TSTP Solution File: SWW208+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW208+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:22:01 EDT 2023
% Result : Theorem 54.44s 13.30s
% Output : Refutation 55.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1394
% Syntax : Number of formulae : 2662 ( 851 unt; 128 typ; 0 def)
% Number of atoms : 6327 (1670 equ; 0 cnn)
% Maximal formula atoms : 26 ( 2 avg)
% Number of connectives : 42138 ( 334 ~; 150 |; 505 &;38011 @)
% ( 216 <=>;2922 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 159 ( 159 >; 0 *; 0 +; 0 <<)
% Number of symbols : 130 ( 128 usr; 12 con; 0-5 aty)
% Number of variables : 5377 ( 0 ^;5277 !; 100 ?;5377 :)
% Comments :
%------------------------------------------------------------------------------
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_Orderings_Oord__class_Oless_type,type,
c_Orderings_Oord__class_Oless: $i > $i > $i ).
thf(tc_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
thf(c_Groups_Ozero__class_Ozero_type,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
thf(c_Groups_Oplus__class_Oplus_type,type,
c_Groups_Oplus__class_Oplus: $i > $i ).
thf(v_r_type,type,
v_r: $i ).
thf(c_Groups_Oone__class_Oone_type,type,
c_Groups_Oone__class_Oone: $i > $i ).
thf(c_Orderings_Oord__class_Oless__eq_type,type,
c_Orderings_Oord__class_Oless__eq: $i > $i > $i ).
thf(c_Groups_Oabs__class_Oabs_type,type,
c_Groups_Oabs__class_Oabs: $i > $i > $i ).
thf(c_Complex_OIm_type,type,
c_Complex_OIm: $i ).
thf(v_s_type,type,
v_s: $i ).
thf(v_f_____type,type,
v_f____: $i ).
thf(v_ga_____type,type,
v_ga____: $i ).
thf(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: $i > $i ).
thf(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
thf(c_Complex_Orcis_type,type,
c_Complex_Orcis: $i > $i > $i ).
thf(c_Groups_Otimes__class_Otimes_type,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
thf(c_RealDef_Oreal_type,type,
c_RealDef_Oreal: $i > $i > $i ).
thf(tc_Nat_Onat_type,type,
tc_Nat_Onat: $i ).
thf(class_Groups_Ocancel__semigroup__add_type,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
thf(class_Divides_Osemiring__div_type,type,
class_Divides_Osemiring__div: $i > $o ).
thf(c_Divides_Odiv__class_Odiv_type,type,
c_Divides_Odiv__class_Odiv: $i > $i > $i > $i ).
thf(class_Power_Opower_type,type,
class_Power_Opower: $i > $o ).
thf(c_Power_Opower_Opower_type,type,
c_Power_Opower_Opower: $i > $i > $i > $i ).
thf(class_Rings_Oordered__cancel__semiring_type,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
thf(class_Rings_Olinordered__comm__semiring__strict_type,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
thf(tc_Int_Oint_type,type,
tc_Int_Oint: $i ).
thf(c_Nat_OSuc_type,type,
c_Nat_OSuc: $i > $i ).
thf(class_Groups_Ocomm__monoid__add_type,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
thf(class_Groups_Omonoid__add_type,type,
class_Groups_Omonoid__add: $i > $o ).
thf(tc_Polynomial_Opoly_type,type,
tc_Polynomial_Opoly: $i > $i ).
thf(class_Orderings_Oord_type,type,
class_Orderings_Oord: $i > $o ).
thf(class_Groups_Oone_type,type,
class_Groups_Oone: $i > $o ).
thf(class_Groups_Oab__group__add_type,type,
class_Groups_Oab__group__add: $i > $o ).
thf(class_Rings_Ocomm__semiring__0_type,type,
class_Rings_Ocomm__semiring__0: $i > $o ).
thf(class_Rings_Osemiring_type,type,
class_Rings_Osemiring: $i > $o ).
thf(c_Groups_Ominus__class_Ominus_type,type,
c_Groups_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(c_Complex_ORe_type,type,
c_Complex_ORe: $i ).
thf(c_Transcendental_Ocos_type,type,
c_Transcendental_Ocos: $i > $i ).
thf(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_type,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
thf(class_RealVector_Oreal__normed__vector_type,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
thf(c_SEQ_OBseq_type,type,
c_SEQ_OBseq: $i > $i > $o ).
thf(c_COMBB_type,type,
c_COMBB: $i > $i > $i > $i > $i > $i ).
thf(c_COMBC_type,type,
c_COMBC: $i > $i > $i > $i > $i > $i ).
thf(class_RealVector_Oreal__field_type,type,
class_RealVector_Oreal__field: $i > $o ).
thf(class_Groups_Omonoid__mult_type,type,
class_Groups_Omonoid__mult: $i > $o ).
thf(class_Groups_Oordered__ab__semigroup__add_type,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
thf(class_Rings_Olinordered__idom_type,type,
class_Rings_Olinordered__idom: $i > $o ).
thf(class_Rings_Oordered__comm__semiring_type,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
thf(class_Rings_Oordered__semiring_type,type,
class_Rings_Oordered__semiring: $i > $o ).
thf(class_RealVector_Oreal__normed__field_type,type,
class_RealVector_Oreal__normed__field: $i > $o ).
thf(c_Rings_Oinverse__class_Odivide_type,type,
c_Rings_Oinverse__class_Odivide: $i > $i ).
thf(class_Orderings_Opreorder_type,type,
class_Orderings_Opreorder: $i > $o ).
thf(c_Groups_Osgn__class_Osgn_type,type,
c_Groups_Osgn__class_Osgn: $i > $i > $i ).
thf(c_RealVector_Onorm__class_Onorm_type,type,
c_RealVector_Onorm__class_Onorm: $i > $i > $i ).
thf(class_Groups_Ogroup__add_type,type,
class_Groups_Ogroup__add: $i > $o ).
thf(class_RealVector_Oreal__normed__algebra_type,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
thf(class_Rings_Ocomm__semiring_type,type,
class_Rings_Ocomm__semiring: $i > $o ).
thf(class_Rings_Ocomm__semiring__1_type,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
thf(c_RComplete_Onatceiling_type,type,
c_RComplete_Onatceiling: $i > $i ).
thf(class_Rings_Oring__1__no__zero__divisors_type,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
thf(class_Groups_Oab__semigroup__add_type,type,
class_Groups_Oab__semigroup__add: $i > $o ).
thf(class_Rings_Olinordered__ring_type,type,
class_Rings_Olinordered__ring: $i > $o ).
thf(class_Groups_Oordered__ab__group__add__abs_type,type,
class_Groups_Oordered__ab__group__add__abs: $i > $o ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(tc_fun_type,type,
tc_fun: $i > $i > $i ).
thf(class_Groups_Oordered__ab__semigroup__add__imp__le_type,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
thf(class_Rings_Ocomm__ring_type,type,
class_Rings_Ocomm__ring: $i > $o ).
thf(class_Rings_Olinordered__semiring__1_type,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
thf(class_Rings_Olinordered__semiring__1__strict_type,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
thf(class_Rings_Oidom_type,type,
class_Rings_Oidom: $i > $o ).
thf(class_Rings_Omult__zero_type,type,
class_Rings_Omult__zero: $i > $o ).
thf(c_Complex_Ocomplex_OComplex_type,type,
c_Complex_Ocomplex_OComplex: $i > $i > $i ).
thf(c_Transcendental_Osin_type,type,
c_Transcendental_Osin: $i > $i ).
thf(c_Complex_Ocis_type,type,
c_Complex_Ocis: $i > $i ).
thf(class_Rings_Ocomm__ring__1_type,type,
class_Rings_Ocomm__ring__1: $i > $o ).
thf(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(c_SEQ_Odecseq_type,type,
c_SEQ_Odecseq: $i > $i > $o ).
thf(c_SEQ_Omonoseq_type,type,
c_SEQ_Omonoseq: $i > $i > $o ).
thf(class_Rings_Olinordered__semidom_type,type,
class_Rings_Olinordered__semidom: $i > $o ).
thf(class_Groups_Oab__semigroup__mult_type,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
thf(class_Rings_Olinordered__semiring__strict_type,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
thf(class_Groups_Oordered__comm__monoid__add_type,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
thf(class_Groups_Ocancel__comm__monoid__add_type,type,
class_Groups_Ocancel__comm__monoid__add: $i > $o ).
thf(class_Groups_Olinordered__ab__group__add_type,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
thf(class_Rings_Odivision__ring_type,type,
class_Rings_Odivision__ring: $i > $o ).
thf(class_RealVector_Oreal__normed__div__algebra_type,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
thf(class_Rings_Oring_type,type,
class_Rings_Oring: $i > $o ).
thf(class_Rings_Oring__1_type,type,
class_Rings_Oring__1: $i > $o ).
thf(class_RealVector_Ometric__space_type,type,
class_RealVector_Ometric__space: $i > $o ).
thf(c_SEQ_Oconvergent_type,type,
c_SEQ_Oconvergent: $i > $i > $o ).
thf(c_COMBK_type,type,
c_COMBK: $i > $i > $i > $i ).
thf(c_COMBS_type,type,
c_COMBS: $i > $i > $i > $i > $i > $i ).
thf(class_Fields_Ofield_type,type,
class_Fields_Ofield: $i > $o ).
thf(class_Groups_Ocomm__monoid__mult_type,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
thf(class_Rings_Ozero__neq__one_type,type,
class_Rings_Ozero__neq__one: $i > $o ).
thf(class_Rings_Ono__zero__divisors_type,type,
class_Rings_Ono__zero__divisors: $i > $o ).
thf(class_Groups_Oordered__ab__group__add_type,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
thf(class_Groups_Ocancel__ab__semigroup__add_type,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
thf(c_RComplete_Onatfloor_type,type,
c_RComplete_Onatfloor: $i > $i ).
thf(class_Rings_Osemiring__0_type,type,
class_Rings_Osemiring__0: $i > $o ).
thf(class_Groups_Osgn__if_type,type,
class_Groups_Osgn__if: $i > $o ).
thf(class_Groups_Ozero_type,type,
class_Groups_Ozero: $i > $o ).
thf(class_Rings_Olinordered__semiring_type,type,
class_Rings_Olinordered__semiring: $i > $o ).
thf(class_Rings_Olinordered__ring__strict_type,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
thf(class_Rings_Oordered__ring__abs_type,type,
class_Rings_Oordered__ring__abs: $i > $o ).
thf(class_Rings_Oordered__ring_type,type,
class_Rings_Oordered__ring: $i > $o ).
thf(c_SEQ_Oincseq_type,type,
c_SEQ_Oincseq: $i > $i > $o ).
thf(class_Fields_Ofield__inverse__zero_type,type,
class_Fields_Ofield__inverse__zero: $i > $o ).
thf(class_Rings_Oring__no__zero__divisors_type,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
thf(class_Groups_Oordered__cancel__ab__semigroup__add_type,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
thf(class_RealVector_Oreal__normed__algebra__1_type,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
thf(class_Rings_Odivision__ring__inverse__zero_type,type,
class_Rings_Odivision__ring__inverse__zero: $i > $o ).
thf(c_Complex_Oarg_type,type,
c_Complex_Oarg: $i > $i ).
thf(c_Transcendental_Oln_type,type,
c_Transcendental_Oln: $i > $i ).
thf(c_Complex_Ocomplex_Ocomplex__case_type,type,
c_Complex_Ocomplex_Ocomplex__case: $i > $i > $i > $i ).
thf(c_Nat__Transfer_Otsub_type,type,
c_Nat__Transfer_Otsub: $i > $i > $i ).
thf(c_Complex_Oii_type,type,
c_Complex_Oii: $i ).
thf(c_SEQ_Osubseq_type,type,
c_SEQ_Osubseq: $i > $o ).
thf(c_Transcendental_Oarccos_type,type,
c_Transcendental_Oarccos: $i > $i ).
thf(c_Nat_Osize__class_Osize_type,type,
c_Nat_Osize__class_Osize: $i > $i > $i ).
thf(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize_type,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize: $i > $i > $i ).
thf(class_Fields_Olinordered__field__inverse__zero_type,type,
class_Fields_Olinordered__field__inverse__zero: $i > $o ).
thf(class_Fields_Olinordered__field_type,type,
class_Fields_Olinordered__field: $i > $o ).
thf(c_Complex_Ocomplex_Ocomplex__size_type,type,
c_Complex_Ocomplex_Ocomplex__size: $i > $i ).
thf(c_Complex_Oexpi_type,type,
c_Complex_Oexpi: $i > $i ).
thf(c_Complex_Ocomplex_Ocomplex__rec_type,type,
c_Complex_Ocomplex_Ocomplex__rec: $i > $i > $i > $i ).
thf(380,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ B ) ) @ ( c_Transcendental_Oln @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ln__less__cancel__iff) ).
thf(2163,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ B ) ) @ ( c_Transcendental_Oln @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ B ) ) @ ( c_Transcendental_Oln @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(479,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__less__n__mult__m) ).
thf(2452,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(1087,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
=> ( ( c_Transcendental_Ocos @ ( c_Complex_Oarg @ ( c_Complex_Ocomplex_OComplex @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cos__arg__i__mult__zero__neg) ).
thf(4447,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
=> ( ( c_Transcendental_Ocos @ ( c_Complex_Oarg @ ( c_Complex_Ocomplex_OComplex @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( ( c_SEQ_Odecseq @ B @ A )
=> ( c_SEQ_Omonoseq @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_decseq__imp__monoseq) ).
thf(1411,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( ( c_SEQ_Odecseq @ B @ A )
=> ( c_SEQ_Omonoseq @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(91,axiom,
class_Rings_Oordered__comm__semiring @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).
thf(1469,plain,
class_Rings_Oordered__comm__semiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(166,axiom,
class_Rings_Ocomm__semiring__0 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
thf(1633,plain,
class_Rings_Ocomm__semiring__0 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(840,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).
thf(3661,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(926,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ ( c_Nat_OSuc @ B ) ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).
thf(3930,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ ( c_Nat_OSuc @ B ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ ( c_Nat_OSuc @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(128,axiom,
class_Power_Opower @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Power_Opower) ).
thf(1559,plain,
class_Power_Opower @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(925,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
thf(3927,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(395,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(2199,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(186,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( c_Complex_Ocis @ B ) ) @ A )
= ( c_Complex_Ocis @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DeMoivre) ).
thf(1665,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( c_Complex_Ocis @ B ) ) @ A )
= ( c_Complex_Ocis @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(596,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__is__0__eq_H) ).
thf(2822,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(537,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).
thf(2630,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(1088,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__0__right) ).
thf(4450,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).
thf(747,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le0) ).
thf(3345,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(1093,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq2) ).
thf(4464,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).
thf(444,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(2336,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(1168,axiom,
class_RealVector_Oreal__normed__algebra @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
thf(4824,plain,
class_RealVector_Oreal__normed__algebra @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).
thf(84,axiom,
class_Orderings_Opreorder @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
thf(1454,plain,
class_Orderings_Opreorder @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(842,axiom,
class_RealVector_Ometric__space @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Ometric__space) ).
thf(3666,plain,
class_RealVector_Ometric__space @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(950,axiom,
! [A: $i,B: $i] :
( ( c_Transcendental_Osin @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Transcendental_Osin @ B ) ) @ ( c_Transcendental_Ocos @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Transcendental_Ocos @ B ) ) @ ( c_Transcendental_Osin @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sin__add) ).
thf(4022,plain,
! [A: $i,B: $i] :
( ( c_Transcendental_Osin @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Transcendental_Osin @ B ) ) @ ( c_Transcendental_Ocos @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Transcendental_Ocos @ B ) ) @ ( c_Transcendental_Osin @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(855,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).
thf(3698,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(936,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__not__sym) ).
thf(3979,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__vector @ C )
=> ( ( c_SEQ_OBseq @ C @ B )
=> ( c_SEQ_OBseq @ C @ ( c_COMBB @ tc_Nat_Onat @ C @ tc_Nat_Onat @ B @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bseq__ignore__initial__segment) ).
thf(1315,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__vector @ C )
=> ( ( c_SEQ_OBseq @ C @ B )
=> ( c_SEQ_OBseq @ C @ ( c_COMBB @ tc_Nat_Onat @ C @ tc_Nat_Onat @ B @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(588,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__one__right) ).
thf(2787,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(269,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__vector @ C )
=> ( ( c_SEQ_OBseq @ C @ ( c_COMBB @ tc_Nat_Onat @ C @ tc_Nat_Onat @ B @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) ) )
=> ( c_SEQ_OBseq @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bseq__offset) ).
thf(1850,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__vector @ C )
=> ( ( c_SEQ_OBseq @ C @ ( c_COMBB @ tc_Nat_Onat @ C @ tc_Nat_Onat @ B @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) ) )
=> ( c_SEQ_OBseq @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(1186,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Nat_OSuc @ B ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ ( c_Nat_OSuc @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( C = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__inject__base) ).
thf(4877,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Nat_OSuc @ B ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ ( c_Nat_OSuc @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186]) ).
thf(253,axiom,
class_Orderings_Olinorder @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
thf(1818,plain,
class_Orderings_Olinorder @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(318,axiom,
class_Rings_Odivision__ring__inverse__zero @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero) ).
thf(1956,plain,
class_Rings_Odivision__ring__inverse__zero @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(315,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Oring__no__zero__divisors @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors) ).
thf(1950,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Oring__no__zero__divisors @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(425,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__asym) ).
thf(2280,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(124,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__field @ C )
=> ( ( c_SEQ_Oconvergent @ C @ B )
=> ( c_SEQ_Oconvergent @ C @ ( c_COMBC @ tc_Nat_Onat @ C @ C @ ( c_COMBB @ C @ ( tc_fun @ C @ C ) @ tc_Nat_Onat @ ( c_Rings_Oinverse__class_Odivide @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide_Oconvergent) ).
thf(1554,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__field @ C )
=> ( ( c_SEQ_Oconvergent @ C @ B )
=> ( c_SEQ_Oconvergent @ C @ ( c_COMBC @ tc_Nat_Onat @ C @ C @ ( c_COMBB @ C @ ( tc_fun @ C @ C ) @ tc_Nat_Onat @ ( c_Rings_Oinverse__class_Odivide @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(197,axiom,
class_Groups_Ocancel__ab__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
thf(1686,plain,
class_Groups_Ocancel__ab__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(415,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__increasing__iff) ).
thf(2250,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(702,axiom,
! [A: $i] :
( ( c_Nat_OSuc @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
thf(3185,plain,
! [A: $i] :
( ( c_Nat_OSuc @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(940,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono) ).
thf(3990,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(535,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) ) @ C ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__inject__exp) ).
thf(2622,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) ) @ C ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(639,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oord @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funD) ).
thf(2953,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oord @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(677,axiom,
! [A: $i] :
( ( c_Complex_Ocomplex_OComplex @ ( hAPP @ c_Complex_ORe @ A ) @ ( hAPP @ c_Complex_OIm @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__surj) ).
thf(3098,plain,
! [A: $i] :
( ( c_Complex_Ocomplex_OComplex @ ( hAPP @ c_Complex_ORe @ A ) @ ( hAPP @ c_Complex_OIm @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(552,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( ( c_Nat__Transfer_Otsub @ A @ B )
= ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tsub__eq) ).
thf(2676,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( ( c_Nat__Transfer_Otsub @ A @ B )
= ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(213,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) ).
thf(1728,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(1135,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__diff1__eq) ).
thf(4603,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).
thf(602,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__add__iff2) ).
thf(2837,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E ) @ D ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) ) @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(1053,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__mult__distrib) ).
thf(4326,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Power_Opower @ C )
=> ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ B )
= ( c_Groups_Oone__class_Oone @ C ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_realpow__num__eq__if) ).
thf(1305,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Power_Opower @ C )
=> ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ B )
= ( c_Groups_Oone__class_Oone @ C ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(759,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ A ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__natfloor__le) ).
thf(3382,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ A ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(271,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Rings_Ocomm__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring) ).
thf(1855,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Rings_Ocomm__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(360,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__gt1__lemma) ).
thf(2077,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(958,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I12_J) ).
thf(4043,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(804,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ ( c_Nat_OSuc @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).
thf(3534,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ ( c_Nat_OSuc @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(436,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A ) )
=> ( ( c_Groups_Oabs__class_Oabs @ B @ A )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__of__nonneg) ).
thf(2309,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A ) )
=> ( ( c_Groups_Oabs__class_Oabs @ B @ A )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(496,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__natfloor__gt__diff__one) ).
thf(2512,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(642,axiom,
! [A: $i] :
( ( c_Groups_Osgn__class_Osgn @ tc_RealDef_Oreal @ A )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal ) @ A ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sgn__eq) ).
thf(2976,plain,
! [A: $i] :
( ( c_Groups_Osgn__class_Osgn @ tc_RealDef_Oreal @ A )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal ) @ A ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(669,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__0__less__mult__iff) ).
thf(3072,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(300,axiom,
class_RealVector_Oreal__normed__algebra__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
thf(1924,plain,
class_RealVector_Oreal__normed__algebra__1 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(635,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).
thf(2940,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(64,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__ring__1 @ A )
=> ( class_Rings_Ocomm__ring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring__1) ).
thf(1406,plain,
! [A: $i] :
( ( class_Rings_Ocomm__ring__1 @ A )
=> ( class_Rings_Ocomm__ring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(1018,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ A ) )
=> ( ( c_RComplete_Onatceiling @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ A @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__subtract) ).
thf(4226,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ A ) )
=> ( ( c_RComplete_Onatceiling @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ A @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(1103,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__le__imp__le__exp) ).
thf(4500,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).
thf(12,axiom,
! [A: $i] :
( ( class_Groups_Ocomm__monoid__add @ A )
=> ( class_Groups_Omonoid__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__add) ).
thf(1290,plain,
! [A: $i] :
( ( class_Groups_Ocomm__monoid__add @ A )
=> ( class_Groups_Omonoid__add @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(282,axiom,
class_Rings_Olinordered__semiring @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).
thf(1882,plain,
class_Rings_Olinordered__semiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(111,axiom,
class_Fields_Ofield @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield) ).
thf(1522,plain,
class_Fields_Ofield @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(874,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).
thf(3762,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(541,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ C ) )
& ! [D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) ) @ C ) ) )
<=> ? [C: $i] :
! [D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lemma__NBseq__def) ).
thf(2644,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ C ) )
& ! [D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) ) @ C ) ) )
=> ? [C: $i] :
! [D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) ) ) )
& ( ? [C: $i] :
! [D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ C ) )
& ! [D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(718,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ? [B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reals__Archimedean6) ).
thf(3230,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ? [B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(458,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) )
<=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__power__nat__eq) ).
thf(2381,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) ) ) )
& ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(1248,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( B != A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).
thf(5069,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( B != A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1248]) ).
thf(461,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__0) ).
thf(2395,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(357,axiom,
! [A: $i] :
( ( ( c_Transcendental_Ocos @ A )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ( ( c_Transcendental_Osin @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cos__one__sin__zero) ).
thf(2062,plain,
! [A: $i] :
( ( ( c_Transcendental_Ocos @ A )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ( ( c_Transcendental_Osin @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(1226,axiom,
! [A: $i,B: $i] :
( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= A ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__if) ).
thf(5000,plain,
! [A: $i,B: $i] :
( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= A ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1226]) ).
thf(585,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_RealVector_Onorm__class_Onorm @ B @ ( c_Groups_Osgn__class_Osgn @ B @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_RealVector_Onorm__class_Onorm @ B @ ( c_Groups_Osgn__class_Osgn @ B @ A ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__sgn) ).
thf(2776,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_RealVector_Onorm__class_Onorm @ B @ ( c_Groups_Osgn__class_Osgn @ B @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_RealVector_Onorm__class_Onorm @ B @ ( c_Groups_Osgn__class_Osgn @ B @ A ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(770,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mult__distrib2) ).
thf(3417,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(159,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__mult__distrib2) ).
thf(1618,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(732,axiom,
class_RealVector_Oreal__normed__vector @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
thf(3285,plain,
class_RealVector_Oreal__normed__vector @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(757,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__one) ).
thf(3377,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(692,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) ) ) )
=> ( B
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rabs__ratiotest__lemma) ).
thf(3153,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) ) ) )
=> ( B
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(1422,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(134,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Oidom @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oidom) ).
thf(1569,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Oidom @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(309,axiom,
class_Groups_Oordered__ab__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
thf(1939,plain,
class_Groups_Oordered__ab__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(426,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( c_SEQ_OBseq @ B @ A )
<=> ? [C: $i] :
! [D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bseq__iff1a) ).
thf(2282,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( ( c_SEQ_OBseq @ B @ A )
=> ? [C: $i] :
! [D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) ) ) )
& ( ? [C: $i] :
! [D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) ) )
=> ( c_SEQ_OBseq @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(145,axiom,
class_Groups_Ocomm__monoid__mult @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).
thf(1591,plain,
class_Groups_Ocomm__monoid__mult @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(326,axiom,
class_Rings_Osemiring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring) ).
thf(1971,plain,
class_Rings_Osemiring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(116,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Omonoid__mult @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc2) ).
thf(1533,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Omonoid__mult @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(1074,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).
thf(4408,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(1217,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less0) ).
thf(4973,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1217]) ).
thf(1153,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(4747,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153]) ).
thf(1132,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__divide__square__eq) ).
thf(4592,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).
thf(240,axiom,
class_Rings_Oordered__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).
thf(1788,plain,
class_Rings_Oordered__semiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(190,axiom,
class_Rings_Osemiring__0 @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).
thf(1671,plain,
class_Rings_Osemiring__0 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(181,axiom,
class_Rings_Olinordered__semiring__strict @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).
thf(1655,plain,
class_Rings_Olinordered__semiring__strict @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(556,axiom,
~ ! [A: $i] :
( ( c_SEQ_Osubseq @ A )
=> ~ ( c_SEQ_Omonoseq @ tc_RealDef_Oreal @ ( c_COMBB @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_Nat_Onat @ c_Complex_OIm @ ( c_COMBB @ tc_Nat_Onat @ tc_Complex_Ocomplex @ tc_Nat_Onat @ v_s @ ( c_COMBB @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat @ v_f____ @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bg_O_A_091_124_Asubseq_Ag_059_Amonoseq_A_I_Fn_O_AIm_A_Is_A_If_A_Ig_An_J_J_J_J_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(2686,plain,
~ ! [A: $i] :
( ( c_SEQ_Osubseq @ A )
=> ~ ( c_SEQ_Omonoseq @ tc_RealDef_Oreal @ ( c_COMBB @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_Nat_Onat @ c_Complex_OIm @ ( c_COMBB @ tc_Nat_Onat @ tc_Complex_Ocomplex @ tc_Nat_Onat @ v_s @ ( c_COMBB @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat @ v_f____ @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(224,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ C @ B ) ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib) ).
