i,B: $i] :
( ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ hAPP ) @ hBOOL )
=> ? [C: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ hAPP ) @ hBOOL )
& ! [D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( D @ ( B @ hAPP ) @ hBOOL ) )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(743,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( A @ ( B @ ( D @ c_Polynomial_Osmult ) ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_dvd__smult__cancel) ).
thf(3658,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( A @ ( B @ ( D @ c_Polynomial_Osmult ) ) @ ( 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)],[743]) ).
thf(371,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/sandbox2/benchmark/theBenchmark.p',fact_zmult__commute) ).
thf(2302,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)],[371]) ).
thf(801,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring )
=> ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_Opoly ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Polynomial_Opoly ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__minus) ).
thf(3865,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring )
=> ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_Opoly ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Polynomial_Opoly ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(635,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/sandbox2/benchmark/theBenchmark.p',fact_power__mult__distrib) ).
thf(3264,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)],[635]) ).
thf(663,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 ) ) @ ( C @ ( D @ c_Polynomial_Opoly ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__offset__poly) ).
thf(3373,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 ) ) @ ( C @ ( D @ c_Polynomial_Opoly ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(1032,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/sandbox2/benchmark/theBenchmark.p',fact_pcompose__0) ).
thf(4597,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)],[1032]) ).
thf(934,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
thf(4367,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(289,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__eq ) ) )
<=> ( ( 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__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel1) ).
thf(2003,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__eq ) ) ) )
=> ( 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__eq ) ) ) )
& ( ( 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__eq ) ) )
=> ( ( 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__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(665,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ( ( A @ ( B @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) )
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( B @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__degree) ).
thf(3379,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ( ( A @ ( B @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) )
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( B @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(163,axiom,
tc_Int_Oint @ class_Rings_Oordered__comm__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).
thf(1578,plain,
tc_Int_Oint @ class_Rings_Oordered__comm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(947,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring__inverse__zero )
=> ( ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__nonzero__iff__nonzero) ).
thf(4399,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 ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(1062,axiom,
tc_Complex_Ocomplex @ class_Rings_Odivision__ring__inverse__zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero) ).
thf(4687,plain,
tc_Complex_Ocomplex @ class_Rings_Odivision__ring__inverse__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).
thf(396,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 ) ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__gt__zero__iff) ).
thf(2385,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 ) ) @ ( 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 ) ) @ ( 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)],[396]) ).
thf(1057,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Polynomial_Opos__poly ) )
| ( A @ ( B @ c_Polynomial_Opos__poly ) )
| ( A
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__total) ).
thf(4670,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) @ ( 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)],[1057]) ).
thf(779,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/sandbox2/benchmark/theBenchmark.p',fact_leading__coeff__neq__0) ).
thf(3785,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)],[779]) ).
thf(707,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 ) )
= ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__left) ).
thf(3511,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 ) )
= ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(765,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__minus) ).
thf(3733,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(454,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/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__pos) ).
thf(2587,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)],[454]) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B != A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
thf(1229,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B != A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(728,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__minus) ).
thf(3601,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Polynomial_Ocoeff ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(556,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_zmod__zminus1__not__zero) ).
thf(2951,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( 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)],[556]) ).
thf(1001,axiom,
tc_Complex_Ocomplex @ class_Rings_Odivision__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring) ).
thf(4523,plain,
tc_Complex_Ocomplex @ class_Rings_Odivision__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(782,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 ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self1) ).
thf(3790,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 ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(652,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__minus) ).
thf(3337,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( 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)],[652]) ).
thf(597,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( 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 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ominus__right) ).
thf(3132,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( 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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(301,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( 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__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__imp__le) ).
thf(2050,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( 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__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(988,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__0 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Osemiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring__0) ).
thf(4491,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)],[988]) ).
thf(928,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__0 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Osemiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring) ).
thf(4357,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__0 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Osemiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(971,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/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__0__0) ).
thf(4455,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)],[971]) ).
thf(586,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/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__unique) ).
thf(3062,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)],[586]) ).
thf(694,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 ) ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Polynomial_Omonom ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__monom) ).
thf(3469,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 ) ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Polynomial_Omonom ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(609,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(3164,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(121,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/sandbox2/benchmark/theBenchmark.p',fact_zpower__zpower) ).
thf(1436,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)],[121]) ).
thf(908,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0) ).
thf(4286,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(611,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/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__left__eq) ).
thf(3177,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)],[611]) ).
thf(958,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 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__poly__def) ).
thf(4427,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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(502,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/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel1) ).
thf(2746,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)],[502]) ).
thf(389,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__eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
thf(2366,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__eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(48,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 ) ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mod__if) ).
thf(1197,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 ) ) @ ( 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)],[48]) ).
thf(489,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mono) ).
thf(2714,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(704,axiom,
tc_Nat_Onat @ class_Groups_Ocomm__monoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
thf(3506,plain,
tc_Nat_Onat @ class_Groups_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(439,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mono) ).
thf(2549,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(649,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/sandbox2/benchmark/theBenchmark.p',fact_zmult__1) ).
thf(3309,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)],[649]) ).
thf(470,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/sandbox2/benchmark/theBenchmark.p',fact_dvd__0__right) ).
thf(2636,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)],[470]) ).
thf(811,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 ) ) @ ( C @ c_Polynomial_Odegree ) )
= ( B @ ( C @ c_Polynomial_Odegree ) @ c_Nat_OSuc ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__pCons__eq) ).
thf(3897,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 ) ) @ ( C @ c_Polynomial_Odegree ) )
= ( B @ ( C @ c_Polynomial_Odegree ) @ c_Nat_OSuc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(1019,axiom,
tc_Complex_Ocomplex @ class_Rings_Ozero__neq__one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ozero__neq__one) ).
thf(4565,plain,
tc_Complex_Ocomplex @ class_Rings_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).
thf(719,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__minus__self__iff) ).
thf(3558,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 ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( 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)],[719]) ).
thf(892,axiom,
tc_Nat_Onat @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(4210,plain,
tc_Nat_Onat @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(856,axiom,
tc_Nat_Onat @ class_Rings_Osemiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).
thf(4083,plain,
tc_Nat_Onat @ class_Rings_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(761,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/sandbox2/benchmark/theBenchmark.p',fact_one__reorient) ).
thf(3716,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)],[761]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( 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 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zminus__zminus) ).
thf(1172,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( 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 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(405,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 @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_order__2) ).
thf(2417,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 @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( 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)],[405]) ).
thf(964,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict) ).
thf(4442,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)],[964]) ).
thf(845,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Osmult ) ) @ ( C @ c_Polynomial_Odegree ) )
= ( A @ ( C @ c_Polynomial_Odegree ) ) ) )
& ( ( B
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Osmult ) ) @ ( C @ c_Polynomial_Odegree ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__smult__eq) ).
thf(4034,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Osmult ) ) @ ( C @ c_Polynomial_Odegree ) )
= ( A @ ( C @ c_Polynomial_Odegree ) ) ) )
& ( ( B
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Osmult ) ) @ ( C @ c_Polynomial_Odegree ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(774,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/sandbox2/benchmark/theBenchmark.p',fact_mod__eq__0__iff) ).
thf(3765,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)],[774]) ).
thf(348,axiom,
tc_Int_Oint @ class_Rings_Ocomm__semiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).
thf(2223,plain,
tc_Int_Oint @ class_Rings_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(131,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__imp__neq) ).
thf(1473,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)],[131]) ).
thf(293,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__le__trans) ).
thf(2021,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)],[293]) ).
thf(174,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/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__dvd1) ).
thf(1610,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)],[174]) ).
thf(630,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_OpCons ) ) @ ( 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 ) ) @ ( A @ ( C @ ( D @ c_Polynomial_Osmult ) ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pCons__left) ).
thf(3244,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_OpCons ) ) @ ( 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 ) ) @ ( A @ ( C @ ( D @ c_Polynomial_Osmult ) ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(353,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leD) ).
thf(2241,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(869,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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(4129,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)],[869]) ).
thf(32,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/sandbox2/benchmark/theBenchmark.p',fact_power__strict__increasing) ).
thf(1152,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)],[32]) ).
thf(146,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zadd__distrib) ).
thf(1532,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(661,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 ) )
= ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inverse) ).
thf(3360,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 ) )
= ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Oinverse ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(996,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add) ).
thf(4506,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(252,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/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__neg) ).
thf(1885,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)],[252]) ).
thf(816,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono) ).
thf(3918,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(323,axiom,
tc_Int_Oint @ class_Groups_Oone,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oone) ).
thf(2138,plain,
tc_Int_Oint @ class_Groups_Oone,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(267,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__eq__diff__pred) ).
thf(1930,plain,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(384,axiom,
! [A: $i] : ( A @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessI) ).
thf(2353,plain,
! [A: $i] : ( A @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(329,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( 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_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__diffD1) ).
thf(2159,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( 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_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(495,axiom,
tc_Nat_Onat @ class_Groups_Ocancel__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
thf(2731,plain,
tc_Nat_Onat @ class_Groups_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(831,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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(3974,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)],[831]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__iff) ).
thf(1261,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(562,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_Opoly__gcd ) ) )
= ( A @ ( B @ ( C @ c_Polynomial_Opoly__gcd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__minus__left) ).
thf(2966,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield )
=> ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_Opoly__gcd ) ) )
= ( A @ ( B @ ( C @ c_Polynomial_Opoly__gcd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(409,axiom,
tc_Int_Oint @ class_Groups_Oab__semigroup__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).
thf(2430,plain,
tc_Int_Oint @ class_Groups_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B
= ( A @ c_Nat_OSuc ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SucE) ).
thf(1268,plain,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B
= ( A @ c_Nat_OSuc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(459,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
thf(2600,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 ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( 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)],[459]) ).
thf(543,axiom,
tc_Nat_Onat @ class_Groups_Oordered__ab__semigroup__add__imp__le,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(2898,plain,
tc_Nat_Onat @ class_Groups_Oordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(673,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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(3411,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)],[673]) ).
thf(426,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__assoc) ).
thf(2485,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(788,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/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1) ).
thf(3817,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)],[788]) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( D @ c_Groups_Oone__class_Oone @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( 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__eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__decreasing) ).
thf(1500,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( D @ c_Groups_Oone__class_Oone @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( 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__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(901,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 ) ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_dvd__smult__iff) ).