thf(1756,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ C @ B ) ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(755,axiom,
! [A: $i] :
( ( c_SEQ_Osubseq @ A )
<=> ! [B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ A @ B ) ) @ ( hAPP @ A @ ( c_Nat_OSuc @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subseq__Suc__iff) ).
thf(3367,plain,
! [A: $i] :
( ( ( c_SEQ_Osubseq @ A )
=> ! [B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ A @ B ) ) @ ( hAPP @ A @ ( c_Nat_OSuc @ B ) ) ) ) )
& ( ! [B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ A @ B ) ) @ ( hAPP @ A @ ( c_Nat_OSuc @ B ) ) ) )
=> ( c_SEQ_Osubseq @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(947,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) )
<=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ A ) ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ B ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__right__disj) ).
thf(4011,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ A ) ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ B ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ A ) @ C ) ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ A ) ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ B ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ A ) @ C ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(1181,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( B
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ C ) )
<=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__eq__divide__eq) ).
thf(4856,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( B
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C )
= A ) )
& ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C )
= A )
=> ( B
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1181]) ).
thf(28,axiom,
class_Rings_Oordered__semiring @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).
thf(1327,plain,
class_Rings_Oordered__semiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(382,axiom,
! [A: $i,B: $i] :
( ( c_Transcendental_Ocos @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ B ) @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Transcendental_Ocos @ B ) ) @ ( c_Transcendental_Ocos @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Transcendental_Osin @ B ) ) @ ( c_Transcendental_Osin @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cos__add) ).
thf(2168,plain,
! [A: $i,B: $i] :
( ( c_Transcendental_Ocos @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ B ) @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Transcendental_Ocos @ B ) ) @ ( c_Transcendental_Ocos @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Transcendental_Osin @ B ) ) @ ( c_Transcendental_Osin @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(1042,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__increasing__iff) ).
thf(4294,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(317,axiom,
! [A: $i] :
( ( c_SEQ_Oconvergent @ tc_Complex_Ocomplex @ A )
=> ( c_SEQ_Oconvergent @ tc_RealDef_Oreal @ ( c_COMBB @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_Nat_Onat @ c_Complex_OIm @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Im_Oconvergent) ).
thf(1954,plain,
! [A: $i] :
( ( c_SEQ_Oconvergent @ tc_Complex_Ocomplex @ A )
=> ( c_SEQ_Oconvergent @ tc_RealDef_Oreal @ ( c_COMBB @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_Nat_Onat @ c_Complex_OIm @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(519,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__le) ).
thf(2575,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(886,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono1) ).
thf(3794,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(153,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0__right) ).
thf(1608,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(665,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex ) @ B ) @ A ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__mod__triangle__sub) ).
thf(3049,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex ) @ B ) @ A ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(869,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).
thf(3745,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(573,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ E )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Oabs__class_Oabs @ E @ ( c_Groups_Ominus__class_Ominus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ B ) @ A ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( c_Groups_Oabs__class_Oabs @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) ) @ ( c_Groups_Oabs__class_Oabs @ E @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__diff__triangle__ineq) ).
thf(2740,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ E )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Oabs__class_Oabs @ E @ ( c_Groups_Ominus__class_Ominus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ B ) @ A ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( c_Groups_Oabs__class_Oabs @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) ) @ ( c_Groups_Oabs__class_Oabs @ E @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(628,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ A @ ( c_Groups_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ A ) @ ( c_Groups_Oone__class_Oone @ A ) ) @ ( c_Groups_Oone__class_Oone @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__two) ).
thf(2918,plain,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ A @ ( c_Groups_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ A ) @ ( c_Groups_Oone__class_Oone @ A ) ) @ ( c_Groups_Oone__class_Oone @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(979,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__vector @ E )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ ( c_Groups_Ominus__class_Ominus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ B ) @ A ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ E @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__diff__triangle__ineq) ).
thf(4110,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__vector @ E )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ ( c_Groups_Ominus__class_Ominus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ B ) @ A ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ E @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(277,axiom,
! [A: $i] :
( ( c_Complex_Ocis @ A )
= ( c_Complex_Ocomplex_OComplex @ ( c_Transcendental_Ocos @ A ) @ ( c_Transcendental_Osin @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cis__def) ).
thf(1867,plain,
! [A: $i] :
( ( c_Complex_Ocis @ A )
= ( c_Complex_Ocomplex_OComplex @ ( c_Transcendental_Ocos @ A ) @ ( c_Transcendental_Osin @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(340,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Omult__zero @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__zero__left) ).
thf(1999,plain,
! [A: $i,B: $i] :
( ( class_Rings_Omult__zero @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(779,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).
thf(3446,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(473,axiom,
class_RealVector_Oreal__normed__algebra__1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).
thf(2434,plain,
class_RealVector_Oreal__normed__algebra__1 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(563,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono) ).
thf(2712,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(723,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
& ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__le) ).
thf(3253,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
& ( B != A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
& ( B != A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(334,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).
thf(1988,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(172,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__eq__diff__pred) ).
thf(1640,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(521,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) ) @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__add__iff1) ).
thf(2580,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E ) @ D ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) ) @ B ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(1157,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ln__add__one__self__le__self) ).
thf(4762,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).
thf(87,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__ring @ A )
=> ( class_Rings_Oring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring) ).
thf(1458,plain,
! [A: $i] :
( ( class_Rings_Ocomm__ring @ A )
=> ( class_Rings_Oring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(744,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__less__imp__less) ).
thf(3335,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(222,axiom,
class_Fields_Ofield__inverse__zero @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield__inverse__zero) ).
thf(1746,plain,
class_Fields_Ofield__inverse__zero @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(1161,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oordered__ring @ F )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) ) @ D ) ) @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__iff1) ).
thf(4792,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oordered__ring @ F )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) ) @ D ) ) @ C ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) ) @ D ) ) @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).
thf(236,axiom,
! [A: $i] :
( ( c_RComplete_Onatfloor @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__real__of__nat) ).
thf(1782,plain,
! [A: $i] :
( ( c_RComplete_Onatfloor @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(794,axiom,
( ( c_Transcendental_Oln @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ln__one) ).
thf(3502,plain,
( ( c_Transcendental_Oln @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(408,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__mono) ).
thf(2227,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(797,axiom,
! [A: $i] :
( ( class_Rings_Ozero__neq__one @ A )
=> ( ( c_Groups_Ozero__class_Ozero @ A )
!= ( c_Groups_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__neq__one) ).
thf(3513,plain,
! [A: $i] :
( ( class_Rings_Ozero__neq__one @ A )
=> ( ( c_Groups_Ozero__class_Ozero @ A )
!= ( c_Groups_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(879,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E ) @ D ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__add__eq1) ).
thf(3777,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E ) @ D ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(156,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Rings_Osemiring__0 @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring__0) ).
thf(1613,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Rings_Osemiring__0 @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(784,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( c_Nat_OSuc @ B ) ) ) ) )
<=> ( B
= ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__div__lemma) ).
thf(3466,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( c_Nat_OSuc @ B ) ) ) ) )
=> ( B
= ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ C ) ) )
& ( ( B
= ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( c_Nat_OSuc @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(1010,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
thf(4198,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(95,axiom,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).
thf(1475,plain,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(1094,axiom,
class_Rings_Osemiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring) ).
thf(4467,plain,
class_Rings_Osemiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).
thf(97,axiom,
class_Groups_Omonoid__mult @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).
thf(1482,plain,
class_Groups_Omonoid__mult @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(285,axiom,
! [A: $i] :
( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zero) ).
thf(1887,plain,
! [A: $i] :
( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(899,axiom,
class_Rings_Ocomm__ring__1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring__1) ).
thf(3836,plain,
class_Rings_Ocomm__ring__1 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(1059,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ B ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__antisym) ).
thf(4343,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ B ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).
thf(806,axiom,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0I) ).
thf(3545,plain,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(566,axiom,
( ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex )
= ( c_Complex_Ocomplex_OComplex @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__zero__def) ).
thf(2723,plain,
( ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex )
= ( c_Complex_Ocomplex_OComplex @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(989,axiom,
! [A: $i,B: $i] :
( ( c_SEQ_Osubseq @ B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_seq__suble) ).
thf(4142,plain,
! [A: $i,B: $i] :
( ( c_SEQ_Osubseq @ B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(352,axiom,
! [A: $i] :
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__Suc) ).
thf(2046,plain,
! [A: $i] :
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(1070,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
thf(4371,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).
thf(969,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1) ).
thf(4079,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(78,axiom,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
thf(1441,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(1033,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Divides_Odiv__class_Odiv @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ A ) @ B ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( c_Divides_Odiv__class_Odiv @ C @ A @ B ) ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__add__self2) ).
thf(4266,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Divides_Odiv__class_Odiv @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ A ) @ B ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( c_Divides_Odiv__class_Odiv @ C @ A @ B ) ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).
thf(343,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).
thf(2010,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(307,axiom,
class_Rings_Ocomm__ring @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring) ).
thf(1935,plain,
class_Rings_Ocomm__ring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(174,axiom,
class_Divides_Osemiring__div @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Osemiring__div) ).
thf(1645,plain,
class_Divides_Osemiring__div @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(299,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(1921,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(890,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__le__trans) ).
thf(3809,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(44,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Orderings_Oord @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oord) ).
thf(1366,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Orderings_Oord @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(1213,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__shift) ).
thf(4963,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1213]) ).
thf(597,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__less__iff1) ).
thf(2825,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(114,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__comm__semiring__strict @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict) ).
thf(1529,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__comm__semiring__strict @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(996,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_Transcendental_Oln @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ln__gt__zero) ).
thf(4156,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_Transcendental_Oln @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(246,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__commute) ).
thf(1803,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(373,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__less__cancel1) ).
thf(2136,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(1137,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).
thf(4610,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).
thf(206,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(1703,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(851,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ F ) @ E ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ D ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C ) @ F ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).
thf(3688,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ F ) @ E ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ D ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C ) @ F ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(615,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__less) ).
thf(2869,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(913,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oab__group__add @ E )
=> ( ( c_Groups_Ominus__class_Ominus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Deriv_Oadd__diff__add) ).
thf(3891,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oab__group__add @ E )
=> ( ( c_Groups_Ominus__class_Ominus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(1023,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).
thf(4238,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(1120,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) )
<=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
| ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ D ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Nat_OSuc @ D ) ) ) )
& ( hBOOL @ ( hAPP @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__div_H) ).
thf(4546,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
| ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ D ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Nat_OSuc @ D ) ) ) )
& ( hBOOL @ ( hAPP @ C @ D ) ) ) ) )
& ( ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
| ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ D ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Nat_OSuc @ D ) ) ) )
& ( hBOOL @ ( hAPP @ C @ D ) ) ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).
thf(1061,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__iff) ).
thf(4348,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).
thf(593,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__zero) ).
thf(2814,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(729,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__neg) ).
thf(3275,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(423,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__le__imp__le) ).
thf(2269,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(562,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I1_J) ).
thf(2708,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(293,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Groups_Osgn__class_Osgn @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Osgn__class_Osgn @ C @ B ) ) @ ( c_Groups_Osgn__class_Osgn @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__times) ).
thf(1907,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Groups_Osgn__class_Osgn @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Osgn__class_Osgn @ C @ B ) ) @ ( c_Groups_Osgn__class_Osgn @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(836,axiom,
class_Groups_Oordered__ab__semigroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add) ).
thf(3653,plain,
class_Groups_Oordered__ab__semigroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(1036,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__0) ).
thf(4275,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).
thf(676,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ E )
=> ( ( ( D != C )
& ( B != A ) )
<=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) )
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_crossproduct__noteq) ).
thf(3089,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ E )
=> ( ( ( ( D != C )
& ( B != A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) )
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ B ) ) ) )
& ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) )
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ B ) ) )
=> ( ( D != C )
& ( B != A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(1262,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
| ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).
thf(5108,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
| ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1262]) ).
thf(1025,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel__left__neg) ).
thf(4243,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(529,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__ab__semigroup__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mono) ).
thf(2603,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__ab__semigroup__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(627,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__mono) ).
thf(2916,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(1183,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).
thf(4866,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183]) ).
thf(1191,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ C )
= A )
<=> ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__divide__eq__eq) ).
thf(4896,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ C )
= A )
=> ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) )
& ( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ C )
= A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191]) ).
thf(834,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) )
= ( c_Divides_Odiv__class_Odiv @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__mult2) ).
thf(3644,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) )
= ( c_Divides_Odiv__class_Odiv @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(684,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__cancel) ).
thf(3131,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(1210,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leD) ).
thf(4956,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1210]) ).
thf(680,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__1) ).
thf(3116,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(549,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leD) ).
thf(2667,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(445,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__le__mult__iff) ).
thf(2339,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(663,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__imp__add1__zle) ).
thf(3046,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(108,axiom,
class_Rings_Omult__zero @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).
thf(1511,plain,
class_Rings_Omult__zero @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(788,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__mono2) ).
thf(3485,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(554,axiom,
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__one) ).
thf(2682,plain,
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(258,axiom,
! [A: $i,B: $i] :
( ( ( c_Nat_OSuc @ B )
= ( c_Nat_OSuc @ A ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__inject) ).
thf(1826,plain,
! [A: $i,B: $i] :
( ( ( c_Nat_OSuc @ B )
= ( c_Nat_OSuc @ A ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(85,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Rings_Ocomm__semiring__0 @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__0) ).
thf(1455,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Rings_Ocomm__semiring__0 @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(731,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__add1__eq__le) ).
thf(3280,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(1124,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oabs__class_Oabs @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__le__zero__iff) ).
thf(4568,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oabs__class_Oabs @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oabs__class_Oabs @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).
thf(751,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( ( ( c_Groups_Oabs__class_Oabs @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__eq__0) ).
thf(3353,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( ( ( ( c_Groups_Oabs__class_Oabs @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Oabs__class_Oabs @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(89,axiom,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
thf(1462,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(1080,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__power) ).
thf(4428,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).
thf(575,axiom,
! [A: $i,B: $i] :
( ( hAPP @ c_Complex_OIm @ ( c_Complex_Ocomplex_OComplex @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Im) ).
thf(2745,plain,
! [A: $i,B: $i] :
( ( hAPP @ c_Complex_OIm @ ( c_Complex_Ocomplex_OComplex @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(517,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__le__dividend) ).
thf(2571,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(451,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__add__strict) ).
thf(2356,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(245,axiom,
! [A: $i,B: $i] :
( ( c_Complex_Ocis @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Complex_Ocis @ A ) ) @ ( c_Complex_Ocis @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cis__real__of__nat__Suc__mult) ).
thf(1800,plain,
! [A: $i,B: $i] :
( ( c_Complex_Ocis @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Complex_Ocis @ A ) ) @ ( c_Complex_Ocis @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(51,axiom,
class_Rings_Olinordered__semiring__1__strict @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).
thf(1379,plain,
class_Rings_Olinordered__semiring__1__strict @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(609,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ominus__class_Ominus @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) @ ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__triangle__ineq2__sym) ).
thf(2857,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ominus__class_Ominus @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) @ ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(286,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
= ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__div__cancel__disj) ).
thf(1890,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
= ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(1479,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(379,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ ( c_Nat_OSuc @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).
thf(2158,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ ( c_Nat_OSuc @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ ( c_Nat_OSuc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(230,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__diff) ).
thf(1773,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(323,axiom,
class_Rings_Ocomm__ring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring) ).
thf(1963,plain,
class_Rings_Ocomm__ring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(1251,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).
thf(5077,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1251]) ).
thf(267,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__semiring__1__strict @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict) ).
thf(1847,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__semiring__1__strict @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(1133,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(4595,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).
thf(353,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( c_Nat_OSuc @ A ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( B
= ( c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucE) ).
thf(2049,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( c_Nat_OSuc @ A ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( B
= ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(511,axiom,
class_Groups_Olinordered__ab__group__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) ).
thf(2552,plain,
class_Groups_Olinordered__ab__group__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(456,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr__implies__not0) ).
thf(2373,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(37,axiom,
class_Rings_Oring__1__no__zero__divisors @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors) ).
thf(1347,plain,
class_Rings_Oring__1__no__zero__divisors @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(922,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( ( c_RComplete_Onatfloor @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal ) @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) )
= ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__div__nat) ).
thf(3919,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( ( c_RComplete_Onatfloor @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal ) @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) )
= ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(219,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal ) @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ C @ A ) @ ( hAPP @ C @ B ) ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ A @ B ) ) ) @ B ) )
= ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal ) @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ C @ A ) @ ( hAPP @ C @ B ) ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ A @ B ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lemma__MVT) ).
thf(1741,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal ) @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ C @ A ) @ ( hAPP @ C @ B ) ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ A @ B ) ) ) @ B ) )
= ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal ) @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ C @ A ) @ ( hAPP @ C @ B ) ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ A @ B ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(1171,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).
thf(4830,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).
thf(673,axiom,
class_Groups_Ocancel__comm__monoid__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add) ).
thf(3084,plain,
class_Groups_Ocancel__comm__monoid__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(631,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).
thf(2929,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(539,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__div2) ).
thf(2635,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(1241,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ B )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ B ) @ A ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ B ) @ A ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__self__if) ).
thf(5052,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ B )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ B ) @ A ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ B ) @ A ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1241]) ).
thf(739,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__algebra @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__mult__less) ).
thf(3312,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__algebra @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(133,axiom,
class_Groups_Oordered__ab__group__add @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add) ).
thf(1568,plain,
class_Groups_Oordered__ab__group__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(917,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__is__0__eq) ).
thf(3902,plain,
! [A: $i,B: $i] :
( ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(838,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__mono) ).
thf(3657,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(304,axiom,
class_Rings_Oring @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring) ).
thf(1931,plain,
class_Rings_Oring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(865,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_COMBS @ F @ E @ D @ C @ B ) @ A )
= ( hAPP @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBS__1) ).
thf(3734,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_COMBS @ F @ E @ D @ C @ B ) @ A )
= ( hAPP @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(654,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__ring__abs @ C )
=> ( ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) )
=> ( ( c_Groups_Oabs__class_Oabs @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Oabs__class_Oabs @ C @ B ) ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__eq__mult) ).
thf(3014,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__ring__abs @ C )
=> ( ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) )
=> ( ( c_Groups_Oabs__class_Oabs @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Oabs__class_Oabs @ C @ B ) ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(1208,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Complex_Ocomplex_OComplex @ D @ C ) ) @ ( c_Complex_Ocomplex_OComplex @ B @ A ) )
= ( c_Complex_Ocomplex_OComplex @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__mult) ).
thf(4952,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Complex_Ocomplex_OComplex @ D @ C ) ) @ ( c_Complex_Ocomplex_OComplex @ B @ A ) )
= ( c_Complex_Ocomplex_OComplex @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1208]) ).
thf(1107,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) )
=> ( ( c_RComplete_Onatceiling @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__eq) ).
thf(4507,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) )
=> ( ( c_RComplete_Onatceiling @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).
thf(281,axiom,
! [A: $i,B: $i] :
( ( ( c_RealDef_Oreal @ tc_Nat_Onat @ B )
= ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__inject) ).
thf(1875,plain,
! [A: $i,B: $i] :
( ( ( ( c_RealDef_Oreal @ tc_Nat_Onat @ B )
= ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_RealDef_Oreal @ tc_Nat_Onat @ B )
= ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(233,axiom,
class_Rings_Ozero__neq__one @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).
thf(1778,plain,
class_Rings_Ozero__neq__one @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(1110,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonneg1__imp__zdiv__pos__iff) ).
thf(4514,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).
thf(504,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__mono2) ).
thf(2533,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(1029,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__left) ).
thf(4253,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(725,axiom,
class_Groups_Oordered__ab__group__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add) ).
thf(3268,plain,
class_Groups_Oordered__ab__group__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(706,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( hAPP @ c_Complex_OIm @ A ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__Im__le__cmod) ).
thf(3199,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( hAPP @ c_Complex_OIm @ A ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(1031,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl) ).
thf(4258,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).
thf(542,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( hAPP @ c_Complex_ORe @ A ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__Re__le__cmod) ).
thf(2650,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( hAPP @ c_Complex_ORe @ A ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(856,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add2) ).
thf(3702,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(1233,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( ( c_Transcendental_Oln @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( c_Transcendental_Oln @ B ) ) @ ( c_Transcendental_Oln @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ln__mult) ).
thf(5032,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( ( c_Transcendental_Oln @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( c_Transcendental_Oln @ B ) ) @ ( c_Transcendental_Oln @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1233]) ).
thf(1160,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ A ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__add1__eq) ).
thf(4783,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ A ) )
| ( B = A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ A ) )
| ( B = A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).
thf(8,axiom,
class_Rings_Oordered__cancel__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).
thf(1283,plain,
class_Rings_Oordered__cancel__semiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(406,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hAPP @ B @ C )
= ( hAPP @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ext) ).
thf(2222,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hAPP @ B @ C )
= ( hAPP @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(1075,axiom,
( ( hAPP @ c_Complex_OIm @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Im_Ozero) ).
thf(4411,plain,
( ( hAPP @ c_Complex_OIm @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring__1 @ C )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_realpow__two__diff) ).
thf(1489,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring__1 @ C )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(1141,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( ( c_Nat__Transfer_Otsub @ A @ B )
= ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ A @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( ( c_Nat__Transfer_Otsub @ A @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tsub__def) ).
thf(4696,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( ( c_Nat__Transfer_Otsub @ A @ B )
= ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ A @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( ( c_Nat__Transfer_Otsub @ A @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).
thf(1013,axiom,
! [A: $i] :
( ( class_RealVector_Oreal__normed__vector @ A )
=> ( ( c_RealVector_Onorm__class_Onorm @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__zero) ).
thf(4205,plain,
! [A: $i] :
( ( class_RealVector_Oreal__normed__vector @ A )
=> ( ( c_RealVector_Onorm__class_Onorm @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Power_Opower @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc) ).
thf(1302,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Power_Opower @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(185,axiom,
class_Groups_Omonoid__add @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).
thf(1664,plain,
class_Groups_Omonoid__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(1054,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex ) @ ( c_Complex_Ocomplex_OComplex @ D @ C ) ) @ ( c_Complex_Ocomplex_OComplex @ B @ A ) )
= ( c_Complex_Ocomplex_OComplex @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__add) ).
thf(4329,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex ) @ ( c_Complex_Ocomplex_OComplex @ D @ C ) ) @ ( c_Complex_Ocomplex_OComplex @ B @ A ) )
= ( c_Complex_Ocomplex_OComplex @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).
thf(932,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__cancel) ).
thf(3966,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(211,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Complex_Ocomplex_OComplex @ D @ C )
= ( c_Complex_Ocomplex_OComplex @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex_Oinject) ).
thf(1714,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( c_Complex_Ocomplex_OComplex @ D @ C )
= ( c_Complex_Ocomplex_OComplex @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( c_Complex_Ocomplex_OComplex @ D @ C )
= ( c_Complex_Ocomplex_OComplex @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(1192,axiom,
! [A: $i,B: $i] :
( ( c_Complex_Oexpi @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Complex_Oexpi @ B ) ) @ ( c_Complex_Oexpi @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_expi__add) ).
thf(4903,plain,
! [A: $i,B: $i] :
( ( c_Complex_Oexpi @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Complex_Oexpi @ B ) ) @ ( c_Complex_Oexpi @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1192]) ).
thf(1255,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__comm__semiring @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__mult__left__mono) ).
thf(5084,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__comm__semiring @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1255]) ).
thf(82,axiom,
class_RealVector_Oreal__normed__div__algebra @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
thf(1450,plain,
class_RealVector_Oreal__normed__div__algebra @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(948,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__power__less__imp__less) ).
thf(4018,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(764,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( c_RComplete_Onatfloor @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_RComplete_Onatfloor @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__add) ).
thf(3393,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( c_RComplete_Onatfloor @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_RComplete_Onatfloor @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(1228,axiom,
( ( c_RComplete_Onatceiling @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__zero) ).
thf(5013,plain,
( ( c_RComplete_Onatceiling @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1228]) ).
thf(295,axiom,
class_Groups_Ozero @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).
thf(1911,plain,
class_Groups_Ozero @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(586,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__1) ).
thf(2782,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(622,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__left__mono__neg) ).
thf(2893,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(165,axiom,
class_Rings_Oordered__comm__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).
thf(1632,plain,
class_Rings_Oordered__comm__semiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(1043,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(4297,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).
thf(619,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__left__mono) ).
thf(2880,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(1177,axiom,
class_Groups_Oab__group__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__group__add) ).
thf(4847,plain,
class_Groups_Oab__group__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).
thf(273,axiom,
class_Rings_Ocomm__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).
thf(1858,plain,
class_Rings_Ocomm__semiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(276,axiom,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0__eq__0) ).
thf(1864,plain,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(1166,axiom,
! [A: $i] :
( ( c_SEQ_Osubseq @ A )
<=> ! [B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ A @ B ) ) @ ( hAPP @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subseq__def) ).
thf(4815,plain,
! [A: $i] :
( ( ( c_SEQ_Osubseq @ A )
=> ! [B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ A @ B ) ) @ ( hAPP @ A @ C ) ) ) ) )
& ( ! [B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ A @ B ) ) @ ( hAPP @ A @ C ) ) ) )
=> ( c_SEQ_Osubseq @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166]) ).
thf(1147,axiom,
class_Rings_Oidom @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oidom) ).
thf(4724,plain,
class_Rings_Oidom @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147]) ).
thf(54,axiom,
class_Rings_Ocomm__semiring__0 @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__0) ).
thf(1383,plain,
class_Rings_Ocomm__semiring__0 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(986,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Oone__class_Oone @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_realpow__Suc__le__self) ).
thf(4134,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Oone__class_Oone @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(322,axiom,
! [A: $i,B: $i] :
( ( hAPP @ c_Complex_ORe @ ( c_Complex_Ocomplex_OComplex @ B @ A ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Re) ).
thf(1960,plain,
! [A: $i,B: $i] :
( ( hAPP @ c_Complex_ORe @ ( c_Complex_Ocomplex_OComplex @ B @ A ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(1163,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__right) ).
thf(4798,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).
thf(981,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__conv) ).
thf(4115,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(140,axiom,
class_Orderings_Oord @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).
thf(1581,plain,
class_Orderings_Oord @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(443,axiom,
c_SEQ_Omonoseq @ tc_RealDef_Oreal @ ( c_COMBB @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_Nat_Onat @ c_Complex_ORe @ ( c_COMBB @ tc_Nat_Onat @ tc_Complex_Ocomplex @ tc_Nat_Onat @ v_s @ v_f____ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_f_I2_J) ).
thf(2335,plain,
c_SEQ_Omonoseq @ tc_RealDef_Oreal @ ( c_COMBB @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_Nat_Onat @ c_Complex_ORe @ ( c_COMBB @ tc_Nat_Onat @ tc_Complex_Ocomplex @ tc_Nat_Onat @ v_s @ v_f____ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(877,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__zeroE) ).