thf(4239,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 ) ) @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( D @ c_Polynomial_Osmult ) ) @ ( 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)],[901]) ).
thf(431,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__eq ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing__iff) ).
thf(2507,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__eq ) ) )
=> ( 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__eq ) ) ) )
& ( ( 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__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(484,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( 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 ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__le__zero__iff) ).
thf(2687,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 ) ) )
=> ( 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 ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( 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 ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funE) ).
thf(1431,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(839,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 ) ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self3) ).
thf(4019,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 ) ) @ ( 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)],[839]) ).
thf(77,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/sandbox2/benchmark/theBenchmark.p',fact_zdvd__not__zless) ).
thf(1299,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)],[77]) ).
thf(852,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/sandbox2/benchmark/theBenchmark.p',fact_degree__mod__less) ).
thf(4071,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)],[852]) ).
thf(258,axiom,
! [A: $i] :
( ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__self__eq__0) ).
thf(1902,plain,
! [A: $i] :
( ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(923,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/sandbox2/benchmark/theBenchmark.p',fact_mult__left__idem) ).
thf(4345,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)],[923]) ).
thf(993,axiom,
tc_Complex_Ocomplex @ class_Int_Oring__char__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Oring__char__0) ).
thf(4501,plain,
tc_Complex_Ocomplex @ class_Int_Oring__char__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(896,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos2) ).
thf(4221,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(932,axiom,
! [A: $i] :
( ( A @ class_Groups_Oab__group__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ominus) ).
thf(4363,plain,
! [A: $i] :
( ( A @ class_Groups_Oab__group__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(391,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/sandbox2/benchmark/theBenchmark.p',fact_zmult__assoc) ).
thf(2372,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)],[391]) ).
thf(712,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/sandbox2/benchmark/theBenchmark.p',fact_leading__coeff__0__iff) ).
thf(3526,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)],[712]) ).
thf(696,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Olinordered__semiring__1__strict )
=> ( ( D @ ( E @ ( F @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ ( C @ ( F @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( A @ ( B @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= ( F @ c_Groups_Oone__class_Oone ) )
=> ( D @ ( C @ ( A @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__lt) ).
thf(3474,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Olinordered__semiring__1__strict )
=> ( ( D @ ( E @ ( F @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ ( C @ ( F @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( A @ ( B @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= ( F @ c_Groups_Oone__class_Oone ) )
=> ( D @ ( C @ ( A @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(921,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) )
<=> ( ( B @ c_Groups_Ozero__class_Ozero )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__equal__iff__equal) ).
thf(4335,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 ) ) ) )
& ( ( ( B @ c_Groups_Ozero__class_Ozero )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) )
=> ( ( B @ c_Groups_Ozero__class_Ozero )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(723,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 ) ) @ ( B @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Polynomial_Opoly ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__iff__poly__eq__0) ).
thf(3580,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( 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 ) ) @ ( B @ ( C @ c_Polynomial_OpCons ) ) @ ( 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 ) ) @ ( B @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Polynomial_Opoly ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(1024,axiom,
tc_Complex_Ocomplex @ class_Groups_Ouminus,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ouminus) ).
thf(4584,plain,
tc_Complex_Ocomplex @ class_Groups_Ouminus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(671,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/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd_Oassoc) ).
thf(3405,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)],[671]) ).
thf(571,axiom,
! [A: $i,B: $i] :
( ( B @ class_Fields_Ofield__inverse__zero )
=> ( ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse ) )
= ( B @ c_Groups_Oone__class_Oone ) )
<=> ( A
= ( B @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__eq__1__iff) ).
thf(2998,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 ) )
= ( B @ c_Groups_Oone__class_Oone ) ) )
& ( ( ( A @ ( B @ c_Rings_Oinverse__class_Oinverse ) )
= ( B @ c_Groups_Oone__class_Oone ) )
=> ( A
= ( B @ c_Groups_Oone__class_Oone ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(1014,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__right) ).
thf(4547,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(239,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__le__cancel1) ).
thf(1848,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(737,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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(3637,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)],[737]) ).
thf(421,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/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ole__imp__less__or__eq) ).
thf(2470,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)],[421]) ).
thf(477,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B != A )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__le) ).
thf(2655,plain,
! [A: $i,B: $i] :
( ( ( ( B != A )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B != A )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(1054,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( ( A @ ( B @ ( C @ c_Polynomial_Osmult ) ) )
= ( 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/sandbox2/benchmark/theBenchmark.p',fact_smult__eq__0__iff) ).
thf(4655,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 ) ) )
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( C @ c_Polynomial_Osmult ) ) )
= ( 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)],[1054]) ).
thf(479,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 ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__simps_I1_J) ).
thf(2672,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 ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(538,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 ) )
= ( B @ ( C @ c_Rings_Oinverse__class_Oinverse ) @ ( A @ ( C @ c_Rings_Oinverse__class_Oinverse ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__mult__distrib) ).
thf(2879,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 ) )
= ( B @ ( C @ c_Rings_Oinverse__class_Oinverse ) @ ( A @ ( C @ c_Rings_Oinverse__class_Oinverse ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(1000,axiom,
! [A: $i] :
( ( A @ class_Fields_Ofield__inverse__zero )
=> ( ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Rings_Oinverse__class_Oinverse ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__inverse__zero) ).