thf(3771,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(903,axiom,
! [A: $i] :
( ( class_RealVector_Oreal__normed__algebra__1 @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ A @ ( c_Groups_Oone__class_Oone @ A ) )
= ( c_Groups_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__one) ).
thf(3851,plain,
! [A: $i] :
( ( class_RealVector_Oreal__normed__algebra__1 @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ A @ ( c_Groups_Oone__class_Oone @ A ) )
= ( c_Groups_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(302,axiom,
class_Rings_Ocomm__semiring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring) ).
thf(1928,plain,
class_Rings_Ocomm__semiring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(600,axiom,
class_Rings_Oordered__cancel__semiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) ).
thf(2833,plain,
class_Rings_Oordered__cancel__semiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(860,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( ( c_SEQ_Oincseq @ B @ A )
<=> ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( hAPP @ A @ C ) ) @ ( hAPP @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_incseq__def) ).
thf(3712,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( ( ( c_SEQ_Oincseq @ B @ A )
=> ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( hAPP @ A @ C ) ) @ ( hAPP @ A @ D ) ) ) ) )
& ( ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( hAPP @ A @ C ) ) @ ( hAPP @ A @ D ) ) ) )
=> ( c_SEQ_Oincseq @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(81,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times__divide__eq__right) ).
thf(1447,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(1224,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__le__mono) ).
thf(4996,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1224]) ).
thf(1169,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__left__mono) ).
thf(4825,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).
thf(312,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(1943,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(148,axiom,
! [A: $i,B: $i] :
( ( class_Divides_Osemiring__div @ B )
=> ( ( c_Divides_Odiv__class_Odiv @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__by__0) ).
thf(1600,plain,
! [A: $i,B: $i] :
( ( class_Divides_Osemiring__div @ B )
=> ( ( c_Divides_Odiv__class_Odiv @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(397,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ A ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__ge__self) ).
thf(2205,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ A ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(1238,axiom,
class_Rings_Ocomm__ring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring) ).
thf(5045,plain,
class_Rings_Ocomm__ring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1238]) ).
thf(762,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Complex_Ocis @ B ) ) @ ( c_Complex_Ocis @ A ) )
= ( c_Complex_Ocis @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cis__mult) ).
thf(3389,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Complex_Ocis @ B ) ) @ ( c_Complex_Ocis @ A ) )
= ( c_Complex_Ocis @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(265,axiom,
! [A: $i] :
( ( class_Groups_Ocancel__comm__monoid__add @ A )
=> ( class_Groups_Ocancel__comm__monoid__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add) ).
thf(1843,plain,
! [A: $i] :
( ( class_Groups_Ocancel__comm__monoid__add @ A )
=> ( class_Groups_Ocancel__comm__monoid__add @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(356,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl2) ).
thf(2058,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(960,axiom,
c_SEQ_Osubseq @ v_f____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_f_I1_J) ).
thf(4055,plain,
c_SEQ_Osubseq @ v_f____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(1020,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__less__power) ).
thf(4230,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).
thf(850,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
thf(3685,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(284,axiom,
class_Rings_Osemiring @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).
thf(1886,plain,
class_Rings_Osemiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(1105,axiom,
? [A: $i] :
! [B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( hAPP @ c_Complex_OIm @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Im_Obounded) ).
thf(4504,plain,
? [A: $i] :
! [B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( hAPP @ c_Complex_OIm @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
thf(243,axiom,
class_Groups_Oab__semigroup__mult @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
thf(1796,plain,
class_Groups_Oab__semigroup__mult @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(661,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add1__zle__eq) ).
thf(3036,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(502,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oabs__class_Oabs @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__not__less__zero) ).
thf(2530,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oabs__class_Oabs @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(1067,axiom,
! [A: $i,B: $i] :
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__add) ).
thf(4364,plain,
! [A: $i,B: $i] :
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).
thf(972,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_Transcendental_Oln @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ln__ge__zero__imp__ge__one) ).
thf(4087,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_Transcendental_Oln @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(643,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ ( c_Groups_Oone__class_Oone @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__decreasing) ).
thf(2979,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ ( c_Groups_Oone__class_Oone @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(113,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__mult @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__mult__distrib) ).
thf(1526,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__mult @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(1047,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E ) @ D ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ A ) )
<=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) ) @ B )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__eq__add__iff1) ).
thf(4307,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E ) @ D ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) ) @ B )
= A ) )
& ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) ) @ B )
= A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).
thf(847,axiom,
( ( c_Transcendental_Ocos @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cos__zero) ).
thf(3676,plain,
( ( c_Transcendental_Ocos @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(753,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
= ( c_Divides_Odiv__class_Odiv @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__mult1) ).
thf(3361,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
= ( c_Divides_Odiv__class_Odiv @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(341,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__vector @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__triangle__ineq) ).
thf(2002,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__vector @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(929,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__strict__right__mono) ).
thf(3955,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(721,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__imp__zdiv__nonneg__iff) ).
thf(3243,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(591,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__div__less__self) ).
thf(2809,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(413,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__le__eq__one) ).
thf(2242,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(427,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__less__imp__less__base) ).
thf(2286,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(956,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Olinordered__semiring__1__strict @ F )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ F @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ F @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) ) @ A ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ F ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ A ) @ C ) ) ) @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_convex__bound__lt) ).
thf(4038,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Olinordered__semiring__1__strict @ F )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ F @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ F @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) ) @ A ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ F ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ A ) @ C ) ) ) @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(742,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ ( c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessI) ).
thf(3327,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ ( c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(74,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__semiring__strict @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict) ).
thf(1433,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__semiring__strict @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(577,axiom,
( ( hAPP @ c_Complex_ORe @ c_Complex_Oii )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__Re__i) ).
thf(2750,plain,
( ( hAPP @ c_Complex_ORe @ c_Complex_Oii )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(63,axiom,
class_Rings_Olinordered__ring @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).
thf(1405,plain,
class_Rings_Olinordered__ring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(818,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).
thf(3588,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(1189,axiom,
( ( c_Transcendental_Osin @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sin__zero) ).
thf(4892,plain,
( ( c_Transcendental_Osin @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189]) ).
thf(203,axiom,
class_Orderings_Oorder @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).
thf(1697,plain,
class_Orderings_Oorder @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(712,axiom,
( c_Complex_Oii
!= ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__i__not__one) ).
thf(3211,plain,
( c_Complex_Oii
!= ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(460,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__pred) ).
thf(2392,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(1130,axiom,
hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ v_r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rp) ).
thf(4588,plain,
hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ v_r ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).
thf(202,axiom,
class_Groups_Ozero @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
thf(1696,plain,
class_Groups_Ozero @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(701,axiom,
class_Groups_Oordered__ab__group__add__abs @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).
thf(3184,plain,
class_Groups_Oordered__ab__group__add__abs @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(1097,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( B != A )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE) ).
thf(4475,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( B != A )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).
thf(523,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__linear) ).
thf(2586,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(621,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__two__squares__add__zero__iff) ).
thf(2884,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(970,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1) ).
thf(4082,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(962,axiom,
class_Rings_Olinordered__ring__strict @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring__strict) ).
thf(4065,plain,
class_Rings_Olinordered__ring__strict @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(775,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__nonpos__pos__le0) ).
thf(3435,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(178,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(1651,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(1180,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Complex_Orcis @ D @ C ) ) @ ( c_Complex_Orcis @ B @ A ) )
= ( c_Complex_Orcis @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rcis__mult) ).
thf(4853,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Complex_Orcis @ D @ C ) ) @ ( c_Complex_Orcis @ B @ A ) )
= ( c_Complex_Orcis @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1180]) ).
thf(905,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).
thf(3857,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(200,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Oordered__cancel__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring) ).
thf(1691,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Oordered__cancel__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(76,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oordered__comm__monoid__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add) ).
thf(1438,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oordered__comm__monoid__add @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(938,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Osgn__class_Osgn @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__less) ).
thf(3984,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Osgn__class_Osgn @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Osgn__class_Osgn @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(1113,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oord @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funE) ).
thf(4531,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oord @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).
thf(832,axiom,
! [A: $i,B: $i] :
( ( ( class_Power_Opower @ B )
& ( class_Rings_Osemiring__0 @ B ) )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__0__left) ).
thf(3635,plain,
! [A: $i,B: $i] :
( ( ( class_Power_Opower @ B )
& ( class_Rings_Osemiring__0 @ B ) )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(967,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__trans) ).
thf(4076,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(1195,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__div__algebra @ C )
=> ( ( c_RealVector_Onorm__class_Onorm @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__mult) ).
thf(4910,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__div__algebra @ C )
=> ( ( c_RealVector_Onorm__class_Onorm @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195]) ).
thf(1001,axiom,
! [A: $i,B: $i] :
( ( class_Divides_Osemiring__div @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Divides_Odiv__class_Odiv @ B @ A @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__self) ).
thf(4172,plain,
! [A: $i,B: $i] :
( ( class_Divides_Osemiring__div @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Divides_Odiv__class_Odiv @ B @ A @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(1266,axiom,
! [A: $i,B: $i] :
( ( B = A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__imp__le) ).
thf(5122,plain,
! [A: $i,B: $i] :
( ( B = A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1266]) ).
thf(150,axiom,
class_Groups_Omonoid__add @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
thf(1604,plain,
class_Groups_Omonoid__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(916,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(3899,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(625,axiom,
! [A: $i] :
( ( ( c_Transcendental_Osin @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Transcendental_Ocos @ A ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sin__zero__abs__cos__one) ).
thf(2910,plain,
! [A: $i] :
( ( ( c_Transcendental_Osin @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Transcendental_Ocos @ A ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(1052,axiom,
! [A: $i,B: $i] :
( ( hAPP @ c_Complex_ORe @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ c_Complex_ORe @ B ) @ ( hAPP @ c_Complex_ORe @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Re_Odiff) ).
thf(4323,plain,
! [A: $i,B: $i] :
( ( hAPP @ c_Complex_ORe @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ c_Complex_ORe @ B ) @ ( hAPP @ c_Complex_ORe @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).
thf(819,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ln__less__zero__iff) ).
thf(3591,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(1131,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__left__pos) ).
thf(4589,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).
thf(1073,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(4407,plain,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).
thf(943,axiom,
class_Rings_Oring__1__no__zero__divisors @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors) ).
thf(3995,plain,
class_Rings_Oring__1__no__zero__divisors @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(1264,axiom,
class_RealVector_Oreal__normed__field @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__field) ).
thf(5117,plain,
class_RealVector_Oreal__normed__field @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1264]) ).
thf(92,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Ometric__space @ B )
=> ( c_SEQ_Oconvergent @ B @ ( c_COMBK @ B @ tc_Nat_Onat @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_convergent__const) ).
thf(1470,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Ometric__space @ B )
=> ( c_SEQ_Oconvergent @ B @ ( c_COMBK @ B @ tc_Nat_Onat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(298,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__0__0) ).
thf(1915,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(208,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Oordered__ring__abs @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring__abs) ).
thf(1708,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Oordered__ring__abs @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( hAPP @ c_Complex_ORe @ ( c_Complex_Orcis @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ ( c_Transcendental_Ocos @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Re__rcis) ).
thf(1311,plain,
! [A: $i,B: $i] :
( ( hAPP @ c_Complex_ORe @ ( c_Complex_Orcis @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ ( c_Transcendental_Ocos @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(431,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ A ) )
| ( B = A )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__linear) ).
thf(2296,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ A ) )
| ( B = A )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(435,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_Transcendental_Oln @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ln__ge__zero) ).
thf(2307,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_Transcendental_Oln @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(490,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord__le__eq__trans) ).
thf(2496,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(589,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) )
<=> ~ ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
| ? [D: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ D ) )
& ~ ( hBOOL @ ( hAPP @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__split__asm) ).
thf(2790,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) )
=> ~ ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
| ? [D: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ D ) )
& ~ ( hBOOL @ ( hAPP @ C @ D ) ) ) ) )
& ( ~ ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
| ? [D: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ D ) )
& ~ ( hBOOL @ ( hAPP @ C @ D ) ) ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(546,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less__trans) ).
thf(2660,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(227,axiom,
class_Groups_Ocomm__monoid__add @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
thf(1768,plain,
class_Groups_Ocomm__monoid__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( class_Divides_Osemiring__div @ B )
=> ( ( c_Divides_Odiv__class_Odiv @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__0) ).
thf(1274,plain,
! [A: $i,B: $i] :
( ( class_Divides_Osemiring__div @ B )
=> ( ( c_Divides_Odiv__class_Odiv @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1197,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ E @ D @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ E @ D @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power_Opower_Opower__Suc) ).
thf(4915,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ E @ D @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ E @ D @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197]) ).
thf(507,axiom,
( ( hAPP @ c_Complex_OIm @ c_Complex_Oii )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__Im__i) ).
thf(2541,plain,
( ( hAPP @ c_Complex_OIm @ c_Complex_Oii )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(372,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ ( c_RComplete_Onatfloor @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__natfloor__eq) ).
thf(2133,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ ( c_RComplete_Onatfloor @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ ( c_RComplete_Onatfloor @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(375,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ono__zero__divisors @ C )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divisors__zero) ).
thf(2147,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ono__zero__divisors @ C )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(868,axiom,
! [A: $i,B: $i] :
( ( hAPP @ c_Complex_OIm @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ c_Complex_OIm @ B ) @ ( hAPP @ c_Complex_OIm @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Im_Odiff) ).
thf(3742,plain,
! [A: $i,B: $i] :
( ( hAPP @ c_Complex_OIm @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ c_Complex_OIm @ B ) @ ( hAPP @ c_Complex_OIm @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(685,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__leE) ).
thf(3134,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(746,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oring @ F )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) ) @ A ) )
<=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) ) @ D ) ) @ C )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__add__iff1) ).
thf(3339,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oring @ F )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) ) @ D ) ) @ C )
= A ) )
& ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) ) @ D ) ) @ C )
= A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(1240,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) ) @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__add__iff1) ).
thf(5049,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E ) @ D ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) ) @ B ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1240]) ).
thf(525,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A ) @ B ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__neg__neg__trivial) ).
thf(2589,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A ) @ B ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) ).
thf(1387,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(288,axiom,
class_Power_Opower @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Power_Opower) ).
thf(1900,plain,
class_Power_Opower @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(895,axiom,
class_Rings_Omult__zero @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Omult__zero) ).
thf(3827,plain,
class_Rings_Omult__zero @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(471,axiom,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less1) ).
thf(2428,plain,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(570,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ B ) ) @ ( c_Transcendental_Oln @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ln__le__cancel__iff) ).
thf(2733,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ B ) ) @ ( c_Transcendental_Oln @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ B ) ) @ ( c_Transcendental_Oln @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(513,axiom,
! [A: $i] :
( ( ( c_RealDef_Oreal @ tc_Nat_Onat @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__zero__iff) ).
thf(2560,plain,
! [A: $i] :
( ( ( ( c_RealDef_Oreal @ tc_Nat_Onat @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_RealDef_Oreal @ tc_Nat_Onat @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(933,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__add__one__gt__zero) ).
thf(3972,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(528,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
<=> ? [C: $i] :
( A
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Suc__ex__iff) ).
thf(2596,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ? [C: $i] :
( A
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) ) )
& ( ? [C: $i] :
( A
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(907,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( c_SEQ_OBseq @ B @ A )
<=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ C ) )
& ! [D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bseq__def) ).
thf(3867,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( ( c_SEQ_OBseq @ B @ A )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ C ) )
& ! [D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) ) @ C ) ) ) )
& ( ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ C ) )
& ! [D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) ) @ C ) ) )
=> ( c_SEQ_OBseq @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(719,axiom,
! [A: $i,B: $i] :
( ( ( c_Complex_Ocomplex_OComplex @ B @ A )
= c_Complex_Oii )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Complex__eq__i) ).
thf(3233,plain,
! [A: $i,B: $i] :
( ( ( ( c_Complex_Ocomplex_OComplex @ B @ A )
= c_Complex_Oii )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
=> ( ( c_Complex_Ocomplex_OComplex @ B @ A )
= c_Complex_Oii ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(912,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
<=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__0__iff) ).
thf(3884,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(256,axiom,
class_Groups_Ocancel__comm__monoid__add @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__comm__monoid__add) ).
thf(1824,plain,
class_Groups_Ocancel__comm__monoid__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(893,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
& ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__less__def) ).
thf(3816,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
& ( B != A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
& ( B != A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(376,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ B ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__le__mono2) ).
thf(2150,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ B ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Oord @ B )
=> ( class_Orderings_Oord @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
thf(1370,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Oord @ B )
=> ( class_Orderings_Oord @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(348,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oring @ F )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) ) @ A ) )
<=> ( C
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) ) @ D ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__add__iff2) ).
thf(2032,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oring @ F )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) ) @ A ) )
=> ( C
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) ) @ D ) ) @ A ) ) )
& ( ( C
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) ) @ D ) ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(1260,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ B @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ c_Complex_ORe @ B ) @ ( hAPP @ c_Complex_ORe @ A ) ) ) ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ c_Complex_OIm @ B ) @ ( hAPP @ c_Complex_OIm @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_metric__bound__lemma) ).
thf(5102,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ B @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ c_Complex_ORe @ B ) @ ( hAPP @ c_Complex_ORe @ A ) ) ) ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ c_Complex_OIm @ B ) @ ( hAPP @ c_Complex_OIm @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1260]) ).
thf(998,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__vector @ D )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ D @ ( hAPP @ B @ E ) ) ) @ A ) ) )
=> ( c_SEQ_OBseq @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_BseqI2_H) ).
thf(4160,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__vector @ D )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ D @ ( hAPP @ B @ E ) ) ) @ A ) ) )
=> ( c_SEQ_OBseq @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(501,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__refl) ).
thf(2528,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(841,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono) ).
thf(3664,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(710,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_RComplete_Onatfloor @ B ) ) @ ( c_RComplete_Onatfloor @ A ) ) ) @ ( c_RComplete_Onatfloor @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__mult__natfloor) ).
thf(3207,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_RComplete_Onatfloor @ B ) ) @ ( c_RComplete_Onatfloor @ A ) ) ) @ ( c_RComplete_Onatfloor @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(849,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
thf(3682,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(733,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__mult__self) ).
thf(3286,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(283,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Odiff) ).
thf(1883,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(129,axiom,
! [A: $i,B: $i] :
( ( B
= ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ B ) ) )
=> ( ( c_RComplete_Onatfloor @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ ( c_RComplete_Onatfloor @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__power) ).
thf(1560,plain,
! [A: $i,B: $i] :
( ( B
= ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ B ) ) )
=> ( ( c_RComplete_Onatfloor @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ ( c_RComplete_Onatfloor @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(727,axiom,
c_SEQ_Oconvergent @ tc_RealDef_Oreal @ ( c_COMBB @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_Nat_Onat @ c_Complex_ORe @ ( c_COMBB @ tc_Nat_Onat @ tc_Complex_Ocomplex @ tc_Nat_Onat @ v_s @ v_f____ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_conv1) ).
thf(3271,plain,
c_SEQ_Oconvergent @ tc_RealDef_Oreal @ ( c_COMBB @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_Nat_Onat @ c_Complex_ORe @ ( c_COMBB @ tc_Nat_Onat @ tc_Complex_Ocomplex @ tc_Nat_Onat @ v_s @ v_f____ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(536,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono2) ).
thf(2628,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(1136,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
thf(4608,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136]) ).
thf(484,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos) ).
thf(2477,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(817,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__is__0) ).
thf(3578,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(616,axiom,
class_Rings_Ocomm__semiring__0 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__0) ).
thf(2872,plain,
class_Rings_Ocomm__semiring__0 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(16,axiom,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).
thf(1296,plain,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(387,axiom,
class_Groups_Ozero @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ozero) ).
thf(2179,plain,
class_Groups_Ozero @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(239,axiom,
class_Groups_Oone @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
thf(1787,plain,
class_Groups_Oone @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(182,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ A ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__power__div__base) ).
thf(1656,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ A ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(400,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__less) ).
thf(2211,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(835,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel2) ).
thf(3647,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(294,axiom,
class_Rings_Oring__no__zero__divisors @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors) ).
thf(1910,plain,
class_Rings_Oring__no__zero__divisors @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(704,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( ( ( c_Transcendental_Oln @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( A
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ln__eq__zero__iff) ).
thf(3191,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( ( ( ( c_Transcendental_Oln @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( A
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
& ( ( A
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ( ( c_Transcendental_Oln @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(580,axiom,
class_Rings_Olinordered__comm__semiring__strict @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict) ).
thf(2758,plain,
class_Rings_Olinordered__comm__semiring__strict @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(617,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ F )
=> ( ( E
!= ( c_Groups_Ozero__class_Ozero @ F ) )
=> ( ( ( D = C )
& ( B != A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ B ) )
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__scale__eq__noteq) ).
thf(2873,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ F )
=> ( ( E
!= ( c_Groups_Ozero__class_Ozero @ F ) )
=> ( ( ( D = C )
& ( B != A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ B ) )
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(262,axiom,
class_Groups_Ocancel__comm__monoid__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add) ).
thf(1837,plain,
class_Groups_Ocancel__comm__monoid__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(726,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ c_Complex_ORe @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__Re__le__cmod) ).
thf(3269,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ c_Complex_ORe @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(828,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing) ).
thf(3618,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(1148,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) )
<=> ( ( C = A )
| ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__cancel2) ).
thf(4725,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( ( C = A )
| ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( C = A )
| ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).
thf(325,axiom,
! [A: $i,B: $i] :
( ( ( class_Power_Opower @ B )
& ( class_Rings_Osemiring__0 @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__0__Suc) ).
thf(1968,plain,
! [A: $i,B: $i] :
( ( ( class_Power_Opower @ B )
& ( class_Rings_Osemiring__0 @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(548,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__idom @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oabs__class_Oabs @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) ) ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) ) @ C ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__diff__less__iff) ).
thf(2663,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__idom @ D )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oabs__class_Oabs @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) ) @ C ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) ) @ C ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oabs__class_Oabs @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(442,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ? [B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reals__Archimedean6a) ).
thf(2332,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ? [B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(995,axiom,
class_Rings_Olinordered__semiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring) ).
thf(4155,plain,
class_Rings_Olinordered__semiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(740,axiom,
! [A: $i,B: $i] :
( ( B != A )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
thf(3314,plain,
! [A: $i,B: $i] :
( ( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ B ) ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(595,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessD) ).
thf(2820,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(793,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__mult__neg__le) ).
thf(3499,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(870,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Groups_Oabs__class_Oabs @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Groups_Oabs__class_Oabs @ C @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__abs) ).
thf(3750,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Groups_Oabs__class_Oabs @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Groups_Oabs__class_Oabs @ C @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(749,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add2) ).
thf(3349,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(810,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
<=> ? [C: $i] :
( A
= ( c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
thf(3556,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ? [C: $i] :
( A
= ( c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) ) ) )
& ( ? [C: $i] :
( A
= ( c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(198,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Olinordered__ab__group__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add) ).
thf(1687,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Olinordered__ab__group__add @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(86,axiom,
class_Groups_Ocancel__semigroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) ).
thf(1457,plain,
class_Groups_Ocancel__semigroup__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(914,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Divides_Odiv__class_Odiv @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ B )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self1__is__id) ).
thf(3894,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Divides_Odiv__class_Odiv @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(359,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__no__zero__divisors @ C )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).
thf(2068,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__no__zero__divisors @ C )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(254,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__assoc) ).
thf(1819,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(161,axiom,
! [A: $i] :
( ( class_Groups_Ocomm__monoid__add @ A )
=> ( class_Groups_Oab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__add) ).
thf(1624,plain,
! [A: $i] :
( ( class_Groups_Ocomm__monoid__add @ A )
=> ( class_Groups_Oab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(1235,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
thf(5038,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1235]) ).
thf(689,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ ( c_Divides_Odiv__class_Odiv @ D @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self1) ).
thf(3144,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ ( c_Divides_Odiv__class_Odiv @ D @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(440,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__mono) ).
thf(2327,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(401,axiom,
class_Groups_Oordered__comm__monoid__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) ).
thf(2213,plain,
class_Groups_Oordered__comm__monoid__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(1151,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__le__D1) ).
thf(4740,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).
thf(446,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__neg__pos) ).
thf(2345,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(167,axiom,
class_Rings_Olinordered__semiring__strict @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).
thf(1634,plain,
class_Rings_Olinordered__semiring__strict @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(1092,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__commute) ).
thf(4461,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(843,axiom,
class_Rings_Olinordered__semidom @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).
thf(3667,plain,
class_Rings_Olinordered__semidom @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(136,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Osgn__if @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Osgn__if) ).
thf(1573,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Osgn__if @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(888,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ C ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__conv2) ).
thf(3799,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ C ) ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(61,axiom,
class_Groups_Oab__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
thf(1402,plain,
class_Groups_Oab__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(332,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ozero__left) ).
thf(1983,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(1109,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).
thf(4512,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__field @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) ) @ A )
= ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide_Odiff) ).
thf(1328,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__field @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) ) @ A )
= ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(520,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__diff) ).
thf(2577,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(143,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(1587,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(70,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oordered__ab__semigroup__add__imp__le @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(1425,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oordered__ab__semigroup__add__imp__le @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(799,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ? [C: $i] :
! [D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Obounded) ).
thf(3518,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ? [C: $i] :
! [D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(761,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__commute) ).
thf(3386,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(1201,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__0__right) ).
thf(4930,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1201]) ).
thf(1253,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ! [B: $i] :
? [C: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reals__Archimedean3) ).
thf(5081,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ! [B: $i] :
? [C: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1253]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__algebra @ E )
=> ( ( c_Groups_Ominus__class_Ominus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Oprod__diff__prod) ).
thf(1350,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__algebra @ E )
=> ( ( c_Groups_Ominus__class_Ominus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(308,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(1936,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(983,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) @ ( c_Nat_OSuc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__Suc) ).
thf(4123,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) @ ( c_Nat_OSuc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(41,axiom,
class_Groups_Oab__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).
thf(1360,plain,
class_Groups_Oab__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(146,axiom,
class_Rings_Osemiring__0 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring__0) ).
thf(1592,plain,
class_Rings_Osemiring__0 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(882,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leI) ).
thf(3784,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(918,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).
thf(3909,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(881,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).
thf(3782,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(827,axiom,
! [A: $i] :
( ( c_Nat_OSuc @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
thf(3615,plain,
! [A: $i] :
( ( c_Nat_OSuc @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(120,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( class_Power_Opower @ C )
& ( class_Rings_Omult__zero @ C )
& ( class_Rings_Ono__zero__divisors @ C )
& ( class_Rings_Ozero__neq__one @ C ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__eq__0__iff) ).
thf(1541,plain,
! [A: $i,B: $i,C: $i] :
( ( ( class_Power_Opower @ C )
& ( class_Rings_Omult__zero @ C )
& ( class_Rings_Ono__zero__divisors @ C )
& ( class_Rings_Ozero__neq__one @ C ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(897,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__semigroup__mult @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(3831,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__semigroup__mult @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(603,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).
thf(2840,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(787,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0) ).
thf(3482,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(226,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( B = A )
<=> ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__iff__diff__eq__0) ).
thf(1762,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( ( B = A )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( c_Complex_Orcis @ C @ B ) ) @ A )
= ( c_Complex_Orcis @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DeMoivre2) ).
thf(1270,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( c_Complex_Orcis @ C @ B ) ) @ A )
= ( c_Complex_Orcis @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(229,axiom,
class_Rings_Ocomm__semiring__0 @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__0) ).
thf(1772,plain,
class_Rings_Ocomm__semiring__0 @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(1258,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__function__closures_I1_J) ).
thf(5098,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1258]) ).
thf(638,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
| ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less) ).
thf(2946,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
| ( B = A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
| ( B = A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(646,axiom,
! [A: $i,B: $i] :
( ( c_Transcendental_Ocos @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Transcendental_Ocos @ B ) ) @ ( c_Transcendental_Ocos @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Transcendental_Osin @ B ) ) @ ( c_Transcendental_Osin @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cos__diff) ).
thf(2990,plain,
! [A: $i,B: $i] :
( ( c_Transcendental_Ocos @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Transcendental_Ocos @ B ) ) @ ( c_Transcendental_Ocos @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Transcendental_Osin @ B ) ) @ ( c_Transcendental_Osin @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(623,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__diff__conv) ).
thf(2895,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(1027,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ A @ B ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_incr__lemma) ).
thf(4248,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ A @ B ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).
thf(48,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(1375,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(1100,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_COMBK @ D @ C @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBK__1) ).
thf(4486,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_COMBK @ D @ C @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).
thf(714,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oone__class_Oone @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oone__class_Oone @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__le__power) ).
thf(3218,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oone__class_Oone @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oone__class_Oone @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(1119,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pos__neg2) ).
thf(4544,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).
thf(495,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__imp__zdiv__neg__iff) ).
thf(2509,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(1022,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).
thf(4233,plain,
! [A: $i,B: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(191,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Omonoid__mult @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__mult) ).
thf(1672,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Omonoid__mult @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(857,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( c_Groups_Osgn__class_Osgn @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__greater) ).
thf(3704,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( c_Groups_Osgn__class_Osgn @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( c_Groups_Osgn__class_Osgn @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(831,axiom,
! [A: $i,B: $i] :
( ( hAPP @ c_Complex_OIm @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_OIm @ B ) ) @ ( hAPP @ c_Complex_OIm @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Im_Oadd) ).
thf(3632,plain,
! [A: $i,B: $i] :
( ( hAPP @ c_Complex_OIm @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_OIm @ B ) ) @ ( hAPP @ c_Complex_OIm @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(681,axiom,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__real__square__gt__zero) ).
thf(3119,plain,
! [A: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(1175,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I3_J) ).
thf(4840,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1175]) ).
thf(670,axiom,
class_Rings_Olinordered__semiring__1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1) ).
thf(3078,plain,
class_Rings_Olinordered__semiring__1 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(1188,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( c_Nat_OSuc @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
| ( B
= ( c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Suc__eq) ).
thf(4883,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( c_Nat_OSuc @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
| ( B
= ( c_Nat_OSuc @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
| ( B
= ( c_Nat_OSuc @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( c_Nat_OSuc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188]) ).
thf(709,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__zless__mono2) ).
thf(3205,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(1015,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B ) @ A ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ D ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ E ) ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C ) @ E ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ E ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lemma__interval) ).
thf(4219,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B ) @ A ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ D ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ E ) ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C ) @ E ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ E ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).
thf(698,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__neg__neg) ).
thf(3176,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(675,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__mono) ).
thf(3087,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(132,axiom,
class_Groups_Ogroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).
thf(1567,plain,
class_Groups_Ogroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(1111,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( B = A )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__iff) ).
thf(4518,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( ( B = A )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).
thf(42,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring) ).
thf(1361,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(1221,axiom,
( ( c_Complex_Oexpi @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
= ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_expi__zero) ).
thf(4983,plain,
( ( c_Complex_Oexpi @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
= ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1221]) ).
thf(13,axiom,
class_Orderings_Oord @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
thf(1292,plain,
class_Orderings_Oord @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(599,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1__no__zero__divisors @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A )
!= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_field__power__not__zero) ).
thf(2830,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1__no__zero__divisors @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A )
!= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(864,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
thf(3728,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(821,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ono__zero__divisors @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A )
!= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_no__zero__divisors) ).
thf(3596,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ono__zero__divisors @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A )
!= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(468,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).
thf(2419,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(412,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__natceiling__ge) ).
thf(2240,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(659,axiom,
? [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
& ! [B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( hAPP @ c_Complex_OIm @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Im_Ononneg__bounded) ).
thf(3032,plain,
? [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
& ! [B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( hAPP @ c_Complex_OIm @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(845,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Groups_Oabs__class_Oabs @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Oabs__class_Oabs @ C @ B ) ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__mult) ).
thf(3671,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Groups_Oabs__class_Oabs @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Oabs__class_Oabs @ C @ B ) ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(1086,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) @ B )
= ( c_Groups_Oabs__class_Oabs @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__mult__pos) ).
thf(4444,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) @ B )
= ( c_Groups_Oabs__class_Oabs @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).
thf(815,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__mono2) ).
thf(3573,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ A )
= ( c_RealDef_Oreal @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__real__of__nat) ).
thf(1419,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ A )
= ( c_RealDef_Oreal @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(104,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(1493,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(195,axiom,
class_Rings_Olinordered__comm__semiring__strict @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).
thf(1683,plain,
class_Rings_Olinordered__comm__semiring__strict @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(688,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Oring @ E )
=> ( ( c_Groups_Ominus__class_Ominus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__diff__mult) ).
thf(3141,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Oring @ E )
=> ( ( c_Groups_Ominus__class_Ominus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(618,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__imp__zdiv__neg__iff) ).
thf(2877,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(324,axiom,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).
thf(1964,plain,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(311,axiom,
class_Groups_Ocancel__ab__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).
thf(1942,plain,
class_Groups_Ocancel__ab__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(183,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Orderings_Oorder @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oorder) ).
thf(1659,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Orderings_Oorder @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(923,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__trans) ).
thf(3922,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(650,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff1) ).
thf(3000,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(1128,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zless__mono) ).
thf(4582,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).
thf(1000,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__real__less) ).
thf(4167,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(1079,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__1) ).
thf(4425,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).
thf(1049,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_Transcendental_Oln @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ln__ge__zero__iff) ).
thf(4315,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_Transcendental_Oln @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_Transcendental_Oln @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).
thf(777,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(3441,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(437,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
thf(2312,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(652,axiom,
! [A: $i] :
( ( c_SEQ_OBseq @ tc_RealDef_Oreal @ A )
=> ( ! [B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ A @ B ) ) @ ( hAPP @ A @ C ) ) ) )
=> ( c_SEQ_Oconvergent @ tc_RealDef_Oreal @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bseq__mono__convergent) ).
thf(3010,plain,
! [A: $i] :
( ( c_SEQ_OBseq @ tc_RealDef_Oreal @ A )
=> ( ! [B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ A @ B ) ) @ ( hAPP @ A @ C ) ) ) )
=> ( c_SEQ_Oconvergent @ tc_RealDef_Oreal @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(1154,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__idom @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oabs__class_Oabs @ E @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oabs__class_Oabs @ E @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Groups_Oabs__class_Oabs @ E @ D ) ) @ ( c_Groups_Oabs__class_Oabs @ E @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__mult__less) ).
thf(4750,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__idom @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oabs__class_Oabs @ E @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oabs__class_Oabs @ E @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Groups_Oabs__class_Oabs @ E @ D ) ) @ ( c_Groups_Oabs__class_Oabs @ E @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).
thf(1006,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).
thf(4191,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(142,axiom,
! [A: $i] :
( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__1) ).
thf(1584,plain,
! [A: $i] :
( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(249,axiom,
! [A: $i,B: $i] :
( ( c_Transcendental_Osin @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Transcendental_Ocos @ A ) ) @ ( c_Transcendental_Osin @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Transcendental_Osin @ A ) ) @ ( c_Transcendental_Ocos @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sin__diff2) ).
thf(1810,plain,
! [A: $i,B: $i] :
( ( c_Transcendental_Osin @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Transcendental_Ocos @ A ) ) @ ( c_Transcendental_Osin @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Transcendental_Osin @ A ) ) @ ( c_Transcendental_Ocos @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(384,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono1__neg) ).
thf(2172,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(349,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) )
= ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__norm__cancel) ).
thf(2038,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) )
= ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(80,axiom,
class_Groups_Olinordered__ab__group__add @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).
thf(1446,plain,
class_Groups_Olinordered__ab__group__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(155,axiom,
class_Groups_Ozero @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).
thf(1612,plain,
class_Groups_Ozero @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(1140,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) )
<=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ! [D: $i] :
( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ E ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ E ) @ A ) )
& ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ! [D: $i] :
( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A ) @ E ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ E ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__zdiv) ).
thf(4621,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ! [D: $i] :
( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ E ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ E ) @ A ) )
& ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ! [D: $i] :
( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A ) @ E ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ E ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) ) ) )
& ( ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ! [D: $i] :
( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ E ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ E ) @ A ) )
& ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ! [D: $i] :
( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A ) @ E ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ E ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).
thf(1004,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__zero__less__power__iff) ).
thf(4180,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(438,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__mono) ).
thf(2317,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(736,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ C ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_decr__lemma) ).
thf(3294,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ C ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(220,axiom,
class_Groups_Ocomm__monoid__mult @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) ).
thf(1744,plain,
class_Groups_Ocomm__monoid__mult @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(682,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add2) ).
thf(3126,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Omonoid__mult @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__commutes) ).
thf(1451,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Omonoid__mult @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(123,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oordered__ab__group__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add) ).
thf(1552,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oordered__ab__group__add @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(482,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
thf(2465,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(1117,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Oone__class_Oone @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__le__one__le) ).
thf(4540,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Oone__class_Oone @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).
thf(270,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Omonoid__mult @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lemma__realpow__diff) ).
thf(1852,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Omonoid__mult @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(612,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add1) ).
thf(2862,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(354,axiom,
! [A: $i,B: $i] :
( ( hAPP @ c_Complex_OIm @ ( c_Complex_Orcis @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ ( c_Transcendental_Osin @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Im__rcis) ).
thf(2052,plain,
! [A: $i,B: $i] :
( ( hAPP @ c_Complex_OIm @ ( c_Complex_Orcis @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ ( c_Transcendental_Osin @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(667,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ A ) @ B )
= ( c_Groups_Oone__class_Oone @ C ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__inverse__eq) ).
thf(3064,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ A ) @ B )
= ( c_Groups_Oone__class_Oone @ C ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ A ) @ B )
= ( c_Groups_Oone__class_Oone @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(455,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__field @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide_Ozero) ).
thf(2370,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__field @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(1165,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ B ) ) @ A ) ) )
<=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__zpower__abs__iff) ).
thf(4804,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ B ) ) @ A ) ) )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).
thf(720,axiom,
class_Groups_Ogroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).
thf(3242,plain,
class_Groups_Ogroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(257,axiom,
class_Rings_Oring__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1) ).
thf(1825,plain,
class_Rings_Oring__1 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(1245,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono1) ).
thf(5063,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1245]) ).
thf(26,axiom,
class_Groups_Oordered__ab__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).
thf(1324,plain,
class_Groups_Oordered__ab__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(493,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__right__mono__neg) ).
thf(2504,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(231,axiom,
class_Rings_Ocomm__semiring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).
thf(1776,plain,
class_Rings_Ocomm__semiring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(825,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ A ) @ ( c_Groups_Oone__class_Oone @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__decreasing) ).
thf(3611,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ A ) @ ( c_Groups_Oone__class_Oone @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(478,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Transcendental_Ocos @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cos__le__one) ).
thf(2450,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Transcendental_Ocos @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(371,axiom,
! [A: $i,B: $i] :
( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ B )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__eq__if) ).
thf(2125,plain,
! [A: $i,B: $i] :
( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ B )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(837,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
thf(3654,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(119,axiom,
! [A: $i] :
( ( class_Fields_Ofield @ A )
=> ( class_Divides_Osemiring__div @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Divides_Osemiring__div) ).
thf(1539,plain,
! [A: $i] :
( ( class_Fields_Ofield @ A )
=> ( class_Divides_Osemiring__div @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(53,axiom,
class_Rings_Omult__zero @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).
thf(1382,plain,
class_Rings_Omult__zero @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(624,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( ( ( C = B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__cases) ).
thf(2900,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( ( ( C = B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(260,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__divide) ).
thf(1831,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(187,axiom,
class_RealVector_Oreal__normed__vector @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
thf(1668,plain,
class_RealVector_Oreal__normed__vector @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(328,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__ge__zero) ).
thf(1974,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(450,axiom,
class_Groups_Ocomm__monoid__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__add) ).
thf(2355,plain,
class_Groups_Ocomm__monoid__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(305,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(1932,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(1242,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__square) ).
thf(5058,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1242]) ).
thf(1146,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
thf(4717,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).
thf(314,axiom,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).
thf(1947,plain,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(982,axiom,
! [A: $i,B: $i] :
( ( class_Power_Opower @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__0) ).
thf(4120,plain,
! [A: $i,B: $i] :
( ( class_Power_Opower @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(830,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__refl) ).
thf(3628,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(280,axiom,
class_Groups_Omonoid__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__add) ).
thf(1874,plain,
class_Groups_Omonoid__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(1232,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ C ) )
& ! [D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) ) @ C ) ) )
<=> ? [C: $i] :
! [D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lemma__NBseq__def2) ).
thf(5026,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ C ) )
& ! [D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) ) @ C ) ) )
=> ? [C: $i] :
! [D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) ) ) )
& ( ? [C: $i] :
! [D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ C ) )
& ! [D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1232]) ).
thf(964,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__vector @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__diff__ineq) ).
thf(4069,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__vector @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(1077,axiom,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neq0__conv) ).
thf(4416,plain,
! [A: $i] :
( ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).
thf(754,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__add @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__left) ).
thf(3364,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__add @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(694,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_RealVector_Oreal__field @ F )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ C ) @ B ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ D @ B ) ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ E @ C ) ) @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DERIV__mult__lemma) ).
thf(3162,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_RealVector_Oreal__field @ F )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ C ) @ B ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ D @ B ) ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ E @ C ) ) @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(707,axiom,
class_Groups_Ocancel__ab__semigroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add) ).
thf(3201,plain,
class_Groups_Ocancel__ab__semigroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(1016,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__self) ).
thf(4223,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(225,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) ) @ A )
= ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Odiff) ).
thf(1759,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) ) @ A )
= ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( c_Transcendental_Osin @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ A ) )
= ( hAPP @ c_Complex_OIm @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( c_Complex_Ocis @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sin__n__Im__cis__pow__n) ).
thf(1393,plain,
! [A: $i,B: $i] :
( ( c_Transcendental_Osin @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ A ) )
= ( hAPP @ c_Complex_OIm @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( c_Complex_Ocis @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(889,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) )
<=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ B ) @ A ) ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__left__disj) ).
thf(3802,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ B ) @ A ) ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ A ) @ B ) ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ B ) @ A ) ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ A ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(251,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Groups_Omonoid__mult @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__mult) ).
thf(1814,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Groups_Omonoid__mult @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(234,axiom,
class_Orderings_Olinorder @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).
thf(1779,plain,
class_Orderings_Olinorder @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(1214,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Complex_Ocomplex_Ocomplex__rec @ D @ C @ ( c_Complex_Ocomplex_OComplex @ B @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex_Orecs) ).
thf(4966,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Complex_Ocomplex_Ocomplex__rec @ D @ C @ ( c_Complex_Ocomplex_OComplex @ B @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1214]) ).
thf(697,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__less__0__iff) ).
thf(3173,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(130,axiom,
! [A: $i,B: $i] :
( ( c_Transcendental_Ocos @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ A ) )
= ( hAPP @ c_Complex_ORe @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( c_Complex_Ocis @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cos__n__Re__cis__pow__n) ).
thf(1563,plain,
! [A: $i,B: $i] :
( ( c_Transcendental_Ocos @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ A ) )
= ( hAPP @ c_Complex_ORe @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( c_Complex_Ocis @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(576,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__le__imp__less) ).
thf(2748,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(90,axiom,
! [A: $i,B: $i] :
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__power) ).
thf(1466,plain,
! [A: $i,B: $i] :
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(1193,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__le__imp__le) ).
thf(4906,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193]) ).
thf(533,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ A @ ( c_Groups_Ozero__class_Ozero @ A ) ) @ ( c_Groups_Oone__class_Oone @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__one) ).
thf(2617,plain,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ A @ ( c_Groups_Ozero__class_Ozero @ A ) ) @ ( c_Groups_Oone__class_Oone @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(338,axiom,
class_Rings_Ocomm__semiring__1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
thf(1996,plain,
class_Rings_Ocomm__semiring__1 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(215,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(1732,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(999,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ C ) )
& ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ C ) @ ( c_Nat_OSuc @ A ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_realpow__pos__nth2) ).
thf(4163,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ C ) )
& ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ C ) @ ( c_Nat_OSuc @ A ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(690,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1__right) ).
thf(3147,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(786,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psize__eq__0__iff) ).
thf(3476,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
=> ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(31,axiom,
! [A: $i] :
( ( hAPP @ c_Complex_ORe @ ( c_Groups_Osgn__class_Osgn @ tc_Complex_Ocomplex @ A ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_ORe @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Re__sgn) ).
thf(1333,plain,
! [A: $i] :
( ( hAPP @ c_Complex_ORe @ ( c_Groups_Osgn__class_Osgn @ tc_Complex_Ocomplex @ A ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_ORe @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(872,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__le) ).
thf(3755,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(1115,axiom,
! [A: $i] :
( ( c_Complex_Orcis @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rcis__zero__mod) ).
thf(4535,plain,
! [A: $i] :
( ( c_Complex_Orcis @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).
thf(992,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ ( c_Groups_Oone__class_Oone @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc__less__one) ).
thf(4148,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ ( c_Groups_Oone__class_Oone @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(272,axiom,
class_Groups_Osgn__if @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Osgn__if) ).
thf(1857,plain,
class_Groups_Osgn__if @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(336,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(1991,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(898,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ A ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2) ).
thf(3834,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ A ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Omonoid__mult @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__add) ).
thf(1318,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Omonoid__mult @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(509,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
thf(2546,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(811,axiom,
class_Rings_Osemiring__0 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__0) ).
thf(3563,plain,
class_Rings_Osemiring__0 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(1008,axiom,
hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ v_s @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) @ v_r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096cmod_A_Is_A0_J_A_060_061_Ar_096) ).
thf(4195,plain,
hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ v_s @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) @ v_r ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(945,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Osemiring @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ B ) ) @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_combine__common__factor) ).
thf(3999,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Osemiring @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ B ) ) @ C ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(11,axiom,
! [A: $i] :
( A
!= ( c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
thf(1286,plain,
! [A: $i] :
( A
!= ( c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(391,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__linear) ).
thf(2189,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(772,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( ( c_SEQ_Odecseq @ B @ A )
<=> ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( hAPP @ A @ D ) ) @ ( hAPP @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_decseq__def) ).
thf(3422,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( ( ( c_SEQ_Odecseq @ B @ A )
=> ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( hAPP @ A @ D ) ) @ ( hAPP @ A @ C ) ) ) ) )
& ( ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( hAPP @ A @ D ) ) @ ( hAPP @ A @ C ) ) ) )
=> ( c_SEQ_Odecseq @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(648,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Oone__class_Oone @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__le__one__le) ).
thf(2995,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Oone__class_Oone @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(1267,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__le__cancel1) ).
thf(5126,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1267]) ).
thf(547,axiom,
hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
thf(2662,plain,
hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(369,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ A @ ( c_Groups_Oone__class_Oone @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__less__zero) ).
thf(2121,plain,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ A @ ( c_Groups_Oone__class_Oone @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(858,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(3707,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(466,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Complex_Ocomplex_Ocomplex__case @ D @ C @ ( c_Complex_Ocomplex_OComplex @ B @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex_Osimps_I2_J) ).
thf(2413,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Complex_Ocomplex_Ocomplex__case @ D @ C @ ( c_Complex_Ocomplex_OComplex @ B @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(386,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
=> ( ( B != A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__cases) ).
thf(2176,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
=> ( ( B != A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(1096,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A ) ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__less__0) ).
thf(4470,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A ) ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A ) ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).
thf(416,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__assoc) ).
thf(2253,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(4,axiom,
class_Groups_Ocancel__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
thf(1273,plain,
class_Groups_Ocancel__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(724,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( ( C
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ D ) ) )
& ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
= ( c_Divides_Odiv__class_Odiv @ D @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__mult1__if) ).
thf(3262,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( ( C
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ D ) ) )
& ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
= ( c_Divides_Odiv__class_Odiv @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(734,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oabs__class_Oabs @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( c_Groups_Oabs__class_Oabs @ C @ B ) ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__triangle__ineq) ).
thf(3289,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oabs__class_Oabs @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( c_Groups_Oabs__class_Oabs @ C @ B ) ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(1257,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ ( c_Divides_Odiv__class_Odiv @ D @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self2) ).
thf(5095,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ ( c_Divides_Odiv__class_Odiv @ D @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1257]) ).
thf(1034,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Olinordered__semiring__1 @ F )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) ) @ A ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ F ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ A ) @ C ) ) ) @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_convex__bound__le) ).
thf(4269,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Olinordered__semiring__1 @ F )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) ) @ A ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ F ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ A ) @ C ) ) ) @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(419,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__less__mono) ).
thf(2260,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(1199,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ ( c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc2) ).
thf(4921,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ ( c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1199]) ).
thf(292,axiom,
class_Groups_Ocancel__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).
thf(1906,plain,
class_Groups_Ocancel__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(634,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ D ) @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__fun__def) ).
thf(2936,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ D ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ A ) @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ D ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(177,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ ( c_Groups_Osgn__class_Osgn @ B @ A ) )
= ( c_Groups_Osgn__class_Osgn @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__sgn) ).
thf(1648,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ ( c_Groups_Osgn__class_Osgn @ B @ A ) )
= ( c_Groups_Osgn__class_Osgn @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(1184,axiom,
! [A: $i,B: $i] :
( ( c_Complex_Ocomplex_Ocomplex__size @ ( c_Complex_Ocomplex_OComplex @ B @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex_Osize_I1_J) ).
thf(4872,plain,
! [A: $i,B: $i] :
( ( c_Complex_Ocomplex_Ocomplex__size @ ( c_Complex_Ocomplex_OComplex @ B @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).
thf(194,axiom,
! [A: $i] :
( ( hAPP @ c_Complex_ORe @ ( c_Complex_Ocis @ A ) )
= ( c_Transcendental_Ocos @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Re__cis) ).
thf(1680,plain,
! [A: $i] :
( ( hAPP @ c_Complex_ORe @ ( c_Complex_Ocis @ A ) )
= ( c_Transcendental_Ocos @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(204,axiom,
class_Rings_Oring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).
thf(1698,plain,
class_Rings_Oring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(321,axiom,
class_Groups_Oordered__comm__monoid__add @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).
thf(1959,plain,
class_Groups_Oordered__comm__monoid__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(1063,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__trans__Suc) ).
thf(4354,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).
thf(791,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__diff) ).
thf(3491,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(98,axiom,
class_Orderings_Oorder @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
thf(1483,plain,
class_Orderings_Oorder @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(671,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__not__le) ).
thf(3079,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(516,axiom,
class_Rings_Olinordered__semiring__strict @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) ).
thf(2570,plain,
class_Rings_Olinordered__semiring__strict @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(1030,axiom,
( c_Complex_Oii
= ( c_Complex_Ocomplex_OComplex @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_i__def) ).
thf(4256,plain,
( c_Complex_Oii
= ( c_Complex_Ocomplex_OComplex @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(1084,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( B != A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
thf(4438,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( B != A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).
thf(223,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
<=> ( ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__1__iff) ).
thf(1747,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
& ( ( ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(901,axiom,
! [A: $i,B: $i] :
( ( hAPP @ c_Complex_OIm @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_ORe @ B ) ) @ ( hAPP @ c_Complex_OIm @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_OIm @ B ) ) @ ( hAPP @ c_Complex_ORe @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__Im__mult) ).
thf(3839,plain,
! [A: $i,B: $i] :
( ( hAPP @ c_Complex_OIm @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_ORe @ B ) ) @ ( hAPP @ c_Complex_OIm @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_OIm @ B ) ) @ ( hAPP @ c_Complex_ORe @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(802,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
& ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__le) ).
thf(3523,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
& ( B != A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
& ( B != A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(1126,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__order) ).
thf(4577,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).
thf(885,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__less__mono2) ).
thf(3792,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(854,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__natfloor) ).
thf(3696,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(1101,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__imp__less__left) ).
thf(4489,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).
thf(499,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Nat__Transfer_Otsub @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) ).
thf(2524,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Nat__Transfer_Otsub @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(765,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Oordered__semiring @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__mono) ).
thf(3396,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Oordered__semiring @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(1089,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).
thf(4453,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).
thf(1225,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
=> ( c_SEQ_OBseq @ tc_RealDef_Oreal @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bseq__realpow) ).
thf(4998,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
=> ( c_SEQ_OBseq @ tc_RealDef_Oreal @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1225]) ).
thf(610,axiom,
class_Fields_Ofield__inverse__zero @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield__inverse__zero) ).
thf(2859,plain,
class_Fields_Ofield__inverse__zero @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(891,axiom,
class_Rings_Odivision__ring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring) ).
thf(3811,plain,
class_Rings_Odivision__ring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(954,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( ( c_Transcendental_Oln @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal ) @ B ) @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ B ) @ ( c_Transcendental_Oln @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ln__div) ).
thf(4032,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( ( c_Transcendental_Oln @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal ) @ B ) @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ B ) @ ( c_Transcendental_Oln @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(590,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Ozero) ).
thf(2806,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(62,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Power_Opower @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Power_Opower) ).
thf(1403,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Power_Opower @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(462,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__cancel) ).
thf(2398,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(565,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc0) ).
thf(2716,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(1207,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( c_Groups_Ozero__class_Ozero @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__zero__sym) ).
thf(4946,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( ( c_Groups_Ozero__class_Ozero @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Ozero__class_Ozero @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1207]) ).
thf(822,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( ( c_SEQ_Omonoseq @ B @ A )
<=> ( ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( hAPP @ A @ C ) ) @ ( hAPP @ A @ D ) ) ) )
| ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( hAPP @ A @ D ) ) @ ( hAPP @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_monoseq__def) ).