thf(4520,plain,
! [A: $i] :
( ( A @ class_Fields_Ofield__inverse__zero )
=> ( ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Rings_Oinverse__class_Oinverse ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(904,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( 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 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Odiff__right) ).
thf(4274,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(352,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( F @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__lemma) ).
thf(2238,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( F @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(135,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 ) ) @ c_Nat_OSuc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
thf(1490,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) )
=> ( 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 ) ) @ c_Nat_OSuc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(887,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__iff__equal) ).
thf(4189,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( B = A )
=> ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) )
& ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(11,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__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__one) ).
thf(1088,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__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(619,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 ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__sum__squares__lt__zero) ).
thf(3200,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 ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(227,axiom,
tc_Int_Oint @ class_Rings_Osemiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).
thf(1812,plain,
tc_Int_Oint @ class_Rings_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(311,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__function__closures_I2_J) ).
thf(2087,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(819,axiom,
tc_Nat_Onat @ class_Groups_Ocancel__comm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__comm__monoid__add) ).
thf(3933,plain,
tc_Nat_Onat @ class_Groups_Ocancel__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(973,axiom,
tc_Complex_Ocomplex @ class_Power_Opower,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Power_Opower) ).
thf(4459,plain,
tc_Complex_Ocomplex @ class_Power_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(5275,plain,
$false,
inference(e,[status(thm)],[3021,3873,1879,1823,3008,3661,4022,2463,1956,1686,2295,4101,4450,2263,3930,3434,3167,2876,1237,4183,3477,1315,2787,1982,2427,2480,2280,1554,1406,3858,3813,3285,3098,1728,1205,1591,4408,4487,3382,1855,3680,1750,3185,3681,1211,1158,2976,2808,2644,2395,2908,3549,2527,3040,4391,3153,3460,2248,4326,4215,2854,4614,3402,4532,4105,3848,3217,4090,4647,1735,4528,1164,4440,4564,1954,1354,1458,3276,3794,4633,3439,3049,3745,3135,3649,1275,2141,4638,1872,2476,2627,4058,3253,3826,3414,1761,4247,3562,2580,1507,2360,1835,3836,2723,4371,4618,4124,1359,1601,4030,2400,3688,4386,4142,2046,2972,3634,2491,3915,2985,4496,1391,1650,3730,1645,2173,4607,1366,2819,1803,4665,4322,3878,2136,1518,1265,2531,4467,1709,4524,4348,3425,2039,3046,4415,2708,1907,3776,1279,1191,2745,3820,4637,4539,3442,4439,1287,4546,2735,2814,2698,1298,2682,1826,2185,1577,3845,2488,1462,1132,3043,2420,1922,1147,1704,4368,3708,4460,1875,4302,1100,1232,3517,3998,1892,3385,3463,1379,2169,2403,1347,1572,1398,3084,2929,4675,3312,1568,1362,1963,3180,4471,2829,3788,4595,4696,3431,2090,3724,2893,2259,2650,1334,1682,1858,3569,4686,2777,3851,2178,4411,2616,1946,4396,1664,2794,3887,2324,4173,3934,4578,2105,4454,4600,2451,2236,1828,1978,2291,3357,2254,2555,3300,1183,2073,2058,1169,4033,1896,1394,1526,1351,1433,3226,3870,4211,2205,2982,2367,1928,4055,3068,4230,1072,2530,1622,4087,2979,2002,4536,3955,1345,2799,3588,1697,1242,1104,4379,2154,1521,4065,1564,1863,2954,2011,3503,3591,3303,4480,1306,2307,2641,3037,1074,1604,2922,4589,4629,2364,2164,1067,4312,2790,1768,2905,2382,2061,2000,2441,2596,4375,1123,4609,1502,1666,1487,4493,3250,3514,3711,1343,4016,2560,2805,2969,4091,3233,2937,4499,2606,3816,1619,4044,1883,3958,3980,4140,1920,1968,4155,1296,2609,3546,4417,4080,2653,3282,1423,3948,3191,4280,2758,2873,4585,2433,3297,3349,1836,2181,1195,2211,1407,2547,1128,3727,2741,3408,1910,3445,4027,1402,1983,2