thf(3599,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( ( ( c_SEQ_Omonoseq @ B @ A )
=> ( ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( hAPP @ A @ C ) ) @ ( hAPP @ A @ D ) ) ) )
| ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( hAPP @ A @ D ) ) @ ( hAPP @ A @ C ) ) ) ) ) )
& ( ( ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( hAPP @ A @ C ) ) @ ( hAPP @ A @ D ) ) ) )
| ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( hAPP @ A @ D ) ) @ ( hAPP @ A @ C ) ) ) ) )
=> ( c_SEQ_Omonoseq @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(805,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__1__eq__mult__iff) ).
thf(3536,plain,
! [A: $i,B: $i] :
( ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
& ( ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
=> ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(1206,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ C ) )
& ! [D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ D ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Opos__bounded) ).
thf(4943,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ C ) )
& ! [D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ D ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1206]) ).
thf(957,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pos__neg) ).
thf(4041,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(990,axiom,
class_Rings_Oordered__ring__abs @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring__abs) ).
thf(4144,plain,
class_Rings_Oordered__ring__abs @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(756,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Oone__class_Oone @ B ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__1__pos) ).
thf(3372,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Oone__class_Oone @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A ) )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(1058,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__vector @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__triangle__ineq2) ).
thf(4341,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__vector @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(668,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD1) ).
thf(3070,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(407,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__mult__pos2) ).
thf(2225,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(795,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( ( c_Nat_OSuc @ B )
!= A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessI) ).
thf(3504,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( ( c_Nat_OSuc @ B )
!= A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(1039,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) )
=> ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__diff__iff) ).
thf(4283,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) )
=> ( ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).
thf(157,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Ono__zero__divisors @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ono__zero__divisors) ).
thf(1615,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Ono__zero__divisors @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(1246,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__mult__ineq) ).
thf(5065,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1246]) ).
thf(545,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff2) ).
thf(2657,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(390,axiom,
class_Rings_Oordered__ring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring) ).
thf(2188,plain,
class_Rings_Oordered__ring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(644,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__inverse) ).
thf(2981,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(1247,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra__1 @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__power__ineq) ).
thf(5067,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra__1 @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1247]) ).
thf(179,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oordered__ab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add) ).
thf(1652,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oordered__ab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(303,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__semidom @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semidom) ).
thf(1929,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__semidom @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(551,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Oordered__semiring @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__mono_H) ).
thf(2674,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Oordered__semiring @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(344,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( ( c_Transcendental_Ocos @ ( c_Complex_Oarg @ ( c_Complex_Ocomplex_OComplex @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cos__arg__i__mult__zero__pos) ).
thf(2016,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( ( c_Transcendental_Ocos @ ( c_Complex_Oarg @ ( c_Complex_Ocomplex_OComplex @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(497,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__le__eq) ).
thf(2514,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(728,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__div__algebra @ C )
=> ( ( c_RealVector_Onorm__class_Onorm @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__power) ).
thf(3272,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__div__algebra @ C )
=> ( ( c_RealVector_Onorm__class_Onorm @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(1164,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leE) ).
thf(4801,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164]) ).
thf(110,axiom,
! [A: $i] :
( ( class_Groups_Ocancel__comm__monoid__add @ A )
=> ( class_Groups_Ocancel__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add) ).
thf(1520,plain,
! [A: $i] :
( ( class_Groups_Ocancel__comm__monoid__add @ A )
=> ( class_Groups_Ocancel__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(594,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__diff__iff) ).
thf(2817,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(1231,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( ( c_SEQ_Omonoseq @ B @ A )
<=> ( ! [C: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( hAPP @ A @ C ) ) @ ( hAPP @ A @ ( c_Nat_OSuc @ C ) ) ) )
| ! [C: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( hAPP @ A @ ( c_Nat_OSuc @ C ) ) ) @ ( hAPP @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_monoseq__Suc) ).
thf(5022,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( ( ( c_SEQ_Omonoseq @ B @ A )
=> ( ! [C: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( hAPP @ A @ C ) ) @ ( hAPP @ A @ ( c_Nat_OSuc @ C ) ) ) )
| ! [C: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( hAPP @ A @ ( c_Nat_OSuc @ C ) ) ) @ ( hAPP @ A @ C ) ) ) ) )
& ( ( ! [C: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( hAPP @ A @ C ) ) @ ( hAPP @ A @ ( c_Nat_OSuc @ C ) ) ) )
| ! [C: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( hAPP @ A @ ( c_Nat_OSuc @ C ) ) ) @ ( hAPP @ A @ C ) ) ) )
=> ( c_SEQ_Omonoseq @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1231]) ).
thf(101,axiom,
class_Rings_Ocomm__ring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).
thf(1488,plain,
class_Rings_Ocomm__ring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(887,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ B ) @ A )
= ( c_Complex_Ocomplex_OComplex @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_ORe @ B ) ) @ ( hAPP @ c_Complex_ORe @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_OIm @ B ) ) @ ( hAPP @ c_Complex_OIm @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_ORe @ B ) ) @ ( hAPP @ c_Complex_OIm @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_OIm @ B ) ) @ ( hAPP @ c_Complex_ORe @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__mult__def) ).
thf(3796,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ B ) @ A )
= ( c_Complex_Ocomplex_OComplex @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_ORe @ B ) ) @ ( hAPP @ c_Complex_ORe @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_OIm @ B ) ) @ ( hAPP @ c_Complex_OIm @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_ORe @ B ) ) @ ( hAPP @ c_Complex_OIm @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_OIm @ B ) ) @ ( hAPP @ c_Complex_ORe @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(1219,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) )
=> ( ( c_RComplete_Onatfloor @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__eq) ).
thf(4978,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) )
=> ( ( c_RComplete_Onatfloor @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1219]) ).
thf(863,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__less__imp__less) ).
thf(3726,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(980,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ C ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__power__divide) ).
thf(4112,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ C ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(1076,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__ab__semigroup__add @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__imp__eq) ).
thf(4413,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__ab__semigroup__add @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).
thf(1158,axiom,
! [A: $i] :
( ( class_RealVector_Oreal__normed__algebra @ A )
=> ? [B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
& ! [C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ A @ C ) ) @ ( c_RealVector_Onorm__class_Onorm @ A @ D ) ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ononneg__bounded) ).
thf(4764,plain,
! [A: $i] :
( ( class_RealVector_Oreal__normed__algebra @ A )
=> ? [B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
& ! [C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ A @ C ) ) @ ( c_RealVector_Onorm__class_Onorm @ A @ D ) ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).
thf(561,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
=> ( c_SEQ_Oconvergent @ tc_RealDef_Oreal @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_convergent__realpow) ).
thf(2706,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
=> ( c_SEQ_Oconvergent @ tc_RealDef_Oreal @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(381,axiom,
! [A: $i] :
( ( class_RealVector_Oreal__normed__algebra @ A )
=> ? [B: $i] :
! [C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ A @ C ) ) @ ( c_RealVector_Onorm__class_Onorm @ A @ D ) ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Obounded) ).
thf(2166,plain,
! [A: $i] :
( ( class_RealVector_Oreal__normed__algebra @ A )
=> ? [B: $i] :
! [C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ A @ C ) ) @ ( c_RealVector_Onorm__class_Onorm @ A @ D ) ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(833,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__not__less) ).
thf(3641,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(470,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__cancel) ).
thf(2425,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(813,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff) ).
thf(3568,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(170,axiom,
class_Divides_Osemiring__div @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Divides_Osemiring__div) ).
thf(1638,plain,
class_Divides_Osemiring__div @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(192,axiom,
! [A: $i,B: $i] :
( ( c_Transcendental_Osin @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Transcendental_Osin @ B ) ) @ ( c_Transcendental_Ocos @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Transcendental_Ocos @ B ) ) @ ( c_Transcendental_Osin @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sin__diff) ).
thf(1675,plain,
! [A: $i,B: $i] :
( ( c_Transcendental_Osin @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Transcendental_Osin @ B ) ) @ ( c_Transcendental_Ocos @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Transcendental_Ocos @ B ) ) @ ( c_Transcendental_Osin @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(803,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).
thf(3532,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(72,axiom,
! [A: $i] :
( ( class_RealVector_Oreal__normed__vector @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__zero) ).
thf(1428,plain,
! [A: $i] :
( ( class_RealVector_Oreal__normed__vector @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(716,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ ( c_RComplete_Onatfloor @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__natfloor__eq__one) ).
thf(3223,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ ( c_RComplete_Onatfloor @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ ( c_RComplete_Onatfloor @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(238,axiom,
class_Rings_Ozero__neq__one @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ozero__neq__one) ).
thf(1786,plain,
class_Rings_Ozero__neq__one @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(655,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
thf(3023,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(188,axiom,
class_Rings_Odivision__ring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring) ).
thf(1669,plain,
class_Rings_Odivision__ring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(405,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
thf(2220,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(931,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leI) ).
thf(3964,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(347,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Oadd) ).
thf(2029,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(976,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
<=> ( ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).
thf(4096,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( B = A ) ) )
& ( ( ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( B = A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(1265,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__neq) ).
thf(5118,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1265]) ).
thf(430,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( A
= ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__pred_H) ).
thf(2293,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( A
= ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(666,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ A ) )
=> ( ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A ) @ C ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ) )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ D @ C )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__rel__div__eq) ).
thf(3051,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ A ) )
=> ( ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A ) @ C ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ) )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ D @ C )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(168,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__vector @ C )
=> ( ( c_SEQ_Oconvergent @ C @ B )
=> ( ( c_SEQ_Oconvergent @ C @ A )
=> ( c_SEQ_Oconvergent @ C @ ( c_COMBS @ tc_Nat_Onat @ C @ C @ ( c_COMBB @ C @ ( tc_fun @ C @ C ) @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_convergent__add) ).
thf(1635,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__vector @ C )
=> ( ( c_SEQ_Oconvergent @ C @ B )
=> ( ( c_SEQ_Oconvergent @ C @ A )
=> ( c_SEQ_Oconvergent @ C @ ( c_COMBS @ tc_Nat_Onat @ C @ C @ ( c_COMBB @ C @ ( tc_fun @ C @ C ) @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(1167,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__left__mono) ).
thf(4822,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).
thf(216,axiom,
class_Rings_Omult__zero @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Omult__zero) ).
thf(1733,plain,
class_Rings_Omult__zero @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(820,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__right__mono) ).
thf(3594,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(1256,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ ( c_Nat_OSuc @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq) ).
thf(5086,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ ( c_Nat_OSuc @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
| ( B = A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
| ( B = A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ ( c_Nat_OSuc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1256]) ).
thf(339,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__1__mult) ).
thf(1997,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(581,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) ) )
<=> ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__abs__iff) ).
thf(2759,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) ) )
=> ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(579,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__one__le__iff__zero__less) ).
thf(2753,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(789,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__less__power__Suc) ).
thf(3487,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(355,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).
thf(2055,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(452,axiom,
! [A: $i,B: $i] :
( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__if) ).
thf(2358,plain,
! [A: $i,B: $i] :
( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(439,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__eq__zero__iff) ).
thf(2319,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(1082,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__assoc) ).
thf(4433,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).
thf(518,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__ring @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__mono__neg) ).
thf(2573,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__ring @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(862,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
thf(3719,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(848,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( c_SEQ_OBseq @ B @ A )
<=> ? [C: $i] :
! [D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bseq__iff) ).
thf(3678,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( ( c_SEQ_OBseq @ B @ A )
=> ? [C: $i] :
! [D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) ) ) )
& ( ? [C: $i] :
! [D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) ) )
=> ( c_SEQ_OBseq @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(361,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).
thf(2079,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(678,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( ( c_Groups_Oabs__class_Oabs @ A @ ( c_Groups_Oone__class_Oone @ A ) )
= ( c_Groups_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__one) ).
thf(3101,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( ( c_Groups_Oabs__class_Oabs @ A @ ( c_Groups_Oone__class_Oone @ A ) )
= ( c_Groups_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(368,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__mono1) ).
thf(2119,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(553,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ C ) @ ( c_Nat_OSuc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq1) ).
thf(2679,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ C ) @ ( c_Nat_OSuc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(1069,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ C @ A ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__le__mono) ).
thf(4369,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ C @ A ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).
thf(409,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__less__cancel1) ).
thf(2229,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(489,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( c_Transcendental_Oln @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) @ ( c_Transcendental_Oln @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ln__realpow) ).
thf(2493,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( c_Transcendental_Oln @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) @ ( c_Transcendental_Oln @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(247,axiom,
class_Rings_Ono__zero__divisors @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).
thf(1806,plain,
class_Rings_Ono__zero__divisors @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(930,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ C ) )
& ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ C ) @ B )
= A )
& ! [D: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ D ) )
& ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ D ) @ B )
= A ) )
=> ( D = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_realpow__pos__nth__unique) ).
thf(3957,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ C ) )
& ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ C ) @ B )
= A )
& ! [D: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ D ) )
& ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ D ) @ B )
= A ) )
=> ( D = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(1044,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).
thf(4300,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).
thf(760,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).
thf(3384,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(358,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ C ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ B ) ) @ C ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__add__mult__distrib) ).
thf(2065,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ C ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ B ) ) @ C ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(944,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Divides_Odiv__class_Odiv @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) @ B )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self2__is__id) ).
thf(3996,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Divides_Odiv__class_Odiv @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(506,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ B ) ) @ A )
= ( c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc) ).
thf(2538,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ B ) ) @ A )
= ( c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__zpower) ).
thf(1408,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(363,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I4_J) ).
thf(2084,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(402,axiom,
class_Groups_Ocomm__monoid__mult @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__mult) ).
thf(2214,plain,
class_Groups_Ocomm__monoid__mult @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(540,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
& ( B != A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__le) ).
thf(2637,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
& ( B != A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
& ( B != A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(808,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ B ) ) @ ( c_RComplete_Onatceiling @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__mono) ).
thf(3551,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ B ) ) @ ( c_RComplete_Onatceiling @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(469,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ ( c_Groups_Oone__class_Oone @ B ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(2422,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ ( c_Groups_Oone__class_Oone @ B ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(640,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
<=> ( ( ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__1) ).
thf(2955,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) )
& ( ( ( ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(103,axiom,
class_RealVector_Oreal__normed__field @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
thf(1492,plain,
class_RealVector_Oreal__normed__field @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(149,axiom,
class_Groups_Ocomm__monoid__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__add) ).
thf(1603,plain,
class_Groups_Ocomm__monoid__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(432,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( c_SEQ_OBseq @ B @ A )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ C ) )
& ! [D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_BseqD) ).
thf(2299,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( c_SEQ_OBseq @ B @ A )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ C ) )
& ! [D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(550,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__gt__zero__cancel__iff) ).
thf(2669,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(988,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__assoc) ).
thf(4139,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(859,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).
thf(3710,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(1211,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ ( c_Nat_OSuc @ A ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucE) ).
thf(4958,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ ( c_Nat_OSuc @ A ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1211]) ).
thf(1138,axiom,
! [A: $i] :
( ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ A )
= ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__norm__def) ).
thf(4616,plain,
! [A: $i] :
( ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ A )
= ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).
thf(705,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) @ B ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_LIMSEQ__inverse__realpow__zero__lemma) ).
thf(3197,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) @ B ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(457,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__diff__le__0) ).
thf(2378,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(1071,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A ) )
=> ( ( c_Groups_Oabs__class_Oabs @ B @ A )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__of__pos) ).
thf(4374,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A ) )
=> ( ( c_Groups_Oabs__class_Oabs @ B @ A )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).
thf(135,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__idom @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__idom) ).
thf(1571,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__idom @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(49,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__ring @ A )
=> ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring) ).
thf(1376,plain,
! [A: $i] :
( ( class_Rings_Ocomm__ring @ A )
=> ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(394,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__vector @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__triangle__ineq4) ).
thf(2197,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__vector @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(978,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Transcendental_Ocos @ A ) ) @ ( c_Transcendental_Ocos @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Transcendental_Osin @ A ) ) @ ( c_Transcendental_Osin @ A ) ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sin__cos__squared__add3) ).
thf(4107,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Transcendental_Ocos @ A ) ) @ ( c_Transcendental_Ocos @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Transcendental_Osin @ A ) ) @ ( c_Transcendental_Osin @ A ) ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(388,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__field @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_RealVector_Onorm__class_Onorm @ C @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__norm__divide) ).
thf(2180,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__field @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_RealVector_Onorm__class_Onorm @ C @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(1012,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonneg__nonneg) ).
thf(4203,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(1081,axiom,
! [A: $i] :
( ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
= ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__real__of__nat__cancel) ).
thf(4430,plain,
! [A: $i] :
( ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
= ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).
thf(1234,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ozero__right) ).
thf(5035,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1234]) ).
thf(574,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Groups_Oabs__class_Oabs @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Osgn__class_Osgn @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__sgn) ).
thf(2742,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Groups_Oabs__class_Oabs @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Osgn__class_Osgn @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(126,axiom,
class_Rings_Olinordered__idom @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).
thf(1557,plain,
class_Rings_Olinordered__idom @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(164,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__ring__strict @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring__strict) ).
thf(1630,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__ring__strict @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(214,axiom,
class_RealVector_Ometric__space @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Ometric__space) ).
thf(1731,plain,
class_RealVector_Ometric__space @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(1222,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__le__zero__iff) ).
thf(4985,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1222]) ).
thf(476,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(2446,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(1055,axiom,
! [A: $i] :
( ( c_Complex_Ocis @ A )
= ( c_Complex_Orcis @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cis__rcis__eq) ).
thf(4332,plain,
! [A: $i] :
( ( c_Complex_Ocis @ A )
= ( c_Complex_Orcis @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).
thf(36,axiom,
! [A: $i] :
( ( c_RComplete_Onatceiling @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__real__of__nat) ).
thf(1344,plain,
! [A: $i] :
( ( c_RComplete_Onatceiling @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(481,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord__eq__less__trans) ).
thf(2461,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(33,axiom,
class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
thf(1339,plain,
class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(530,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(2605,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(657,axiom,
! [A: $i,B: $i] :
( ( hAPP @ c_Complex_ORe @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ B ) @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_ORe @ B ) ) @ ( hAPP @ c_Complex_ORe @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_OIm @ B ) ) @ ( hAPP @ c_Complex_OIm @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__Re__mult) ).
thf(3027,plain,
! [A: $i,B: $i] :
( ( hAPP @ c_Complex_ORe @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ B ) @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_ORe @ B ) ) @ ( hAPP @ c_Complex_ORe @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_OIm @ B ) ) @ ( hAPP @ c_Complex_OIm @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(844,axiom,
! [A: $i] :
( ( class_RealVector_Oreal__normed__algebra__1 @ A )
=> ( ( c_RealVector_Onorm__class_Onorm @ A @ ( c_Groups_Oone__class_Oone @ A ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__one) ).
thf(3668,plain,
! [A: $i] :
( ( class_RealVector_Oreal__normed__algebra__1 @ A )
=> ( ( c_RealVector_Onorm__class_Onorm @ A @ ( c_Groups_Oone__class_Oone @ A ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(1172,axiom,
class_Orderings_Opreorder @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Opreorder) ).
thf(4833,plain,
class_Orderings_Opreorder @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).
thf(422,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ominus__class_Ominus @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) @ ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__triangle__ineq2) ).
thf(2267,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ominus__class_Ominus @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) @ ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(952,axiom,
class_Fields_Olinordered__field__inverse__zero @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) ).
thf(4028,plain,
class_Fields_Olinordered__field__inverse__zero @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(695,axiom,
? [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
& ! [B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( hAPP @ c_Complex_ORe @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Re_Opos__bounded) ).
thf(3165,plain,
? [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
& ! [B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( hAPP @ c_Complex_ORe @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(275,axiom,
! [A: $i] :
( ( class_Groups_Oab__group__add @ A )
=> ( class_Groups_Ogroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ogroup__add) ).
thf(1862,plain,
! [A: $i] :
( ( class_Groups_Oab__group__add @ A )
=> ( class_Groups_Ogroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(1014,axiom,
! [A: $i,B: $i] :
( ( B = A )
<=> ( ( ( hAPP @ c_Complex_ORe @ B )
= ( hAPP @ c_Complex_ORe @ A ) )
& ( ( hAPP @ c_Complex_OIm @ B )
= ( hAPP @ c_Complex_OIm @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_expand__complex__eq) ).
thf(4208,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( ( hAPP @ c_Complex_ORe @ B )
= ( hAPP @ c_Complex_ORe @ A ) )
& ( ( hAPP @ c_Complex_OIm @ B )
= ( hAPP @ c_Complex_OIm @ A ) ) ) )
& ( ( ( ( hAPP @ c_Complex_ORe @ B )
= ( hAPP @ c_Complex_ORe @ A ) )
& ( ( hAPP @ c_Complex_OIm @ B )
= ( hAPP @ c_Complex_OIm @ A ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(935,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__less__m__mult__n) ).
thf(3977,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(465,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).
thf(2410,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(630,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E ) @ D ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ A ) )
<=> ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__eq__add__iff2) ).
thf(2923,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E ) @ D ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ A ) )
=> ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) ) @ A ) ) )
& ( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(263,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__zadd__distrib) ).
thf(1838,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(27,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Oordered__comm__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__comm__semiring) ).
thf(1325,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Oordered__comm__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(587,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( c_RComplete_Onatfloor @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__natfloor) ).
thf(2785,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( c_RComplete_Onatfloor @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(1179,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ F ) @ E ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C ) @ F ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ E ) @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2__lemma) ).
thf(4850,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ F ) @ E ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C ) @ F ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ E ) @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).
thf(125,axiom,
class_Groups_Oab__group__add @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).
thf(1556,plain,
class_Groups_Oab__group__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(88,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__ring__1 @ A )
=> ( class_Rings_Oring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1) ).
thf(1460,plain,
! [A: $i] :
( ( class_Rings_Ocomm__ring__1 @ A )
=> ( class_Rings_Oring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(14,axiom,
class_Groups_Oone @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oone) ).
thf(1293,plain,
class_Groups_Oone @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(1223,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Ozero) ).
thf(4993,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1223]) ).
thf(512,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
<=> ? [B: $i] :
( A
= ( c_Nat_OSuc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
thf(2553,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ? [B: $i] :
( A
= ( c_Nat_OSuc @ B ) ) )
& ( ? [B: $i] :
( A
= ( c_Nat_OSuc @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(604,axiom,
class_Rings_Olinordered__ring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring) ).
thf(2842,plain,
class_Rings_Olinordered__ring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(316,axiom,
! [A: $i] :
( ( c_SEQ_Oconvergent @ tc_Complex_Ocomplex @ A )
=> ( c_SEQ_Oconvergent @ tc_RealDef_Oreal @ ( c_COMBB @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_Nat_Onat @ c_Complex_ORe @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Re_Oconvergent) ).
thf(1952,plain,
! [A: $i] :
( ( c_SEQ_Oconvergent @ tc_Complex_Ocomplex @ A )
=> ( c_SEQ_Oconvergent @ tc_RealDef_Oreal @ ( c_COMBB @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_Nat_Onat @ c_Complex_ORe @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(691,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A ) )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__pos) ).
thf(3150,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A ) )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(441,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__semigroup__add @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(2329,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__semigroup__add @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(383,axiom,
class_Groups_Osgn__if @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Osgn__if) ).
thf(2171,plain,
class_Groups_Osgn__if @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(79,axiom,
class_Groups_Ocomm__monoid__add @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).
thf(1445,plain,
class_Groups_Ocomm__monoid__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(921,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__less__imp__less__exp) ).
thf(3917,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(374,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).
thf(2139,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(459,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__ring @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonpos__nonpos) ).
thf(2390,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__ring @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(699,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield__inverse__zero @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ ( c_Groups_Oone__class_Oone @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ ( c_Groups_Oone__class_Oone @ C ) ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__one__over) ).
thf(3178,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield__inverse__zero @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ ( c_Groups_Oone__class_Oone @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ ( c_Groups_Oone__class_Oone @ C ) ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(398,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ A ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono1) ).
thf(2207,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ A ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(558,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ A ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(2693,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ A ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(584,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( ( c_RealVector_Onorm__class_Onorm @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__eq__zero) ).
thf(2770,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( ( ( c_RealVector_Onorm__class_Onorm @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_RealVector_Onorm__class_Onorm @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(1202,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A )
= ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le__raw) ).
thf(4933,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A )
= ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1202]) ).
thf(1176,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff__inverse) ).
thf(4844,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176]) ).
thf(264,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oordered__cancel__ab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(1841,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oordered__cancel__ab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ tc_Complex_Ocomplex ) @ ( c_Complex_Ocis @ B ) ) @ ( c_Complex_Ocis @ A ) )
= ( c_Complex_Ocis @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cis__divide) ).
thf(1396,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ tc_Complex_Ocomplex ) @ ( c_Complex_Ocis @ B ) ) @ ( c_Complex_Ocis @ A ) )
= ( c_Complex_Ocis @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(1021,axiom,
class_Rings_Oring__1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1) ).
thf(4232,plain,
class_Rings_Oring__1 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(448,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ B ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__antisym) ).
thf(2350,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ B ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(567,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
=> ( ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ B )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__zmult__eq__1) ).
thf(2725,plain,
! [A: $i,B: $i] :
( ( ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
=> ( ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ B )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(205,axiom,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
thf(1699,plain,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(582,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
=> ( ( c_RComplete_Onatceiling @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__neg) ).
thf(2765,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
=> ( ( c_RComplete_Onatceiling @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(486,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
thf(2481,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(1104,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__less__mult) ).
thf(4502,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).
thf(173,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( c_SEQ_Oconvergent @ C @ B )
=> ( c_SEQ_Oconvergent @ C @ ( c_COMBC @ tc_Nat_Onat @ C @ C @ ( c_COMBB @ C @ ( tc_fun @ C @ C ) @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Oconvergent) ).
thf(1643,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( c_SEQ_Oconvergent @ C @ B )
=> ( c_SEQ_Oconvergent @ C @ ( c_COMBC @ tc_Nat_Onat @ C @ C @ ( c_COMBB @ C @ ( tc_fun @ C @ C ) @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(971,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__ge__zero) ).
thf(4085,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(454,axiom,
class_Rings_Olinordered__idom @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
thf(2369,plain,
class_Rings_Olinordered__idom @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(1066,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring @ C )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__sum__squares__lt__zero) ).
thf(4362,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring @ C )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).
thf(846,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less) ).
thf(3674,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(1170,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex ) @ B ) @ A )
= ( c_Complex_Ocomplex_OComplex @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_ORe @ B ) ) @ ( hAPP @ c_Complex_ORe @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_OIm @ B ) ) @ ( hAPP @ c_Complex_OIm @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__add__def) ).
thf(4827,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex ) @ B ) @ A )
= ( c_Complex_Ocomplex_OComplex @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_ORe @ B ) ) @ ( hAPP @ c_Complex_ORe @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_OIm @ B ) ) @ ( hAPP @ c_Complex_OIm @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170]) ).
thf(632,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
=> ( ( c_Transcendental_Ocos @ ( c_Transcendental_Oarccos @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cos__arccos__abs) ).
thf(2931,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
=> ( ( c_Transcendental_Ocos @ ( c_Transcendental_Oarccos @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(1237,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__0) ).
thf(5042,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1237]) ).
thf(428,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Transcendental_Osin @ A ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__sin__le__one) ).
thf(2288,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Transcendental_Osin @ A ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(526,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ A @ ( c_Groups_Oone__class_Oone @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__le__zero) ).
thf(2592,plain,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ A @ ( c_Groups_Oone__class_Oone @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(578,axiom,
class_Groups_Ocancel__semigroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) ).
thf(2752,plain,
class_Groups_Ocancel__semigroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(75,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__Suc) ).
thf(1435,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(1198,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oordered__ring @ F )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) ) @ D ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__iff2) ).
thf(4918,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oordered__ring @ F )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) ) @ D ) ) @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) ) @ D ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198]) ).
thf(538,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__semiring @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__mono) ).
thf(2633,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__semiring @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(346,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__le__zero__cancel__iff) ).
thf(2022,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(1142,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
<=> ? [C: $i] :
( A
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__add) ).
thf(4703,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ? [C: $i] :
( A
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) ) )
& ( ? [C: $i] :
( A
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).
thf(505,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__field @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide_Oadd) ).
thf(2535,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__field @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(105,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) ) @ A )
= ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__divide__distrib) ).
thf(1496,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) ) @ A )
= ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(1009,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__neg__pos__less0) ).
thf(4196,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(645,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ ( c_Nat_OSuc @ A ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).
thf(2984,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ ( c_Nat_OSuc @ A ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ ( c_Nat_OSuc @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(1099,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__less__iff) ).
thf(4481,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).
thf(997,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__trans) ).
thf(4158,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(494,axiom,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ A )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__self) ).
thf(2506,plain,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ A )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(758,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( c_RComplete_Onatfloor @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__natfloor) ).
thf(3380,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( c_RComplete_Onatfloor @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(279,axiom,
class_Groups_Oab__semigroup__mult @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).
thf(1873,plain,
class_Groups_Oab__semigroup__mult @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(1091,axiom,
! [A: $i,B: $i] :
( ( B != A )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
thf(4458,plain,
! [A: $i,B: $i] :
( ( B != A )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).
thf(1149,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_q__pos__lemma) ).
thf(4735,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).
thf(34,axiom,
class_Rings_Ocomm__semiring @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).
thf(1340,plain,
class_Rings_Ocomm__semiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(93,axiom,
class_Groups_Oordered__comm__monoid__add @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
thf(1472,plain,
class_Groups_Oordered__comm__monoid__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(320,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(1958,plain,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(122,axiom,
class_Groups_Oab__group__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__group__add) ).
thf(1551,plain,
class_Groups_Oab__group__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(67,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__zero__iff) ).
thf(1413,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(911,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B ) @ A ) )
<=> ! [E: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ B @ E ) ) @ ( hAPP @ A @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__fun__def) ).
thf(3881,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B ) @ A ) )
=> ! [E: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ B @ E ) ) @ ( hAPP @ A @ E ) ) ) )
& ( ! [E: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ B @ E ) ) @ ( hAPP @ A @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(162,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__commute) ).
thf(1626,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(801,axiom,
hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
thf(3522,plain,
hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(778,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_Transcendental_Oln @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ln__gt__zero__imp__gt__one) ).
thf(3444,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_Transcendental_Oln @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(411,axiom,
class_Rings_Oordered__comm__semiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__comm__semiring) ).
thf(2239,plain,
class_Rings_Oordered__comm__semiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(1085,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self1__is__m) ).
thf(4441,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).
thf(987,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(4136,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(532,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
= ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__div__cancel1) ).
thf(2614,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
= ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(927,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Divides_Odiv__class_Odiv @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( c_Divides_Odiv__class_Odiv @ C @ A @ B ) ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__add__self1) ).
thf(3936,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Divides_Odiv__class_Odiv @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( c_Divides_Odiv__class_Odiv @ C @ A @ B ) ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(365,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ B )
= ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__le) ).
thf(2107,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ B )
= ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(424,axiom,
! [A: $i,B: $i] :
( ( ( c_Complex_Ocomplex_OComplex @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Complex__eq__0) ).
thf(2271,plain,
! [A: $i,B: $i] :
( ( ( ( c_Complex_Ocomplex_OComplex @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
=> ( ( c_Complex_Ocomplex_OComplex @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(1090,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__mult__pos) ).
thf(4456,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).
thf(543,axiom,
! [A: $i,B: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__self__implies__10) ).
thf(2652,plain,
! [A: $i,B: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(1134,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ ( c_Nat_OSuc @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__eq) ).
thf(4598,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ ( c_Nat_OSuc @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ ( c_Nat_OSuc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).
thf(937,axiom,
! [A: $i] :
( ( class_Rings_Ozero__neq__one @ A )
=> ( ( c_Groups_Oone__class_Oone @ A )
!= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__neq__zero) ).
thf(3981,plain,
! [A: $i] :
( ( class_Rings_Ozero__neq__one @ A )
=> ( ( c_Groups_Oone__class_Oone @ A )
!= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(196,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Oordered__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__semiring) ).
thf(1684,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Oordered__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( class_Divides_Osemiring__div @ B )
=> ( ( c_Divides_Odiv__class_Odiv @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__by__1) ).
thf(1277,plain,
! [A: $i,B: $i] :
( ( class_Divides_Osemiring__div @ B )
=> ( ( c_Divides_Odiv__class_Odiv @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(410,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__ab__group__add @ E )
=> ( ( ( c_Groups_Ominus__class_Ominus @ E @ D @ C )
= ( c_Groups_Ominus__class_Ominus @ E @ B @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ D ) @ C ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq__diff__less__eq) ).
thf(2234,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__ab__group__add @ E )
=> ( ( ( c_Groups_Ominus__class_Ominus @ E @ D @ C )
= ( c_Groups_Ominus__class_Ominus @ E @ B @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ D ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(1041,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__gt1) ).
thf(4292,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(107,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( c_SEQ_Oconvergent @ C @ B )
=> ( c_SEQ_Oconvergent @ C @ ( c_COMBB @ C @ C @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Oconvergent) ).
thf(1509,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( c_SEQ_Oconvergent @ C @ B )
=> ( c_SEQ_Oconvergent @ C @ ( c_COMBB @ C @ C @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(335,axiom,
class_Rings_Ocomm__semiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring) ).
thf(1990,plain,
class_Rings_Ocomm__semiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(664,axiom,
class_Rings_Odivision__ring__inverse__zero @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero) ).
thf(3048,plain,
class_Rings_Odivision__ring__inverse__zero @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(1123,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Transcendental_Ocos @ A ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__cos__le__one) ).
thf(4566,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Transcendental_Ocos @ A ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).
thf(555,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add1) ).
thf(2684,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(396,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ A ) )
=> ( ( c_RComplete_Onatfloor @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ A @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__subtract) ).
thf(2202,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ A ) )
=> ( ( c_RComplete_Onatfloor @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ A @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(606,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__mono) ).
thf(2846,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(417,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__ge__zero) ).
thf(2256,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(636,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__vector @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ! [D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ ( hAPP @ A @ D ) ) ) @ B ) )
=> ( c_SEQ_OBseq @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_BseqI) ).
thf(2942,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__vector @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ! [D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ ( hAPP @ A @ D ) ) ) @ B ) )
=> ( c_SEQ_OBseq @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(866,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( B != A )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
thf(3737,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( B != A )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(955,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__real__of__nat__less__zero) ).
thf(4035,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(902,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B ) @ A ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__real__def) ).
thf(3842,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B ) @ A ) )
| ( B = A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B ) @ A ) )
| ( B = A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(1035,axiom,
! [A: $i,B: $i] :
( ( hAPP @ c_Complex_ORe @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_ORe @ B ) ) @ ( hAPP @ c_Complex_ORe @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Re_Oadd) ).
thf(4272,plain,
! [A: $i,B: $i] :
( ( hAPP @ c_Complex_ORe @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_ORe @ B ) ) @ ( hAPP @ c_Complex_ORe @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(672,axiom,
( ( hAPP @ c_Complex_ORe @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__Re__one) ).
thf(3082,plain,
( ( hAPP @ c_Complex_ORe @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(713,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ C )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__eq__imp) ).
thf(3214,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ C )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(131,axiom,
class_Rings_Osemiring__0 @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).
thf(1566,plain,
class_Rings_Osemiring__0 @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(176,axiom,
class_Rings_Oordered__ring @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).
thf(1647,plain,
class_Rings_Oordered__ring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(839,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__ring @ B )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__square__less__zero) ).
thf(3659,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__ring @ B )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(620,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__vector @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__add__less) ).
thf(2882,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__vector @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(514,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
thf(2567,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(266,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Groups_Ocomm__monoid__mult @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult) ).
thf(1845,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Groups_Ocomm__monoid__mult @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(1065,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__mono) ).
thf(4360,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).
thf(796,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel1) ).
thf(3507,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(1204,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
thf(4937,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1204]) ).
thf(154,axiom,
class_Rings_Oring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring) ).
thf(1611,plain,
class_Rings_Oring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(1263,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel1) ).
thf(5111,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1263]) ).
thf(151,axiom,
class_Rings_Ocomm__ring__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring__1) ).
thf(1605,plain,
class_Rings_Ocomm__ring__1 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(524,axiom,
class_Rings_Ozero__neq__one @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ozero__neq__one) ).
thf(2588,plain,
class_Rings_Ozero__neq__one @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(782,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__add__one__not__less__self) ).
thf(3462,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(1011,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(4200,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(1250,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
=> ( ( c_RComplete_Onatfloor @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__neg) ).
thf(5074,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
=> ( ( c_RComplete_Onatfloor @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1250]) ).
thf(45,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Orderings_Olinorder @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Olinorder) ).
thf(1368,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Orderings_Olinorder @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(717,axiom,
( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_One__nat__def) ).
thf(3228,plain,
( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(235,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
thf(1780,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(711,axiom,
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__zero) ).
thf(3209,plain,
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(464,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
thf(2407,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(883,axiom,
( c_Complex_Oii
!= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__i__not__zero) ).
thf(3786,plain,
( c_Complex_Oii
!= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(1190,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__linear) ).
thf(4894,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190]) ).
thf(1212,axiom,
( ( c_Complex_Ocis @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cis__zero) ).
thf(4961,plain,
( ( c_Complex_Ocis @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1212]) ).
thf(908,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Omult__zero @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__zero__right) ).
thf(3872,plain,
! [A: $i,B: $i] :
( ( class_Rings_Omult__zero @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(1072,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) )
<=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ E ) @ A ) )
=> ( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ D ) ) @ E ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__div) ).
thf(4377,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ E ) @ A ) )
=> ( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ D ) ) @ E ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) ) ) ) )
& ( ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ E ) @ A ) )
=> ( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ D ) ) @ E ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
thf(1252,axiom,
( ( hAPP @ c_Complex_OIm @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__Im__one) ).
thf(5079,plain,
( ( hAPP @ c_Complex_OIm @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1252]) ).
thf(115,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Rings_Omult__zero @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Omult__zero) ).
thf(1531,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Rings_Omult__zero @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(824,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self__is__m) ).
thf(3608,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(99,axiom,
class_Groups_Omonoid__mult @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).
thf(1484,plain,
class_Groups_Omonoid__mult @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(780,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__0) ).
thf(3448,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(738,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ B ) )
| ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
thf(3305,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ B ) )
| ( B = A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ B ) )
| ( B = A ) )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(629,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__commute) ).
thf(2920,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(708,axiom,
! [A: $i,B: $i] :
( ( c_Nat_Osize__class_Osize @ tc_Complex_Ocomplex @ ( c_Complex_Ocomplex_OComplex @ B @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex_Osize_I2_J) ).
thf(3202,plain,
! [A: $i,B: $i] :
( ( c_Nat_Osize__class_Osize @ tc_Complex_Ocomplex @ ( c_Complex_Ocomplex_OComplex @ B @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(237,axiom,
class_Groups_Omonoid__mult @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__mult) ).
thf(1785,plain,
class_Groups_Omonoid__mult @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(785,axiom,
class_Fields_Ofield @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield) ).
thf(3475,plain,
class_Fields_Ofield @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(991,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_Transcendental_Oln @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ln__gt__zero__iff) ).
thf(4145,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_Transcendental_Oln @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_Transcendental_Oln @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(331,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__zero__left) ).
thf(1980,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(139,axiom,
! [A: $i] :
( ( class_Groups_Ocancel__comm__monoid__add @ A )
=> ( class_Groups_Ocancel__ab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add) ).
thf(1579,plain,
! [A: $i] :
( ( class_Groups_Ocancel__comm__monoid__add @ A )
=> ( class_Groups_Ocancel__ab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(1244,axiom,
class_RealVector_Oreal__normed__div__algebra @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).
thf(5062,plain,
class_RealVector_Oreal__normed__div__algebra @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1244]) ).
thf(210,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__vector @ C )
=> ( ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) )
= ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Ominus__class_Ominus @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__minus__commute) ).
thf(1711,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__vector @ C )
=> ( ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) )
= ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Ominus__class_Ominus @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(106,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
<=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__power__eq__Suc__0__iff) ).
thf(1499,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
& ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(515,axiom,
class_Rings_Oring__no__zero__divisors @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__no__zero__divisors) ).
thf(2569,plain,
class_Rings_Oring__no__zero__divisors @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(722,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__0__eq) ).
thf(3246,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(1122,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
| ( B = A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
thf(4561,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
| ( B = A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).
thf(1060,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add1) ).
thf(4346,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).
thf(1024,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
| ( B = A )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
thf(4240,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
| ( B = A )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(974,axiom,
hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__0__less__1) ).
thf(4092,plain,
hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(242,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__minus__eq) ).
thf(1790,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(480,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel1) ).
thf(2454,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(250,axiom,
class_Rings_Oidom @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).
thf(1813,plain,
class_Rings_Oidom @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(17,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Rings_Osemiring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring) ).
thf(1300,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Rings_Osemiring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(852,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__cancel) ).
thf(3691,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(169,axiom,
class_Rings_Olinordered__semidom @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
thf(1637,plain,
class_Rings_Olinordered__semidom @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(1229,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hBOOL @ ( hAPP @ B @ A ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ A ) )
& ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D ) @ C ) )
=> ~ ( hBOOL @ ( hAPP @ B @ D ) ) )
& ( hBOOL @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__least__nat__less) ).
thf(5015,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hBOOL @ ( hAPP @ B @ A ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ A ) )
& ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D ) @ C ) )
=> ~ ( hBOOL @ ( hAPP @ B @ D ) ) )
& ( hBOOL @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1229]) ).
thf(949,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ln__less__zero) ).
thf(4020,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(878,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ c_Complex_ORe @ B )
= ( hAPP @ c_Complex_ORe @ A ) )
=> ( ( ( hAPP @ c_Complex_OIm @ B )
= ( hAPP @ c_Complex_OIm @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__equality) ).
thf(3774,plain,
! [A: $i,B: $i] :
( ( ( hAPP @ c_Complex_ORe @ B )
= ( hAPP @ c_Complex_ORe @ A ) )
=> ( ( ( hAPP @ c_Complex_OIm @ B )
= ( hAPP @ c_Complex_OIm @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(23,axiom,
class_RealVector_Oreal__field @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__field) ).
thf(1317,plain,
class_RealVector_Oreal__field @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(259,axiom,
class_Rings_Ono__zero__divisors @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ono__zero__divisors) ).
thf(1830,plain,
class_Rings_Ono__zero__divisors @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(1062,axiom,
? [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
& ! [B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( hAPP @ c_Complex_OIm @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Im_Opos__bounded) ).
thf(4351,plain,
? [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
& ! [B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( hAPP @ c_Complex_OIm @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).
thf(289,axiom,
class_Rings_Olinordered__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).
thf(1901,plain,
class_Rings_Olinordered__semiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(896,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(3828,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(985,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__ring @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__mono__neg) ).
thf(4132,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__ring @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(118,axiom,
class_Rings_Ocomm__semiring__1 @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
thf(1538,plain,
class_Rings_Ocomm__semiring__1 @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(560,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__bin__lemma) ).
thf(2701,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(768,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__cancel2) ).
thf(3412,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(812,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ B ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I2_J) ).
thf(3564,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ B ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(752,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
thf(3359,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(743,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__right__cancel) ).
thf(3329,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(1150,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ B ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__antisym) ).
thf(4737,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ B ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).
thf(351,axiom,
( ( hAPP @ c_Complex_ORe @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Re_Ozero) ).
thf(2044,plain,
( ( hAPP @ c_Complex_ORe @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(10,axiom,
class_Rings_Oordered__cancel__semiring @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).
thf(1285,plain,
class_Rings_Oordered__cancel__semiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(662,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
thf(3041,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ B @ A @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__self) ).
thf(1336,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ B @ A @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(876,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonpos__nonneg) ).
thf(3769,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(1185,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ ( c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc1) ).
thf(4875,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ ( c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185]) ).
thf(414,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( ( c_Groups_Osgn__class_Osgn @ tc_RealDef_Oreal @ A )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sgn__pos) ).
thf(2247,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( ( c_Groups_Osgn__class_Osgn @ tc_RealDef_Oreal @ A )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(306,axiom,
class_Groups_Oordered__ab__group__add__abs @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add__abs) ).
thf(1934,plain,
class_Groups_Oordered__ab__group__add__abs @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(491,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__trans) ).
thf(2500,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(117,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Rings_Ozero__neq__one @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ozero__neq__one) ).
thf(1536,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Rings_Ozero__neq__one @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(1218,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_RComplete_Onatfloor @ B ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ge__natfloor__plus__one__imp__gt) ).
thf(4976,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_RComplete_Onatfloor @ B ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1218]) ).
thf(9,axiom,
class_Rings_Olinordered__comm__semiring__strict @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).
thf(1284,plain,
class_Rings_Olinordered__comm__semiring__strict @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(993,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ C ) )
& ! [D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Ononneg__bounded) ).
thf(4150,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ C ) )
& ! [D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(766,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__increasing) ).
thf(3398,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(158,axiom,
class_Groups_Ogroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ogroup__add) ).
thf(1617,plain,
class_Groups_Ogroup__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(287,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Groups_Oone @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oone) ).
thf(1898,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Groups_Oone @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(268,axiom,
class_Rings_Olinordered__ring__strict @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).
thf(1849,plain,
class_Rings_Olinordered__ring__strict @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(367,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__le__zero__iff) ).
thf(2113,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(769,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
thf(3415,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(1083,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).
thf(4436,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).
thf(508,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__assoc2) ).
thf(2543,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(1026,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__refl) ).
thf(4246,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__cancel1) ).
thf(1353,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(1108,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ ( c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).
thf(4510,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).
thf(605,axiom,
! [A: $i,B: $i] :
( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Complex_Orcis @ B @ A ) )
= ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__mod__rcis) ).
thf(2843,plain,
! [A: $i,B: $i] :
( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Complex_Orcis @ B @ A ) )
= ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(100,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Suc) ).
thf(1485,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(327,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ? [C: $i] :
! [D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ D ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Obounded) ).
thf(1972,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ? [C: $i] :
! [D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ D ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(977,axiom,
class_Groups_Omonoid__mult @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__mult) ).
thf(4106,plain,
class_Groups_Omonoid__mult @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(959,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
<=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__1__iff) ).
thf(4046,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
& ( ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(1116,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pos__pos) ).
thf(4538,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).
thf(71,axiom,
class_Rings_Olinordered__semidom @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).
thf(1427,plain,
class_Rings_Olinordered__semidom @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(189,axiom,
class_Rings_Ono__zero__divisors @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).
thf(1670,plain,
class_Rings_Ono__zero__divisors @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(244,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc__0) ).
thf(1797,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(975,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) )
=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).
thf(4093,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ B ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(611,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ D ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ B ) ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ D ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unique__quotient__lemma) ).
thf(2860,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ D ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ B ) ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ D ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(568,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zmult__distrib) ).
thf(2728,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(1017,axiom,
class_RealVector_Oreal__field @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__field) ).
thf(4225,plain,
class_RealVector_Oreal__field @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
= ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult2__eq) ).
thf(1372,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
= ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(1174,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucI) ).
thf(4838,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).
thf(1254,axiom,
class_Groups_Oab__semigroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__add) ).
thf(5083,plain,
class_Groups_Oab__semigroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1254]) ).
thf(1259,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__comm__semiring__strict @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__mult__strict__left__mono) ).
thf(5100,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__comm__semiring__strict @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1259]) ).
thf(1162,axiom,
! [A: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ A )
=> ( ( c_Groups_Oabs__class_Oabs @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__zero) ).
thf(4795,plain,
! [A: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ A )
=> ( ( c_Groups_Oabs__class_Oabs @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).
thf(693,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ C )
=> ( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__iff) ).
thf(3156,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ C )
=> ( ( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(920,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( class_Fields_Ofield__inverse__zero @ C )
& ( class_RealVector_Oreal__normed__field @ C ) )
=> ( ( c_RealVector_Onorm__class_Onorm @ C @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__divide) ).
thf(3914,plain,
! [A: $i,B: $i,C: $i] :
( ( ( class_Fields_Ofield__inverse__zero @ C )
& ( class_RealVector_Oreal__normed__field @ C ) )
=> ( ( c_RealVector_Onorm__class_Onorm @ C @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(800,axiom,
? [A: $i] :
! [B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( hAPP @ c_Complex_ORe @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Re_Obounded) ).
thf(3520,plain,
? [A: $i] :
! [B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( hAPP @ c_Complex_ORe @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(607,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) )
<=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__mult__iff) ).
thf(2848,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(474,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__left__commute) ).
thf(2435,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(767,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ ( c_Nat_OSuc @ A ) ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ? [C: $i] :
( ( B
= ( c_Nat_OSuc @ C ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).
thf(3400,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ ( c_Nat_OSuc @ A ) ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ? [C: $i] :
( ( B
= ( c_Nat_OSuc @ C ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ A ) ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ? [C: $i] :
( ( B
= ( c_Nat_OSuc @ C ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ ( c_Nat_OSuc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(781,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__real__le) ).
thf(3457,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(364,axiom,
! [A: $i,B: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
<=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ A ) ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__eq__0__iff) ).
thf(2088,plain,
! [A: $i,B: $i] :
( ( ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ A ) ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A ) @ B ) ) ) ) )
& ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ A ) ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A ) @ B ) ) ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(559,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ ( c_Nat_OSuc @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__mono) ).
thf(2696,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ ( c_Nat_OSuc @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ ( c_Nat_OSuc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(598,axiom,
( ( c_RComplete_Onatceiling @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__one) ).
thf(2828,plain,
( ( c_RComplete_Onatceiling @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(399,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
thf(2209,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(968,axiom,
class_Orderings_Oord @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oord) ).
thf(4078,plain,
class_Orderings_Oord @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(1125,axiom,
! [A: $i] :
( ( class_Groups_Osgn__if @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn0) ).
thf(4574,plain,
! [A: $i] :
( ( class_Groups_Osgn__if @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).
thf(696,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ ( c_Nat_OSuc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq) ).
thf(3168,plain,
! [A: $i,B: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ ( c_Nat_OSuc @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ ( c_Nat_OSuc @ B ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(310,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oordered__ab__group__add__abs @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs) ).
thf(1940,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oordered__ab__group__add__abs @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(1040,axiom,
! [A: $i] :
( ( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ A @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex ) @ A ) @ c_Complex_Oii ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ A @ c_Complex_Oii ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unimodular__reduce__norm) ).
thf(4289,plain,
! [A: $i] :
( ( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ A @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex ) @ A ) @ c_Complex_Oii ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ A @ c_Complex_Oii ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(1037,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__1__right) ).
thf(4278,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(687,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( c_Groups_Oabs__class_Oabs @ C @ B ) ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__triangle__ineq4) ).
thf(3139,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( c_Groups_Oabs__class_Oabs @ C @ B ) ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(829,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) ) )
<=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__gt__zero__iff) ).
thf(3620,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) ) )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
& ( ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(873,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__le__cancel1) ).
thf(3757,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(485,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__div4) ).
thf(2479,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__mult__distrib) ).
thf(1321,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(261,axiom,
! [A: $i,B: $i] :
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__mult) ).
thf(1834,plain,
! [A: $i,B: $i] :
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(297,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
thf(1913,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(703,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Odiff__diff__eq) ).
thf(3188,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(807,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( ( c_RComplete_Onatfloor @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_RComplete_Onatfloor @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__add__one) ).
thf(3548,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( ( c_RComplete_Onatfloor @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_RComplete_Onatfloor @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(393,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ ( c_Nat_OSuc @ A ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__antisym) ).
thf(2194,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ ( c_Nat_OSuc @ A ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(447,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ A ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__pos__pos__trivial) ).
thf(2347,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ A ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(180,axiom,
class_Orderings_Opreorder @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Opreorder) ).
thf(1654,plain,
class_Orderings_Opreorder @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(403,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zmult__distrib2) ).
thf(2215,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(1121,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__linear) ).
thf(4559,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).
thf(649,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( ( c_Groups_Oabs__class_Oabs @ B @ ( c_Groups_Oabs__class_Oabs @ B @ A ) )
= ( c_Groups_Oabs__class_Oabs @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__idempotent) ).
thf(2997,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( ( c_Groups_Oabs__class_Oabs @ B @ ( c_Groups_Oabs__class_Oabs @ B @ A ) )
= ( c_Groups_Oabs__class_Oabs @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(488,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__divide__distrib) ).
thf(2490,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(366,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( C
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_self__quotient__aux1) ).
thf(2110,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( C
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) ) @ A )
= ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Odiff__left) ).
thf(1390,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) ) @ A )
= ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(434,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
thf(2305,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(137,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Suc__right) ).
thf(1575,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(217,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diffs0__imp__equal) ).
thf(1734,plain,
! [A: $i,B: $i] :
( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(248,axiom,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__1) ).
thf(1807,plain,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(175,axiom,
class_Rings_Ozero__neq__one @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).
thf(1646,plain,
class_Rings_Ozero__neq__one @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(919,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E ) @ D ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__add__eq2) ).
thf(3911,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E ) @ D ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(385,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).
thf(2174,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(1341,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(503,axiom,
class_Groups_Oone @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oone) ).
thf(2532,plain,
class_Groups_Oone @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(1028,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__class_Odistrib) ).
thf(4250,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(221,axiom,
class_Rings_Oring__1__no__zero__divisors @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).
thf(1745,plain,
class_Rings_Oring__1__no__zero__divisors @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(641,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ B ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ B ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ B )
= ( c_Nat_OSuc @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__if) ).
thf(2971,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ B ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ B ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ B )
= ( c_Nat_OSuc @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(1057,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(4338,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).
thf(1215,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__vector @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ ( c_RealVector_Onorm__class_Onorm @ D @ A ) ) ) )
=> ( B
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__ratiotest__lemma) ).