377,2895,1328,2577,1856,1425,1540,2631,3119,3078,4012,1755,3205,3782,3615,1234,3122,2946,1794,2685,1804,3862,1121,4486,4636,1498,1587,1096,4233,1672,3704,2638,1118,3018,1397,1082,3143,3622,3714,4406,1700,3194,4444,1744,4530,1160,3141,4167,1461,4425,2868,4389,4421,4315,3441,2312,4545,2080,3428,1810,1791,2551,3671,1889,3555,1612,4180,3703,2932,2465,2505,3937,4120,1984,4152,3920,4223,4361,1776,3656,1249,2519,1456,4508,1382,2845,3059,1266,3354,4068,2851,2243,2355,4482,3760,1429,3967,3247,2862,4135,2052,2482,3109,3005,1991,2203,1086,3624,1695,2089,2189,2423,4550,3147,3454,4148,2634,3903,3279,3183,3306,1846,2963,1286,1187,4448,3508,1167,2338,1996,2144,2176,2033,2585,3890,1273,1548,4393,4359,4365,1135,1648,1764,2413,4470,1146,4116,4354,4594,3607,3738,1301,3523,3696,4489,3343,3158,2260,1154,4041,3387,1833,2791,3472,4677,1388,2398,1256,2959,3234,2859,4283,4077,2188,4309,1652,3736,3081,4465,3900,4605,1535,2716,3604,4590,1520,3868,2817,2827,4505,4485,4558,3773,2738,4413,3340,3436,2457,3416,1258,3304,4245,3223,2161,4526,1139,3796,3751,4127,2220,3964,2029,4186,1707,2293,1271,1371,3646,4112,3208,4236,4218,3487,1092,2166,1090,2573,4433,1356,2311,3352,3155,3779,1542,1722,4586,3586,1439,1175,4498,1282,4369,2084,2624,2415,1894,2493,4620,1574,1806,2774,1524,1349,2097,3270,1933,2257,1589,2246,1603,4616,3197,1801,2856,4176,3500,3138,4667,2802,4203,4635,4430,1471,4009,4569,1993,2780,4652,4296,1556,1381,2461,2025,1080,4541,2742,2314,2625,3572,1162,4277,2757,3034,3977,1325,2593,3451,1293,2553,3150,2842,2710,2911,3480,3539,2350,2835,3423,1445,2139,3674,3363,1477,2535,4196,3876,2069,1926,2962,2725,1594,2212,3627,4502,4373,3241,1113,2797,1726,1364,3348,2156,1562,4084,1626,1948,2614,1304,1684,4292,1340,4581,4355,2899,1551,2582,1413,1076,2914,3031,1758,2107,4458,2665,3395,2784,3161,1905,1277,2124,1134,3146,4566,2684,4688,2564,2567,1748,2298,3376,3913,2375,3754,1753,1484,1098,2882,3640,1598,4360,3507,1070,4490,1225,2060,2192,4673,1566,2012,3833,4534,2732,4200,1368,4517,2720,3872,4377,4324,4630,3448,2092,3885,4003,2276,1830,4351,1538,2044,2468,3642,4561,1790,3940,2224,2454,1813,3691,1637,3273,3202,1869,4145,3823,4132,2322,1130,4117,1579,1738,3095,4164,3715,1934,2411,1898,1981,4611,4436,2975,2579,1749,1881,2675,1404,2558,3970,1702,2379,4510,2357,1972,1506,1585,1094,2511,4695,3024,2728,3943,1717,4342,3961,3071,1372,3256,3520,2848,3684,3288,2013,4289,1459,1180,1966,2885,2696,2870,1817,4419,3533,3188,1654,2611,3346,1734,1108,2865,1940,1918,3457,4698,1084,4424,4138,3757,2479,2310,1844,2110,3320,2305,4463,4170,2342,3056,2226,1453,2443,1326,2273,3484,3789,2251,2554,2811,3748,1854,2431,3465,2591,3613,1253,2988,2594,2174,2283,3220,4542,2130,3859,1558,2934,4451,2394,1861,2956,4293,2041,3497,2330,1308,4478,1193,3677,1309,3552,1689,2081,3694,4602,4197,4649,3844,2648,1777,4591,3267,4299,3598,3793,1212,2902,2120,4074,4446,4025,4619,3420,1614,3658,2302,3865,3264,3373,4597,4367,2003,3379,1578,4399,4687,2385,4670,3785,3511,3733,2587,1229,3601,2951,4523,3790,3337,3132,2050,4491,4357,4455,3062,3469,3164,1436,4286,3177,4427,2746,2366,1197,2714,3506,2549,3309,2636,3897,4565,3558,4210,4083,3716,1172,2417,4442,4034,3765,2223,1473,2021,1610,3244,2241,4129,1152,1532,3360,4506,1885,3918,2138,1930,2353,2159,2731,3974,1261,2966,2430,1268,2600,2898,3411,2485,3817,1500,4239,2507,2687,1431,4019,1299,4071,1902,4345,4501,4221,4363,2372,3526,3474,4335,3580,4584,3405,2998,4547,1848,3637,2470,2655,4655,2672,2879,4520,4274,2238,1490,4189,1088,3200,1812,2087,3933,4459]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWW272+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.24/0.50 % Computer : n008.cluster.edu
% 0.24/0.50 % Model : x86_64 x86_64
% 0.24/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.50 % Memory : 8046.5625MB
% 0.24/0.50 % OS : Linux 6.8.0-71-generic
% 0.24/0.50 % CPULimit : 300
% 0.24/0.50 % WCLimit : 300
% 0.24/0.50 % DateTime : Sat Sep 26 15:35:26 UTC 2026
% 0.24/0.50 % CPUTime :
% 0.24/0.50 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.55/1.40 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 4.37/2.23 % [INFO] Parsing done (828ms).
% 4.37/2.26 % [INFO] Running in sequential loop mode.
% 5.81/2.77 % [INFO] eprover registered as external prover.
% 5.81/2.78 % [INFO] Scanning for conjecture ...
% 6.37/3.02 % [INFO] Found a conjecture (or negated_conjecture) and 1205 axioms. Running axiom selection ...
% 8.70/3.40 % [INFO] Axiom selection finished. Selected 1064 axioms (removed 141 axioms).
% 11.01/4.04 % [INFO] Problem is first-order (TPTP FOF).