thf(4969,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__vector @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ ( c_RealVector_Onorm__class_Onorm @ D @ A ) ) ) )
=> ( B
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1215]) ).
thf(783,axiom,
class_Power_Opower @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Power_Opower) ).
thf(3465,plain,
class_Power_Opower @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(144,axiom,
class_Groups_Oab__semigroup__mult @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) ).
thf(1590,plain,
class_Groups_Oab__semigroup__mult @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(826,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__lessD1) ).
thf(3613,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(1196,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
thf(4913,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1196]) ).
thf(1143,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(4710,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).
thf(527,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__semiring @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__mono) ).
thf(2594,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__semiring @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(884,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ B ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ B )
= ( c_Nat_OSuc @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__geq) ).
thf(3789,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ B ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ B )
= ( c_Nat_OSuc @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(608,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ A @ ( c_Groups_Ozero__class_Ozero @ A ) ) @ ( c_Groups_Oone__class_Oone @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__one) ).
thf(2855,plain,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ A @ ( c_Groups_Ozero__class_Ozero @ A ) ) @ ( c_Groups_Oone__class_Oone @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(171,axiom,
class_Rings_Oordered__ring__abs @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring__abs) ).
thf(1639,plain,
class_Rings_Oordered__ring__abs @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(429,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ C )
=> ( ( c_Groups_Oabs__class_Oabs @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( c_Groups_Oabs__class_Oabs @ C @ B ) ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( c_Groups_Oabs__class_Oabs @ C @ B ) ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__add__abs) ).
thf(2290,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ C )
=> ( ( c_Groups_Oabs__class_Oabs @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( c_Groups_Oabs__class_Oabs @ C @ B ) ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ ( c_Groups_Oabs__class_Oabs @ C @ B ) ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(894,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ B ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2__neg) ).
thf(3825,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ B ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(291,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) ).
thf(1903,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(1227,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__eq__diff) ).
thf(5008,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1227]) ).
thf(973,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_COMBC @ F @ E @ D @ C @ B ) @ A )
= ( hAPP @ ( hAPP @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBC__1) ).
thf(4089,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_COMBC @ F @ E @ D @ C @ B ) @ A )
= ( hAPP @ ( hAPP @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(1095,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
thf(4468,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).
thf(715,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__add @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__right) ).
thf(3220,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__add @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(1118,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ln__less__self) ).
thf(4542,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).
thf(592,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).
thf(2811,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(1145,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ v_s @ A ) ) ) @ v_r ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_assms) ).
thf(4715,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ v_s @ A ) ) ) @ v_r ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).
thf(163,axiom,
class_Groups_Ocomm__monoid__mult @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
thf(1629,plain,
class_Groups_Ocomm__monoid__mult @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(679,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal ) @ B ) @ A ) ) )
<=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__0__le__divide__iff) ).
thf(3104,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal ) @ B ) @ A ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(342,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ B ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).
thf(2004,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
=> ( ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(531,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__left__cancel) ).
thf(2608,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(472,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD2) ).
thf(2431,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(651,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C )
= A )
<=> ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__diff__is__add) ).
thf(3003,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C )
= A )
=> ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ C ) ) )
& ( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ C ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(255,axiom,
! [A: $i] :
( ( class_Groups_Ocomm__monoid__add @ A )
=> ( class_Groups_Ocomm__monoid__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__add) ).
thf(1822,plain,
! [A: $i] :
( ( class_Groups_Ocomm__monoid__add @ A )
=> ( class_Groups_Ocomm__monoid__add @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(1173,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ C ) )
& ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ C ) @ B )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_realpow__pos__nth) ).
thf(4834,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ C ) )
& ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ C ) @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173]) ).
thf(798,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__ge__zero) ).
thf(3516,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(112,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__div__algebra @ C )
=> ( ( c_Groups_Osgn__class_Osgn @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Osgn__class_Osgn @ C @ B ) ) @ ( c_Groups_Osgn__class_Osgn @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__mult) ).
thf(1523,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__div__algebra @ C )
=> ( ( c_Groups_Osgn__class_Osgn @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Osgn__class_Osgn @ C @ B ) ) @ ( c_Groups_Osgn__class_Osgn @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(686,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__inverse) ).
thf(3136,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(1261,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl3) ).
thf(5104,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1261]) ).
thf(500,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__0__less) ).
thf(2526,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(1112,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C )
= A )
=> ( B
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__divide__imp) ).
thf(4527,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C )
= A )
=> ( B
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).
thf(467,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel__left__pos) ).
thf(2416,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(880,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos2) ).
thf(3780,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(127,axiom,
class_Groups_Ocancel__ab__semigroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add) ).
thf(1558,plain,
class_Groups_Ocancel__ab__semigroup__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(633,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__refl) ).
thf(2934,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(377,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Osgn__class_Osgn @ B @ A ) ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__sgn__abs) ).
thf(2152,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Osgn__class_Osgn @ B @ A ) ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(420,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_COMBB @ F @ E @ D @ C @ B ) @ A )
= ( hAPP @ C @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
thf(2262,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_COMBB @ F @ E @ D @ C @ B ) @ A )
= ( hAPP @ C @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(1032,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__eq) ).
thf(4261,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).
thf(674,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__left__mono) ).
thf(3085,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(741,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ B )
= ( c_Nat_OSuc @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__div__geq) ).
thf(3324,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ B )
= ( c_Nat_OSuc @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(232,axiom,
class_Rings_Oring__no__zero__divisors @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).
thf(1777,plain,
class_Rings_Oring__no__zero__divisors @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(1156,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oordered__ring @ F )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ F @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) ) @ D ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__iff2) ).
thf(4759,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oordered__ring @ F )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ F @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) ) @ D ) ) @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ F @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) ) @ D ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).
thf(77,axiom,
class_Groups_Ocancel__comm__monoid__add @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__comm__monoid__add) ).
thf(1440,plain,
class_Groups_Ocancel__comm__monoid__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(1098,axiom,
! [A: $i] :
( ( class_RealVector_Oreal__normed__algebra @ A )
=> ? [B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
& ! [C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ A @ C ) ) @ ( c_RealVector_Onorm__class_Onorm @ A @ D ) ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Opos__bounded) ).
thf(4478,plain,
! [A: $i] :
( ( class_RealVector_Oreal__normed__algebra @ A )
=> ? [B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
& ! [C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ A @ C ) ) @ ( c_RealVector_Onorm__class_Onorm @ A @ D ) ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).
thf(207,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__semiring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1) ).
thf(1706,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__semiring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(389,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__ab__group__add @ E )
=> ( ( ( c_Groups_Ominus__class_Ominus @ E @ D @ C )
= ( c_Groups_Ominus__class_Ominus @ E @ B @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ D ) @ C ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq__diff__less) ).
thf(2183,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__ab__group__add @ E )
=> ( ( ( c_Groups_Ominus__class_Ominus @ E @ D @ C )
= ( c_Groups_Ominus__class_Ominus @ E @ B @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ D ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(184,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(1661,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(966,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing2) ).
thf(4074,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(572,axiom,
c_SEQ_Osubseq @ v_ga____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_g_I1_J) ).
thf(2739,plain,
c_SEQ_Osubseq @ v_ga____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(771,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).
thf(3420,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(477,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__imp__zdiv__nonneg__iff) ).
thf(2447,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(637,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_q__neg__lemma) ).
thf(2944,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(199,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Oordered__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring) ).
thf(1689,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Oordered__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(362,axiom,
! [A: $i,B: $i] :
( ( c_Transcendental_Ocos @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Transcendental_Ocos @ A ) ) @ ( c_Transcendental_Ocos @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Transcendental_Osin @ A ) ) @ ( c_Transcendental_Osin @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cos__diff2) ).
thf(2081,plain,
! [A: $i,B: $i] :
( ( c_Transcendental_Ocos @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Transcendental_Ocos @ A ) ) @ ( c_Transcendental_Ocos @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Transcendental_Osin @ A ) ) @ ( c_Transcendental_Osin @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(700,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Omonoid__mult @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_realpow__minus__mult) ).
thf(3181,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Omonoid__mult @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(853,axiom,
( ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex )
= ( c_Complex_Ocomplex_OComplex @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__one__def) ).
thf(3694,plain,
( ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex )
= ( c_Complex_Ocomplex_OComplex @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(1051,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__less__dividend) ).
thf(4321,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(350,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ C ) )
& ! [D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Opos__bounded) ).
thf(2041,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ C ) )
& ! [D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(1002,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__imp__zdiv__pos__iff) ).
thf(4175,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(994,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__zpower__abs) ).
thf(4153,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(910,axiom,
( ( c_RComplete_Onatfloor @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__one) ).
thf(3879,plain,
( ( c_RComplete_Onatfloor @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(15,axiom,
! [A: $i] :
( ( class_Groups_Oab__group__add @ A )
=> ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__group__add) ).
thf(1294,plain,
! [A: $i] :
( ( class_Groups_Oab__group__add @ A )
=> ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1236,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oone__class_Oone @ D ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__increasing) ).
thf(5040,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oone__class_Oone @ D ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1236]) ).
thf(1249,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__less__imp__less) ).
thf(5072,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1249]) ).
thf(750,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__not__less__zero) ).
thf(3351,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(942,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing) ).
thf(3993,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(337,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__power) ).
thf(1994,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(1046,axiom,
class_Rings_Ono__zero__divisors @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ono__zero__divisors) ).
thf(4306,plain,
class_Rings_Ono__zero__divisors @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).
thf(951,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__left__neg) ).
thf(4025,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(345,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Oadd) ).
thf(2019,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(1139,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__Suc__gt__zero) ).
thf(4619,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139]) ).
thf(941,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(3992,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(109,axiom,
! [A: $i,B: $i] :
( ( ( c_Nat_OSuc @ B )
= ( c_Nat_OSuc @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Oinject) ).
thf(1512,plain,
! [A: $i,B: $i] :
( ( ( ( c_Nat_OSuc @ B )
= ( c_Nat_OSuc @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Nat_OSuc @ B )
= ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(378,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( C
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_self__quotient__aux2) ).
thf(2155,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( C
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(939,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ D )
& ( class_Orderings_Oord @ C ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ D @ ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ A @ B ) @ ( hAPP @ A @ E ) ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ D @ ( hAPP @ A @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ ( c_RealVector_Onorm__class_Onorm @ D @ ( hAPP @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lemmaCauchy) ).
thf(3987,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ D )
& ( class_Orderings_Oord @ C ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ D @ ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ A @ B ) @ ( hAPP @ A @ E ) ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ D @ ( hAPP @ A @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ ( c_RealVector_Onorm__class_Onorm @ D @ ( hAPP @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(745,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( hAPP @ c_Complex_OIm @ ( hAPP @ v_s @ A ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ v_r ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_th) ).
thf(3337,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( hAPP @ c_Complex_OIm @ ( hAPP @ v_s @ A ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ v_r ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(1068,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__ring @ B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__square) ).
thf(4367,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__ring @ B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).
thf(370,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__trans) ).
thf(2123,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(404,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ D ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ B ) ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ E ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ E ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unique__quotient__lemma__neg) ).
thf(2218,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ D ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ B ) ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ E ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ E ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(984,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( ( c_Groups_Ozero__class_Ozero @ B )
= A )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__reorient) ).
thf(4125,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( ( ( c_Groups_Ozero__class_Ozero @ B )
= A )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Ozero__class_Ozero @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(418,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__semidom @ B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__one) ).
thf(2258,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__semidom @ B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(1187,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( C = A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__eq__imp__eq__base) ).
thf(4880,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( C = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1187]) ).
thf(38,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).
thf(1348,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(433,axiom,
? [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
& ! [B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( hAPP @ c_Complex_ORe @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Re_Ononneg__bounded) ).
thf(2302,plain,
? [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
& ! [B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( hAPP @ c_Complex_ORe @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(498,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zabs__less__one__iff) ).
thf(2517,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(212,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__assoc) ).
thf(1725,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(7,axiom,
! [A: $i] :
( ( class_Power_Opower @ A )
=> ( ( c_Power_Opower__class_Opower @ A )
= ( c_Power_Opower_Opower @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Otimes__class_Otimes @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__power__power) ).
thf(1280,plain,
! [A: $i] :
( ( class_Power_Opower @ A )
=> ( ( c_Power_Opower__class_Opower @ A )
= ( c_Power_Opower_Opower @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Otimes__class_Otimes @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(138,axiom,
class_Rings_Osemiring @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).
thf(1578,plain,
class_Rings_Osemiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(319,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(1957,plain,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(906,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oone @ B )
=> ( ( ( c_Groups_Oone__class_Oone @ B )
= A )
<=> ( A
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__reorient) ).
thf(3860,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oone @ B )
=> ( ( ( ( c_Groups_Oone__class_Oone @ B )
= A )
=> ( A
= ( c_Groups_Oone__class_Oone @ B ) ) )
& ( ( A
= ( c_Groups_Oone__class_Oone @ B ) )
=> ( ( c_Groups_Oone__class_Oone @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(193,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( ( c_SEQ_Oincseq @ B @ A )
=> ( c_SEQ_Omonoseq @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_incseq__imp__monoseq) ).
thf(1678,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( ( c_SEQ_Oincseq @ B @ A )
=> ( c_SEQ_Omonoseq @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(735,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(3291,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(1064,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__le__not__le) ).
thf(4356,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(147,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oab__group__add @ E )
=> ( ( ( c_Groups_Ominus__class_Ominus @ E @ D @ C )
= ( c_Groups_Ominus__class_Ominus @ E @ B @ A ) )
=> ( ( D = C )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq__diff__eq) ).
thf(1593,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oab__group__add @ E )
=> ( ( ( c_Groups_Ominus__class_Ominus @ E @ D @ C )
= ( c_Groups_Ominus__class_Ominus @ E @ B @ A ) )
=> ( ( ( D = C )
=> ( B = A ) )
& ( ( B = A )
=> ( D = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(900,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__vector @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__triangle__ineq3) ).
thf(3837,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__vector @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(52,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Oring__1__no__zero__divisors @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors) ).
thf(1380,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Oring__1__no__zero__divisors @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(571,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ B ) @ A ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__self) ).
thf(2736,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ B ) @ A ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(333,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ ( c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mono) ).
thf(1986,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(1102,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ E )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C ) ) )
<=> ( ( D = B )
| ( C = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_crossproduct__eq) ).
thf(4491,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ E )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C ) ) )
=> ( ( D = B )
| ( C = A ) ) )
& ( ( ( D = B )
| ( C = A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).
thf(792,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym) ).
thf(3496,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(1127,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__add__iff2) ).
thf(4579,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E ) @ D ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) ) @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).
thf(583,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
thf(2768,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(274,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(1859,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(252,axiom,
! [A: $i] :
( ( c_SEQ_OBseq @ tc_RealDef_Oreal @ A )
=> ( ( c_SEQ_Omonoseq @ tc_RealDef_Oreal @ A )
=> ( c_SEQ_Oconvergent @ tc_RealDef_Oreal @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bseq__monoseq__convergent) ).
thf(1816,plain,
! [A: $i] :
( ( c_SEQ_OBseq @ tc_RealDef_Oreal @ A )
=> ( ( c_SEQ_Omonoseq @ tc_RealDef_Oreal @ A )
=> ( c_SEQ_Oconvergent @ tc_RealDef_Oreal @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(1220,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Transcendental_Osin @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sin__le__one) ).
thf(4981,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Transcendental_Osin @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1220]) ).
thf(909,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ B ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord__less__eq__trans) ).
thf(3875,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ B ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(241,axiom,
class_Rings_Oidom @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).
thf(1789,plain,
class_Rings_Oidom @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(453,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ D @ C @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power_Opower_Opower__0) ).
thf(2366,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ D @ C @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(209,axiom,
class_Groups_Oone @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oone) ).
thf(1710,plain,
class_Groups_Oone @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(94,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( c_SEQ_Oconvergent @ C @ B )
=> ( ( c_SEQ_Oconvergent @ C @ A )
=> ( c_SEQ_Oconvergent @ C @ ( c_COMBS @ tc_Nat_Onat @ C @ C @ ( c_COMBB @ C @ ( tc_fun @ C @ C ) @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Oconvergent) ).
thf(1473,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( c_SEQ_Oconvergent @ C @ B )
=> ( ( c_SEQ_Oconvergent @ C @ A )
=> ( c_SEQ_Oconvergent @ C @ ( c_COMBS @ tc_Nat_Onat @ C @ C @ ( c_COMBB @ C @ ( tc_fun @ C @ C ) @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(953,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(4029,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(1003,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ ( c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucI) ).
thf(4178,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(1045,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__ring @ C )
=> ( ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__mult__pos__le) ).
thf(4303,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__ring @ C )
=> ( ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(915,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__left__mono__neg) ).
thf(3897,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ D ) @ A ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ C )
=> ( ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) )
= ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__minus__commute) ).
thf(1363,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ C )
=> ( ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) )
= ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(21,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(1314,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(1038,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Groups_Oabs__class_Oabs @ C @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__power__abs) ).
thf(4281,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Groups_Oabs__class_Oabs @ C @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(748,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex ) @ B ) @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__mod__triangle__ineq2) ).
thf(3347,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex ) @ B ) @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(730,axiom,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( c_Transcendental_Ocos @ ( c_Complex_Oarg @ ( c_Complex_Ocomplex_OComplex @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cos__arg__i__mult__zero) ).
thf(3277,plain,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( c_Transcendental_Ocos @ ( c_Complex_Oarg @ ( c_Complex_Ocomplex_OComplex @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(201,axiom,
! [A: $i] :
( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Complex_Ocomplex_OComplex @ ( c_Transcendental_Ocos @ A ) @ ( c_Transcendental_Osin @ A ) ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cmod__unit__one) ).
thf(1693,plain,
! [A: $i] :
( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Complex_Ocomplex_OComplex @ ( c_Transcendental_Ocos @ A ) @ ( c_Transcendental_Osin @ A ) ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(1230,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__assoc) ).
thf(5019,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1230]) ).
thf(861,axiom,
! [A: $i,B: $i] :
( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ? [C: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex ) @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ C ) @ A ) ) ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reduce__poly__simple) ).
thf(3716,plain,
! [A: $i,B: $i] :
( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ? [C: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex ) @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ C ) @ A ) ) ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(626,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1 @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) ) ) @ ( c_Groups_Ominus__class_Ominus @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__squared__diff__one__factored) ).
thf(2913,plain,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1 @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) ) ) @ ( c_Groups_Ominus__class_Ominus @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(463,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
thf(2404,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(564,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ A ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__natfloor__add__one__gt) ).
thf(2714,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ A ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(773,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( ( ( c_Transcendental_Oln @ B )
= ( c_Transcendental_Oln @ A ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ln__inj__iff) ).
thf(3426,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( ( ( ( c_Transcendental_Oln @ B )
= ( c_Transcendental_Oln @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Transcendental_Oln @ B )
= ( c_Transcendental_Oln @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(658,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( c_RComplete_Onatceiling @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__natceiling) ).
thf(3030,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( c_RComplete_Onatceiling @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(875,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A ) ) @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__nonzero) ).
thf(3765,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A ) ) @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(1007,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).
thf(4193,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(534,axiom,
! [A: $i] :
( ( hAPP @ c_Complex_OIm @ ( c_Complex_Ocis @ A ) )
= ( c_Transcendental_Osin @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Im__cis) ).
thf(2619,plain,
! [A: $i] :
( ( hAPP @ c_Complex_OIm @ ( c_Complex_Ocis @ A ) )
= ( c_Transcendental_Osin @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(1050,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( c_RComplete_Onatceiling @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_RComplete_Onatceiling @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__add) ).
thf(4318,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( c_RComplete_Onatceiling @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_RComplete_Onatceiling @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).
thf(510,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__cancel) ).
thf(2549,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(449,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__pos) ).
thf(2353,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ C ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(1200,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel2) ).
thf(4923,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1200]) ).
thf(569,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) ) @ ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__triangle__ineq3) ).
thf(2731,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) ) @ ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(1,conjecture,
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ v_r ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) )
& ! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( hAPP @ c_Complex_OIm @ ( hAPP @ v_s @ ( hAPP @ v_f____ @ ( hAPP @ v_ga____ @ A ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ v_r ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ v_r ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) )
& ! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( hAPP @ c_Complex_OIm @ ( hAPP @ v_s @ ( hAPP @ v_f____ @ ( hAPP @ v_ga____ @ A ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ v_r ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(1268,plain,
~ ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ v_r ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) )
& ! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( hAPP @ c_Complex_OIm @ ( hAPP @ v_s @ ( hAPP @ v_f____ @ ( hAPP @ v_ga____ @ A ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ v_r ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(50,axiom,
class_Rings_Olinordered__semiring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).
thf(1378,plain,
class_Rings_Olinordered__semiring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(483,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
<=> ( ( B = A )
| ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__cancel1) ).
thf(2467,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( ( B = A )
| ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( B = A )
| ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(790,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__nonneg__neg__le0) ).
thf(3489,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(1243,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__div3) ).
thf(5060,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1243]) ).
thf(1203,axiom,
class_Rings_Olinordered__semiring__1__strict @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict) ).
thf(4936,plain,
class_Rings_Olinordered__semiring__1__strict @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1203]) ).
thf(928,axiom,
! [A: $i,B: $i] :
( ( ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( ( ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__is__add) ).
thf(3939,plain,
! [A: $i,B: $i] :
( ( ( ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) )
& ( ( ( ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
=> ( ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(1209,axiom,
c_SEQ_Omonoseq @ tc_RealDef_Oreal @ ( c_COMBB @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_Nat_Onat @ c_Complex_OIm @ ( c_COMBB @ tc_Nat_Onat @ tc_Complex_Ocomplex @ tc_Nat_Onat @ v_s @ ( c_COMBB @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat @ v_f____ @ v_ga____ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_g_I2_J) ).
thf(4955,plain,
c_SEQ_Omonoseq @ tc_RealDef_Oreal @ ( c_COMBB @ tc_Complex_Ocomplex @ tc_RealDef_Oreal @ tc_Nat_Onat @ c_Complex_OIm @ ( c_COMBB @ tc_Nat_Onat @ tc_Complex_Ocomplex @ tc_Nat_Onat @ v_s @ ( c_COMBB @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat @ v_f____ @ v_ga____ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1209]) ).
thf(492,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__one__le__power) ).
thf(2502,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(1178,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__cube) ).
thf(4848,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178]) ).
thf(683,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__lt__two__imp__zero__or__one) ).
thf(3128,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(330,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Oadd__right) ).
thf(1977,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(934,axiom,
( ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint )
!= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__0__neq__1) ).
thf(3974,plain,
( ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint )
!= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(656,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono1) ).
thf(3025,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(814,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) )
= ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__diff) ).
thf(3570,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) )
= ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(1216,axiom,
class_Groups_Oab__semigroup__mult @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__mult) ).
thf(4972,plain,
class_Groups_Oab__semigroup__mult @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1216]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( c_Complex_Ocomplex_OComplex @ D @ C ) @ ( c_Complex_Ocomplex_OComplex @ B @ A ) )
= ( c_Complex_Ocomplex_OComplex @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ D @ B ) @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__diff) ).
thf(1384,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( c_Complex_Ocomplex_OComplex @ D @ C ) @ ( c_Complex_Ocomplex_OComplex @ B @ A ) )
= ( c_Complex_Ocomplex_OComplex @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ D @ B ) @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(823,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) )
= ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zmult2__eq) ).
thf(3605,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) )
= ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(141,axiom,
! [A: $i] :
( ( class_Groups_Ozero @ A )
=> ( class_Groups_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ozero) ).
thf(1582,plain,
! [A: $i] :
( ( class_Groups_Ozero @ A )
=> ( class_Groups_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(421,axiom,
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__1) ).
thf(2265,plain,
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(329,axiom,
class_Rings_Oordered__semiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__semiring) ).
thf(1976,plain,
class_Rings_Oordered__semiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(121,axiom,
class_Groups_Oab__semigroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__add) ).
thf(1550,plain,
class_Groups_Oab__semigroup__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(1106,axiom,
class_Rings_Oring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring) ).
thf(4506,plain,
class_Rings_Oring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).
thf(522,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Oadd__left) ).
thf(2583,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(963,axiom,
! [A: $i] :
( ( hAPP @ c_Complex_OIm @ ( c_Groups_Osgn__class_Osgn @ tc_Complex_Ocomplex @ A ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_OIm @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Im__sgn) ).
thf(4066,plain,
! [A: $i] :
( ( hAPP @ c_Complex_OIm @ ( c_Groups_Osgn__class_Osgn @ tc_Complex_Ocomplex @ A ) )
= ( hAPP @ ( hAPP @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal ) @ ( hAPP @ c_Complex_OIm @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(763,axiom,
class_Orderings_Oorder @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).
thf(3392,plain,
class_Orderings_Oorder @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(1019,axiom,
class_Fields_Olinordered__field @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field) ).
thf(4229,plain,
class_Fields_Olinordered__field @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).
thf(1239,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__iff__diff__less__0) ).
thf(5046,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1239]) ).
thf(301,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(1925,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(1144,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__imp__less__right) ).
thf(4713,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).
thf(613,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ ( c_Groups_Oone__class_Oone @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc__less) ).
thf(2864,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ ( c_Groups_Oone__class_Oone @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(867,axiom,
( ( c_RComplete_Onatfloor @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__zero) ).
thf(3740,plain,
( ( c_RComplete_Onatfloor @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(73,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Groups_Oab__semigroup__mult @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__mult) ).
thf(1431,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Groups_Oab__semigroup__mult @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(965,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( ( c_RComplete_Onatceiling @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_RComplete_Onatceiling @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__add__one) ).
thf(4071,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( ( c_RComplete_Onatceiling @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_RComplete_Onatceiling @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(290,axiom,
class_Rings_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
thf(1902,plain,
class_Rings_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(487,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) )
<=> ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__norm__iff) ).
thf(2484,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) )
=> ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(892,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= B )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
thf(3812,plain,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= B )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(1399,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(160,axiom,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__self__eq__0) ).
thf(1621,plain,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(1056,axiom,
( ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal )
!= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__zero__not__eq__one) ).
thf(4335,plain,
( ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal )
!= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).
thf(776,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord__eq__le__trans) ).
thf(3437,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(313,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Odiff__right) ).
thf(1944,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(1129,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
=> ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
thf(4584,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).
thf(924,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__assoc2) ).
thf(3924,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(1159,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) )
<=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ! [D: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ D ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__split) ).
thf(4767,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ! [D: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ D ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ! [D: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ D ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).
thf(557,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ C ) ) @ B ) ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reals__Archimedean4) ).
thf(2690,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ C ) ) @ B ) ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(614,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) ) @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff__inverse2) ).
thf(2866,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(774,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__1) ).
thf(3432,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(809,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ C ) )
& ! [D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ D ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Ononneg__bounded) ).
thf(3553,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ C ) )
& ! [D: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ D ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(737,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( B != A )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
thf(3296,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ B ) ) )
=> ( B != A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(278,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__commute) ).