% 11.65/4.11 % [INFO] Type checking passed.
% 11.65/4.11 % [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 ...
% 50.30/12.03 % External prover 'e' found a proof!
% 50.30/12.03 % [INFO] Killing All external provers ...
% 50.30/12.03 % Time passed: 11312ms (effective reasoning time: 9762ms)
% 50.30/12.03 % 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)>
% 50.30/12.04 % Axioms used in derivation (1064): fact_dvd_Oord__less__eq__trans, fact_minus__monom, fact_le__SucI, fact_smult__minus__left, arity_Polynomial__Opoly__Rings_Osemiring__0, fact_dvd__imp__degree__le, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_dvd_Oless__trans, fact_zdvd__zmod, fact_incr__mult__lemma, fact_zle__refl, fact_minus__mult__left, arity_Complex__Ocomplex__Rings_Odvd, fact_add__le__less__mono, fact_mult__strict__left__mono__neg, fact_Nat_Oadd__0__right, fact_degree__pcompose__le, fact_one__dvd, arity_Complex__Ocomplex__Rings_Oidom, fact_nat_Osimps_I3_J, fact_coeff__pCons__0, arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, arity_Nat__Onat__Groups_Ocancel__semigroup__add, fact_power__strict__decreasing, arity_Complex__Ocomplex__Groups_Omonoid__add, arity_Int__Oint__Rings_Ocomm__semiring, fact_pdivmod__rel__mult, fact_pos__add__strict, arity_Int__Oint__Rings_Osemiring, fact_mult__poly__0__right, fact_nonzero__inverse__inverse__eq, fact_add__strict__right__mono, fact_mult__1__left, fact_diff__0__eq__0, fact_dvd__mult__cancel__left, fact_zdvd__not__zless, fact_neg__equal__0__iff__equal, fact_dvdI, fact_ap_I1_J, fact_le__eq__less__or__eq, fact_minus__mult__right, fact_odd__nonzero, fact_trans__less__add1, fact_q__pos__lemma, fact_add__poly__code_I2_J, arity_Complex__Ocomplex__Groups_Oab__group__add, fact_inverse__1, fact_pdivmod__rel__unique__div, fact_le__degree, fact_order, fact_diff__0__right, fact_mult__less__cancel__left__disj, fact_nat__add__left__commute, fact_mult__nonpos__nonpos, fact_dvd_Oeq__iff, arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors, fact_power__power__power, fact_degree__add__eq__right, fact_mult__left_Ominus, fact_zdvd__antisym__nonneg, fact_power__inject__base, arity_Nat__Onat__Rings_Ono__zero__divisors, fact_nat__less__cases, fact_one__is__add, fact_diff__le__mono2, arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add, fact_oop, fact_degree__smult__le, fact_termination__basic__simps_I5_J, arity_Polynomial__Opoly__Rings_Ocomm__semiring__0, fact_dvd_Oorder__trans, fact_zminus__zminus, fact_mult__nonneg__nonpos, fact_poly__eq__0__iff__dvd, fact_less__imp__le__nat, fact_mult__right__less__imp__less, fact_combine__common__factor, fact_poly__gcd__greatest, fact_n__less__m__mult__n, fact_inverse__inverse__eq, fact_unity__coeff__ex, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, fact_Suc__mono, fact_less__nat__zero__code, fact_one__less__inverse__iff, arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le, fact_add__less__mono, fact_zadd__commute, fact_mult__pCons__right, fact_mult__eq__0__iff, fact_pow__divides__pow__int, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, fact_smult__dvd__cancel, fact_mod__mult__cong, fact_le__imp__0__less, fact_dvd__triv__right, fact_add__leD1, fact_split__mult__neg__le, fact_zpower__zmod, fact_dvd_Oless__asym_H, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, 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_Omonoid__mult, fact_power__increasing, 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, fact_add__right__imp__eq, fact_zero__less__diff, fact_nonzero__inverse__eq__imp__eq, fact_diff__diff__cancel, fact_mult__mono, fact_nat__add__right__cancel, fact_field__power__not__zero, fact_assms_I1_J, fact_Suc__le__mono, fact_dvd__smult, fact_mult__poly__0__left, arity_Nat__Onat__Rings_Ozero__neq__one, fact_poly__zero, fact_eq__neg__iff__add__eq__0, arity_Polynomial__Opoly__Groups_Oab__semigroup__mult, arity_Complex__Ocomplex__Groups_Oab__semigroup__mult, arity_Polynomial__Opoly__Rings_Oidom, fact_dvd__mod, 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_mult__le__mono2, fact_Suc__diff__diff, fact_mod__diff__cong, fact_minus__add__cancel, fact_smult__smult, fact_zle__linear, fact_zero__le__one, arity_Int__Oint__Orderings_Oord, fact_nat__add__left__cancel__less, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_mod__mult__distrib2, fact_coeff__inverse, fact_mod__less, fact_coeff__add, fact_mult_Oadd__right, fact_mult_Ominus__right, fact_le__add__iff2, help_c__fequal__2, fact_mult__eq__self__implies__10, fact_minus__pCons, fact_poly__mod__minus__left, fact_le__neq__implies__less, fact_dvd__diffD, arity_Polynomial__Opoly__Rings_Ocomm__ring, fact_degree__linear__power, fact_pow__divides__pow__nat, fact_poly__add, fact_degree__pCons__0, fact_order__1, fact_int__0__less__1, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, fact_linorder__neqE__linordered__idom, arity_Complex__Ocomplex__Rings_Ocomm__semiring__1, fact_mod__if, fact_synthetic__div__correct_H, fact_order__degree, fact_smult__1__left, fact_add__le__imp__le__left, fact_mod__mult__self1, fact_sum__squares__ge__zero, fact_pow__divides__eq__nat, fact_pdivmod__rel__by__0, fact_mult_Ozero__left, fact_dvd__power__le, arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero, fact_mult__smult__right, fact_smult__pCons, fact_mod__by__1, arity_Polynomial__Opoly__Rings_Olinordered__semidom, fact_zadd__left__mono, fact_sum__squares__le__zero__iff, arity_Int__Oint__Rings_Olinordered__semiring__1__strict, fact_mult__right_Ozero, fact_mult__le__cancel__left__neg, fact_dvd__reduce, fact_zero__le__mult__iff, fact_synthetic__div__0, arity_Int__Oint__Groups_Ozero, fact_zdvd__zmod__imp__zdvd, fact_power__commutes, fact_poly__0, fact_add__mono, fact_gr0I, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_add__0__iff, arity_Polynomial__Opoly__Orderings_Oord, fact_degree__1, arity_Int__Oint__Groups_Ocancel__comm__monoid__add, fact_power__strict__increasing, fact_one__le__power, fact_even__less__0__iff, fact_self__quotient__aux1, 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_coeff__1, arity_Int__Oint__Rings_Olinordered__ring, fact_poly__smult, fact_le__funD, fact_add__right__mono, fact_Divides_Otransfer__nat__int__function__closures_I2_J, fact_le__fun__def, fact_minus__add, arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add, fact_power__minus, fact_one__less__power, fact_mod__mult__left__eq, fact_nat__dvd__not__less, fact_leading__coeff__neq__0, arity_Nat__Onat__Rings_Osemiring__0, fact_diff__le__self, arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict, fact_mult__eq__1__iff, fact_smult__add__right, fact_degree__pCons__eq__if, arity_Nat__Onat__Rings_Oordered__comm__semiring, fact_power__eq__0__iff, fact_diff__Suc__eq__diff__pred, fact_less__add__eq__less, fact_nat__mult__1__right, fact_mod__1, arity_Complex__Ocomplex__Rings_Osemiring__0, fact_coeff__linear__power, fact_ord__less__eq__trans, fact_poly__gcd_Oassoc, fact_mult__right_Odiff, fact_termination__basic__simps_I4_J, fact_le__iff__add, fact_one__reorient, fact_diff__commute, arity_fun__Groups_Ouminus, fact_pq0, fact_minus__mult__commute, arity_Polynomial__Opoly__Groups_Omonoid__add, fact_division__ring__inverse__add, fact_mult__left_Odiff, fact_eq__iff__diff__eq__0, fact_add__lessD1, fact_add__le__mono1, fact_IH, fact_poly__gcd__monic, fact_less__eq__nat_Osimps_I1_J, arity_Int__Oint__Rings_Oidom, arity_Complex__Ocomplex__Fields_Ofield, fact_less__degree__imp, fact_dvd__eq__mod__eq__0, arity_Polynomial__Opoly__Int_Oring__char__0, fact_lessI, fact_zero__le__square, fact_dvd_Oantisym__conv, fact_zero__reorient, fact_dvd__mult__cancel2, fact_dvd__0__right, fact_mod__add__self1, arity_Int__Oint__Rings_Oordered__cancel__semiring, fact_synthetic__div__pCons, fact_zadd__zless__mono, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_power__gt1__lemma, fact_dvd_Oord__eq__le__trans, arity_Polynomial__Opoly__Rings_Oring__1, fact_mult__less__mono1, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, fact_Suc__leI, fact_poly__mult, fact_split__mult__pos__le, fact_offset__poly__pCons, fact_nat_Oinject, fact_neg__mod__bound, fact_mult__left__le__one__le, arity_Polynomial__Opoly__Power_Opower, arity_Int__Oint__Rings_Oring__no__zero__divisors, fact_not__add__less2, fact_dvd__trans, fact_less__or__eq__imp__le, fact_mod__mod__trivial, fact_Suc__less__SucD, fact_dvd_Oeq__refl, fact_power__strict__mono, fact_zadd__strict__right__mono, fact_q__neg__lemma, fact_minus__apply, fact_zdvd__reduce, fact_inverse__le__1__iff, fact_add__0__right, fact_unique__quotient__lemma__neg, fact_diff__less, fact_power__Suc2, fact_zpower__zadd__distrib, fact_le__add2, fact_zadd__assoc, arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, fact_power__inverse, fact_less__irrefl__nat, fact_mod__smult__right, fact_mod__diff__right__eq, fact_Suc__lessD, fact_Suc__n__not__le__n, fact_pdivmod__rel__0__iff, fact_not__less__less__Suc__eq, fact_convex__bound__lt, fact__096_B_Bthesis_O_A_I_B_Bs_O_Ap_A_061_A_091_058_N_Aa_M_A1_058_093_A_094_Aorder_Aa_Ap_A_K_As_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_dvd__mult2, fact_nat__mult__1, fact_diff__is__0__eq_H, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J, fact_mult__right__mono__neg, fact_diff__pCons, fact__096_091_058_N_Aa_M_A1_058_093_Advd_Aq_096, fact_dvd_Oless__imp__neq, fact_diff__self, fact_minus__nat_Odiff__0, fact_pos__zmult__eq__1__iff, arity_Int__Oint__Groups_Ocancel__semigroup__add, fact_nonzero__inverse__mult__distrib, fact_poly__gcd__dvd2, 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arity_Int__Oint__Rings_Olinordered__comm__semiring__strict, fact_diff__le__mono, arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring, arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le, arity_Polynomial__Opoly__Rings_Ocomm__ring__1, fact_synthetic__div__unique__lemma, fact_zdvd__period, fact_mult__less__cancel__left__pos, fact_trans__le__add1, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, fact_degree__monom__le, arity_Polynomial__Opoly__Rings_Odvd, arity_Polynomial__Opoly__Rings_Ocomm__semiring, arity_Int__Oint__Groups_Ominus, arity_Complex__Ocomplex__Rings_Omult__zero, fact_zmult__1__right, arity_Polynomial__Opoly__Rings_Ono__zero__divisors, fact_double__eq__0__iff, fact_le__0__eq, fact_assms_I2_J, fact_mult__Suc__right, fact_zdvd__imp__le, fact_dvd__0__left, fact_pcompose__pCons, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J, fact_mult__less__cancel2, fact_zle__add1__eq__le, fact_dvd__1__iff__1, fact_mod__0, fact_mult__1__right, fact_zero__less__two, fact_gcd__lcm__complete__lattice__nat_Obot__least, fact_diff__is__0__eq, arity_Polynomial__Opoly__Groups_Ozero, fact_dvd__iff__poly__eq__0, arity_Nat__Onat__Rings_Osemiring, fact_termination__basic__simps_I1_J, fact_less__iff__Suc__add, fact_add__le__imp__le__right, fact_pdivmod__rel__unique__mod, fact_sum__squares__eq__zero__iff, fact_le__add__diff__inverse, fact_nat__zero__less__power__iff, fact_mod__add__right__eq, arity_Int__Oint__Rings_Ocomm__ring__1, fact_add__le__mono, fact_less__Suc0, fact_pos__poly__def, fact_dvd_Ole__less__trans, fact_dpn, fact_diff__monom, fact_add__diff__inverse, fact_convex__bound__le, arity_Int__Oint__Groups_Olinordered__ab__group__add, fact_nat__mult__eq__cancel__disj, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_le__diff__iff, fact_smult__minus__right, arity_Int__Oint__Rings_Ozero__neq__one, fact_add__imp__eq, fact_power__gt1, fact_no__zero__divisors, fact_le__square, fact_zadd__zmult__distrib, fact_divisors__zero, arity_Polynomial__Opoly__Rings_Olinordered__ring, arity_Polynomial__Opoly__Groups_Ocomm__monoid__add, fact_degree__mult__eq, fact_zadd__zminus__inverse2, fact_double__add__less__zero__iff__single__add__less__zero, 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_nat__less__le, fact_less__SucE, fact_le__cube, fact_zless__add1__eq, fact_add__less__mono1, fact_add__le__cancel__left, fact_smult__diff__left, arity_Polynomial__Opoly__Groups_Oone, fact_poly__eq__iff, arity_Complex__Ocomplex__Power_Opower, fact_ord__eq__le__trans, fact_field__inverse__zero, fact_realpow__Suc__le__self, fact_oa, fact_one__le__inverse__iff, fact_zmod__zminus1__not__zero, fact_less__diff__iff, fact_pdivmod__rel__0, fact_odd__less__0, fact_dvd_Oless__imp__not__eq2, fact_field__inverse, arity_Int__Oint__Groups_Omonoid__add, arity_Int__Oint__Rings_Ocomm__semiring__0, fact_add__Suc__shift, fact_dvd__mult__cancel__right, fact_power__le__imp__le__base, fact_pdivmod__rel__def, fact_mod__add__eq, fact_zdiv__mono2__neg__lemma, arity_Int__Oint__Divides_Oring__div, fact_dvd__imp__mod__0, fact_less__SucI, fact_Suc__not__Zero, fact_dvd__power, arity_Complex__Ocomplex__Groups_Ozero, fact_poly__gcd_Osimps_I2_J, arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add, fact_not__square__less__zero, fact_Suc__lessI, fact_add__Suc__right, fact_mult__pCons__left, arity_Complex__Ocomplex__Groups_Ominus, fact_mult__1, arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add, arity_Int__Oint__Rings_Olinordered__ring__strict, fact_mult_Odiff__right, fact_mod__mult__distrib, arity_Complex__Ocomplex__Rings_Ocomm__semiring__0, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, fact_coeff__diff, fact_dvd__mod__imp__dvd
% 50.30/12.04 % No. of inferences in proof: 2132
% 50.30/12.04 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 11312 ms resp. 9762 ms w/o parsing
% 53.33/12.53 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 53.33/12.55 % [INFO] Killing All external provers ...
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