thf(1870,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(871,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__mono_H) ).
thf(3753,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(1114,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__refl) ).
thf(4533,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).
thf(653,axiom,
class_Orderings_Olinorder @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
thf(3013,plain,
class_Orderings_Olinorder @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(30,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Orderings_Opreorder @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Opreorder) ).
thf(1331,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Orderings_Opreorder @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(152,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring) ).
thf(1606,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(904,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oordered__ring @ F )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) ) @ D ) ) @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__iff1) ).
thf(3854,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oordered__ring @ F )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) ) @ D ) ) @ C ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) ) @ D ) ) @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(218,axiom,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).
thf(1737,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(475,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
<=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__zmult__eq__1__iff) ).
thf(2438,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) )
& ( ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(1155,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__gr__0) ).
thf(4752,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).
thf(1152,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__le__iff) ).
thf(4742,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152]) ).
thf(1048,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ B ) ) @ ( c_RComplete_Onatfloor @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__mono) ).
thf(4313,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ B ) ) @ ( c_RComplete_Onatfloor @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).
thf(228,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib2) ).
thf(1769,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(1078,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
thf(4423,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).
thf(1194,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Nat_OSuc @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ ( c_Nat_OSuc @ B ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__le__imp__le__base) ).
thf(4908,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Nat_OSuc @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ ( c_Nat_OSuc @ B ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194]) ).
thf(961,axiom,
! [A: $i,B: $i] :
( ( ( c_Complex_Ocomplex_OComplex @ B @ A )
= ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) )
<=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Complex__eq__1) ).
thf(4056,plain,
! [A: $i,B: $i] :
( ( ( ( c_Complex_Ocomplex_OComplex @ B @ A )
= ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) )
=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) )
& ( ( ( B
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
=> ( ( c_Complex_Ocomplex_OComplex @ B @ A )
= ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(1182,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1__left) ).
thf(4863,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182]) ).
thf(601,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mult__distrib) ).
thf(2834,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(1005,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__asym_H) ).
thf(4189,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(647,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
=> ( c_SEQ_Omonoseq @ tc_RealDef_Oreal @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_monoseq__realpow) ).
thf(2993,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
=> ( c_SEQ_Omonoseq @ tc_RealDef_Oreal @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(392,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( A != B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I11_J) ).
thf(2191,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( A != B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(1205,axiom,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less2) ).
thf(4940,plain,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1205]) ).
thf(296,axiom,
class_Power_Opower @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Power_Opower) ).
thf(1912,plain,
class_Power_Opower @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(660,axiom,
class_Groups_Omonoid__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__add) ).
thf(3035,plain,
class_Groups_Omonoid__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(816,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ D ) @ C ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
thf(3575,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ D ) @ C ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(544,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).
thf(2655,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(946,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
thf(4002,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
| ( B = A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B ) @ A ) )
| ( B = A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(12405,plain,
$false,
inference(e,[status(thm)],[2163,2452,4447,1411,1469,1633,3661,3930,1559,3927,2199,1665,2822,2630,4450,3345,4464,2336,4824,1454,3666,4022,3698,3979,1315,2787,1850,4877,1818,1956,1950,2280,1554,1686,2250,3185,3990,2622,2953,3098,2676,1728,4603,2837,4326,1305,3382,1855,2077,4043,3534,2309,2512,2976,3072,1924,2940,1406,4226,4500,1290,1882,1522,3762,2644,3230,2381,5069,2395,2062,5000,2776,3417,1618,3285,3377,3153,1422,1569,1939,2282,1591,1971,1533,4408,4973,4747,4592,1788,1671,1655,2686,1756,3367,4011,4856,1327,2168,4294,1954,2575,3794,1608,3049,3745,2740,2918,4110,1867,1999,3446,2434,2712,3253,1988,1640,2580,4762,1458,3335,1746,4792,1782,3502,2227,3513,3777,1613,3466,4198,1475,4467,1482,1887,3836,4343,3545,2723,4142,2046,4371,4079,1441,4266,2010,1935,1645,1921,3809,1366,4963,2825,1529,4156,1803,2136,4610,1703,3688,2869,3891,4238,4546,4348,2814,3275,2269,2708,1907,3653,4275,3089,5108,4243,2603,2916,4866,4896,3644,3131,4956,3116,2667,2339,3046,1511,3485,2682,1826,1455,3280,4568,3353,1462,4428,2745,2571,2356,1800,1379,2857,1890,1479,2158,1773,1963,5077,1847,4595,2049,2552,2373,1347,3919,1741,4830,3084,2929,2635,5052,3312,1568,3902,3657,1931,3734,3014,4952,4507,1875,1778,4514,2533,4253,3268,3199,4258,2650,3702,5032,4783,1283,2222,4411,1489,4696,4205,1302,1664,4329,3966,1714,4903,5084,1450,4018,3393,5013,1911,2782,2893,1632,4297,2880,4847,1858,1864,4815,4724,1383,4134,1960,4798,4115,1581,2335,3771,3851,1928,2833,3712,1447,4996,4825,1943,1600,2205,5045,3389,1843,2058,4055,4230,3685,1886,4504,1796,3036,2530,4364,4087,2979,1526,4307,3676,3361,2002,3955,3243,2809,2242,2286,4038,3327,1433,2750,1405,3588,4892,1697,3211,2392,4588,1696,3184,4475,2586,2884,4082,4065,3435,1651,4853,3857,1691,1438,3984,4531,3635,4076,4910,4172,5122,1604,3899,2910,4323,3591,4589,4407,3995,5117,1470,1915,1708,1311,2296,2307,2496,2790,2660,1768,1274,4915,2541,2133,2147,3742,3134,3339,5049,2589,1387,1900,3827,2428,2733,2560,3972,2596,3867,3233,3884,1824,3816,2150,1370,2032,5102,4160,2528,3664,3207,3682,3286,1883,1560,3271,2628,4608,2477,3578,2872,1296,2179,1787,1656,2211,3647,1910,3191,2758,2873,1837,3269,3618,4725,1968,2663,2332,4155,3314,2820,3499,3750,3349,3556,1687,1457,3894,2068,1819,1624,5038,3144,2327,2213,4740,2345,1634,4461,3667,1573,3799,1402,1983,4512,1328,2577,1587,1425,3518,3386,4930,5081,1350,1936,4123,1360,1592,3784,3909,3782,3615,1541,3831,2840,3482,1762,1270,1772,5098,2946,2990,2895,4248,1375,4486,3218,4544,2509,4233,1672,3704,3632,3119,4840,3078,4883,3205,4219,3176,3087,1567,4518,1361,4983,1292,2830,3728,3596,2419,2240,3032,3671,4444,3573,1419,1493,1683,3141,2877,1964,1942,1659,3922,3000,4582,4167,4425,4315,3441,2312,3010,4750,4191,1584,1810,2172,2038,1446,1612,4621,4180,2317,3294,1744,3126,1451,1552,2465,4540,1852,2862,2052,3064,2370,4804,3242,1825,5063,1324,2504,1776,3611,2450,2125,3654,1539,1382,2900,1831,1668,1974,2355,1932,5058,4717,1947,4120,3628,1874,5026,4069,4416,3364,3162,3201,4223,1759,1393,3802,1814,1779,4966,3173,1563,2748,1466,4906,2617,1996,1732,4163,3147,3476,1333,3755,4535,4148,1857,1991,3834,1318,2546,3563,4195,3999,1286,2189,3422,2995,5126,2662,2121,3707,2413,2176,4470,2253,1273,3262,3289,5095,4269,2260,4921,1906,2936,1648,4872,1680,1698,1959,4354,3491,1483,3079,2570,4256,4438,1747,3839,3523,4577,3792,3696,4489,2524,3396,4453,4998,2859,3811,4032,2806,1403,2398,2716,4946,3599,3536,4943,4041,4144,3372,4341,3070,2225,3504,4283,1615,5065,2657,2188,2981,5067,1652,1929,2674,2016,2514,3272,4801,1520,2817,5022,1488,3796,4978,3726,4112,4413,4764,2706,2166,3641,2425,3568,1638,1675,3532,1428,3223,1786,3023,1669,2220,3964,2029,4096,5118,2293,3051,1635,4822,1733,3594,5086,1997,2759,2753,3487,2055,2358,2319,4433,2573,3719,3678,2079,3101,2119,2679,4369,2229,2493,1806,3957,4300,3384,2065,3996,2538,1408,2084,2214,2637,3551,2422,2955,1492,1603,2299,2669,4139,3710,4958,4616,3197,2378,4374,1571,1376,2197,4107,2180,4203,4430,5035,2742,1557,1630,1731,4985,2446,4332,1344,2461,1339,2605,3027,3668,4833,2267,4028,3165,1862,4208,3977,2410,2923,1838,1325,2785,4850,1556,1460,1293,4993,2553,2842,1952,3150,2329,2171,1445,3917,2139,2390,3178,2207,2693,2770,4933,4844,1841,1396,4232,2350,2725,1699,2765,2481,4502,1643,4085,2369,4362,3674,4827,2931,5042,2288,2592,2752,1435,4918,2633,2022,4703,2535,1496,4196,2984,4481,4158,2506,3380,1873,4458,4735,1340,1472,1958,1551,1413,3881,1626,3522,3444,2239,4441,4136,2614,3936,2107,2271,4456,2652,4598,3981,1684,1277,2234,4292,1509,1990,3048,4566,2684,2202,2846,2256,2942,3737,4035,3842,4272,3082,3214,1566,1647,3659,2882,2567,1845,4360,3507,4937,1611,5111,1605,2588,3462,4200,5074,1368,3228,1780,3209,2407,3786,4894,4961,3872,4377,5079,1531,3608,1484,3448,3305,2920,3202,1785,3475,4145,1980,1579,5062,1711,1499,2569,3246,4561,4346,4240,4092,1790,2454,1813,1300,3691,1637,5015,4020,3774,1317,1830,4351,1901,3828,4132,1538,2701,3412,3564,3359,3329,4737,2044,1285,3041,1336,3769,4875,2247,1934,2500,1536,4976,1284,4150,3398,1617,1898,1849,2113,3415,4436,2543,4246,1353,4510,2843,1485,1972,4106,4046,4538,1427,1670,1797,4093,2860,2728,4225,1372,4838,5083,5100,4795,3156,3914,3520,2848,2435,3400,3457,2088,2696,2828,2209,4078,4574,3168,1940,4289,4278,3139,3620,3757,2479,1321,1834,1913,3188,3548,2194,2347,1654,2215,4559,2997,2490,2110,1390,2305,1575,1734,1807,1646,3911,2174,1341,2532,4250,1745,2971,4338,4969,3465,1590,3613,4913,4710,2594,3789,2855,1639,2290,3825,1903,5008,4089,4468,3220,4542,2811,4715,1629,3104,2004,2608,2431,3003,1822,4834,3516,1523,3136,5104,2526,4527,2416,3780,1558,2934,2152,2262,4261,3085,3324,1777,4759,1440,4478,1706,2183,1661,4074,2739,3420,2447,2944,1689,2081,3181,3694,4321,2041,4175,4153,3879,1294,5040,5072,3351,3993,1994,4306,4025,2019,4619,3992,1512,2155,3987,3337,4367,2123,2218,4125,2258,4880,1348,2302,2517,1725,1280,1578,1957,3860,1678,3291,4356,1593,3837,1380,2736,1986,4491,3496,4579,2768,1859,1816,4981,3875,1789,2366,1710,1473,4029,4178,4303,3897,1363,1314,4281,3347,3277,1693,5019,3716,2913,2404,2714,3426,3030,3765,4193,2619,4318,2549,2353,4923,2731,1268,1378,2467,3489,5060,4936,3939,4955,2502,4848,3128,1977,3974,3025,3570,4972,1384,3605,1582,2265,1976,1550,4506,2583,4066,3392,4229,5046,1925,4713,2864,3740,1431,4071,1902,2484,3812,1399,1621,4335,3437,1944,4584,3924,4767,2690,2866,3432,3553,3296,1870,3753,4533,3013,1331,1606,3854,1737,2438,4752,4742,4313,1769,4423,4908,4056,4863,2834,4189,2993,2191,4940,1912,3035,3575,2655,4002]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW208+1 : TPTP v8.1.2. Released v5.2.0.
% 0.13/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n011.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu May 18 22:11:49 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.96/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.77/1.15 % [INFO] Parsing done (280ms).
% 1.77/1.15 % [INFO] Running in sequential loop mode.
% 2.55/1.36 % [INFO] eprover registered as external prover.
% 2.55/1.36 % [INFO] cvc4 registered as external prover.
% 2.55/1.36 % [INFO] Scanning for conjecture ...
% 3.17/1.52 % [INFO] Found a conjecture and 1268 axioms. Running axiom selection ...
% 4.12/1.75 % [INFO] Axiom selection finished. Selected 1265 axioms (removed 3 axioms).
% 5.43/2.15 % [INFO] Problem is first-order (TPTP FOF).
% 5.43/2.18 % [INFO] Type checking passed.
% 5.43/2.18 % [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 ...
% 54.44/13.29 % External prover 'e' found a proof!
% 54.44/13.29 % [INFO] Killing All external provers ...
% 54.44/13.29 % Time passed: 12765ms (effective reasoning time: 12137ms)
% 54.44/13.29 % 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)>
% 54.44/13.30 % Axioms used in derivation (1265): fact_xt1_I1_J, fact_monoseq__def, arity_fun__Orderings_Oorder, fact_le__imp__diff__is__add, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_power__abs, fact_Re__cis, fact_divide_Oconvergent, fact_natfloor__power, fact_zle__refl, fact_add__le__less__mono, fact_mult__strict__left__mono__neg, fact_order__le__neq__trans, fact_Nat_Oadd__0__right, fact_right__inverse__eq, fact_real__squared__diff__one__factored, fact_div__mult__mult1, fact_le__SucI, arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra, arity_Polynomial__Opoly__Rings_Osemiring__0, fact_abs__of__pos, fact_real__le__refl, arity_Complex__Ocomplex__Rings_Oidom, fact_nat_Osimps_I3_J, fact_real__less__def, arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_mult__right__le__imp__le, arity_Nat__Onat__Groups_Ocancel__semigroup__add, fact_real__le__trans, fact_power__strict__decreasing, arity_Complex__Ocomplex__Groups_Omonoid__add, arity_Int__Oint__Rings_Ocomm__semiring, fact_natfloor__real__of__nat, fact_pos__add__strict, arity_Int__Oint__Rings_Osemiring, arity_RealDef__Oreal__Orderings_Oord, fact_add__strict__right__mono, arity_Int__Oint__Orderings_Olinorder, fact_abs__sin__le__one, fact_Re_Oadd, fact_conv1, fact_natfloor__add, fact_mult__1__left, fact_diff__0__eq__0, fact_Im_Oconvergent, fact_zdiv__eq__0__iff, fact_abs__Re__le__cmod, fact_diff__add__inverse, fact_abs__minus__commute, fact_xt1_I4_J, arity_RealDef__Oreal__Groups_Ozero, fact_trans__less__add1, fact_mult__nonneg__nonpos, fact_q__pos__lemma, fact_abs__ge__self, arity_RealDef__Oreal__Rings_Oordered__comm__semiring, arity_Complex__Ocomplex__Groups_Oab__group__add, fact_diff__0__right, fact_mult__less__cancel__left__disj, fact_nat__add__left__commute, fact_real__mult__left__cancel, fact_Bseq__monoseq__convergent, fact_mult__nonpos__nonpos, fact_order__le__less__trans, fact_power__power__power, fact_real__of__nat__zero, arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors, fact_real__sgn__eq, fact_power__inject__base, fact_norm__power, fact_sin__le__one, fact_le__eq__less__or__eq, arity_Nat__Onat__Rings_Ono__zero__divisors, fact_nat__less__cases, fact_one__is__add, fact_diff__le__mono2, arity_Int__Oint__Rings_Olinordered__semiring__strict, arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add, fact_Complex__eq__1, fact_real__of__nat__diff, fact_termination__basic__simps_I5_J, arity_Polynomial__Opoly__Rings_Ocomm__semiring__0, fact_norm__mult__less, fact_odd__nonzero, fact_mult_Opos__bounded, fact_norm__diff__triangle__ineq, fact_Im_Opos__bounded, fact_mult__eq__0__iff, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, fact_Re_Ononneg__bounded, fact_less__imp__le__nat, fact_combine__common__factor, fact_le__imp__0__less, fact_add__leD1, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, fact_add__less__mono, fact_lemma__interval, fact_mult__0, fact_cis__def, arity_Nat__Onat__Orderings_Oorder, fact_mult__right__less__imp__less, fact_complex__zero__def, fact_abs__eq__mult, fact_split__mult__neg__le, fact_n__less__m__mult__n, fact_ln__eq__zero__iff, fact_ln__inj__iff, fact_Suc__mono, fact_zero__less__power, arity_Nat__Onat__Rings_Ocomm__semiring__0, fact_psize__eq__0__iff, arity_Nat__Onat__Groups_Oordered__comm__monoid__add, fact_less__nat__zero__code, arity_RealDef__Oreal__Rings_Osemiring__0, arity_RealDef__Oreal__Rings_Olinordered__ring, fact_linorder__not__le, arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le, fact_mult__le__less__imp__less, fact_zadd__commute, fact_BseqD, fact_natceiling__le, fact_ln__less__cancel__iff, arity_Nat__Onat__Groups_Omonoid__mult, fact_diff__Suc__less, fact_complex__add, fact_power__increasing, fact_abs__triangle__ineq2__sym, fact_order__less__asym_H, arity_Polynomial__Opoly__Rings_Olinordered__ring__strict, fact_norm__add__less, arity_Nat__Onat__Rings_Ozero__neq__one, fact_div__nonpos__pos__le0, arity_Polynomial__Opoly__Groups_Oab__semigroup__mult, fact_linorder__antisym__conv2, fact_zero__less__diff, fact_mult__mono, fact_complex__Re__le__cmod, fact_gr0__conv__Suc, fact_linorder__neqE, fact_leI, fact_field__power__not__zero, fact_natceiling__le__eq__one, arity_RealDef__Oreal__Rings_Oidom, fact_Suc__le__mono, fact_zero__le__natfloor, fact_order__eq__refl, fact_zero__le__zpower__abs, fact_add__right__imp__eq, fact_realpow__two__diff, arity_Complex__Ocomplex__Groups_Oab__semigroup__mult, arity_Polynomial__Opoly__Rings_Oidom, fact_BseqI, fact_diff__diff__cancel, fact_mult_Ononneg__bounded, fact_nat__add__right__cancel, fact_cos__one__sin__zero, arity_RealDef__Oreal__Groups_Omonoid__add, fact_div__le__dividend, fact_cos__n__Re__cis__pow__n, fact_abs__diff__triangle__ineq, fact_mult__le__mono2, fact_Suc__diff__diff, fact_mult_Oadd__right, fact_le__neq__implies__less, arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add, arity_Polynomial__Opoly__Rings_Ocomm__ring, fact_zle__linear, fact_lemma__NBseq__def2, fact_zero__le__one, fact_cis__zero, fact_nat__add__left__cancel__less, fact_int__0__less__1, fact_complex__Im__i, help_c__COMBC__1, fact_mult__left_Ononneg__bounded, fact_le__add__iff2, fact_mult__eq__self__implies__10, fact_complex_Osize_I2_J, fact_mult__left__le__imp__le, fact_add__pos__nonneg, fact_complex__Re__mult, fact_complex__Im__one, arity_Int__Oint__Orderings_Oord, arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add, fact_sin__cos__squared__add3, arity_RealDef__Oreal__Rings_Ocomm__ring__1, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_linorder__antisym__conv3, fact_add__strict__increasing2, fact_order__less__imp__not__eq, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, fact_linorder__neqE__linordered__idom, arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero, fact_lemma__realpow__diff, arity_Polynomial__Opoly__Rings_Olinordered__semidom, fact_add__le__imp__le__left, arity_RealDef__Oreal__Fields_Ofield__inverse__zero, arity_Int__Oint__Groups_Ozero, fact_add__nonneg__eq__0__iff, fact_real__of__nat__zero__iff, arity_Complex__Ocomplex__Rings_Ocomm__semiring__1, arity_Polynomial__Opoly__Orderings_Olinorder, fact_seq__suble, fact_div__1, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J, fact_div__if, fact_abs__triangle__ineq2, fact_Re_Opos__bounded, fact_zadd__left__mono, fact_sum__squares__le__zero__iff, fact_divide__1, fact_mult__strict__left__mono, arity_Int__Oint__Rings_Olinordered__semiring__1__strict, fact_mult__right_Ozero, fact_mult__le__cancel__left__neg, fact_sum__squares__ge__zero, fact_add__increasing2, fact_zero__le__mult__iff, arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero, fact_split__div_H, fact_natceiling__mono, fact_linorder__antisym__conv1, arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add, fact_zdiv__zero, fact_mult_Ozero__left, fact_real__mult__commute, fact_split__div__lemma, fact_gr0I, fact_i__def, arity_Int__Oint__Rings_Olinordered__ring, fact_add__0__iff, fact_le__funD, fact_add__right__mono, arity_Int__Oint__Groups_Ocancel__comm__monoid__add, fact_nat__less__real__le, fact_real__of__nat__less__iff, fact_one__less__power, fact_power__strict__increasing, fact_real__mult__assoc, fact_power__one__over, fact_one__le__power, fact_even__less__0__iff, fact_self__quotient__aux1, fact_complex__i__not__zero, fact_power__commutes, fact_power__real__of__nat, fact_le__natfloor__eq__one, arity_Int__Oint__Groups_Ocomm__monoid__add, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, arity_RealDef__Oreal__Groups_Omonoid__mult, fact_add__0__left, fact_add__mono, fact_nonneg1__imp__zdiv__pos__iff, fact_add__eq__if, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_le__fun__def, fact_divide__eq__imp, arity_Polynomial__Opoly__Orderings_Oord, fact_reals__Archimedean4, arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add, fact_norm__triangle__ineq3, fact_abs__add__one__gt__zero, fact_lemma__NBseq__def, arity_Nat__Onat__Rings_Osemiring__0, fact_rabs__ratiotest__lemma, fact_diff__le__self, arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict, fact_mult__eq__1__iff, arity_Nat__Onat__Rings_Oordered__comm__semiring, fact_diff__Suc__eq__diff__pred, fact_nat__mult__1__right, arity_Complex__Ocomplex__Rings_Osemiring__0, fact_zero__le__power__abs, fact_Bseq__iff, fact_ord__less__eq__trans, fact_zero__reorient, fact_le__iff__add, fact_one__reorient, fact_diff__commute, fact_power__eq__0__iff, help_c__COMBS__1, fact_xt1_I9_J, fact_less__add__eq__less, fact_linorder__less__linear, arity_Polynomial__Opoly__Groups_Omonoid__add, fact_mult__left_Odiff, fact_eq__iff__diff__eq__0, fact_natceiling__zero, fact_order__less__imp__not__less, 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fact_add__is__0, fact_neg__imp__zdiv__nonneg__iff, fact_nat__diff__add__eq1, fact_termination__basic__simps_I3_J, fact_Im_Ononneg__bounded, arity_Int__Oint__Rings_Oordered__ring, fact_incseq__imp__monoseq, fact_power_Opower_Opower__Suc, fact_complex__diff, fact_abs__triangle__ineq4, fact_le__imp__less__Suc, fact_cos__arg__i__mult__zero__neg, fact_ln__div, fact_Deriv_Oadd__diff__add, fact_mult__right__mono, fact_xt1_I2_J, arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add, fact_add__0, fact_power__mono, fact_lemmaCauchy, fact_mult__le__mono1, fact_Divides_Otransfer__nat__int__function__closures_I1_J, arity_Polynomial__Opoly__Rings_Olinordered__semiring__1, fact_diff__add__0, fact_Im__rcis, fact_Zero__neq__Suc, fact_add__pos__pos, arity_Nat__Onat__Groups_Oab__semigroup__mult, fact_diff__cancel2, arity_Polynomial__Opoly__Rings_Oordered__ring, fact_nat__less__add__iff2, fact_add__nonneg__nonneg, fact_nat__eq__add__iff1, arity_RealDef__Oreal__Power_Opower, fact_Suc__eq__plus1, 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fact_abs__triangle__ineq, arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add, fact_le__mult__natfloor, fact_less__add__one, fact_mult__less__imp__less__right, fact_zero__neq__one, fact_norm__mult__ineq, fact_diff__eq__diff__less__eq, fact_add__leE, fact_natceiling__subtract, arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add, fact_diff__Suc__1, fact_add__less__le__mono, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J, arity_Polynomial__Opoly__Orderings_Opreorder, fact_real__of__nat__Suc__gt__zero, fact_real__two__squares__add__zero__iff, fact_power__less__power__Suc, arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero, arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors, fact_int__one__le__iff__zero__less, fact_zdiv__mono2, arity_Nat__Onat__Rings_Olinordered__semiring__strict, fact_natfloor__add__one, fact_power__eq__imp__eq__base, fact_less__Suc__eq, fact_nat__add__commute, arity_Int__Oint__Rings_Ono__zero__divisors, fact_monoseq__Suc, 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fact_ab__semigroup__add__class_Oadd__ac_I1_J, arity_RealDef__Oreal__Groups_Oab__semigroup__mult, arity_Int__Oint__Rings_Ozero__neq__one, arity_RealDef__Oreal__Fields_Ofield, arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_sin__zero, fact_ln__gt__zero, arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors, fact_power__0__Suc, fact_nat__less__le, arity_Complex__Ocomplex__RealVector_Oreal__normed__vector, fact_no__zero__divisors, fact_sgn__1__pos, fact_less__iff__diff__less__0, fact_mult__eq__if, fact_Bseq__ignore__initial__segment, fact_less__SucE, fact_le__cube, fact_zless__add1__eq, fact_linorder__cases, fact_real__natfloor__le, fact_xt1_I11_J, fact_add__less__mono1, fact_add__le__cancel__left, arity_Polynomial__Opoly__Rings_Olinordered__ring, fact_nonzero__norm__divide, fact_mult__sgn__abs, arity_RealDef__Oreal__Groups_Ogroup__add, arity_Polynomial__Opoly__Groups_Ocomm__monoid__add, fact_Re__rcis, fact_real__le__linear, arity_Complex__Ocomplex__Power_Opower, fact_ord__eq__le__trans, fact_f_I1_J, fact_Re_Obounded, fact_nonzero__eq__divide__eq, fact_realpow__Suc__le__self, fact_DERIV__mult__lemma, arity_RealDef__Oreal__Groups_Olinordered__ab__group__add, fact_less__diff__iff, fact_real__natfloor__gt__diff__one, fact_odd__less__0, arity_Int__Oint__Rings_Ocomm__semiring__0, fact_power__le__imp__le__base, fact_mult__1, fact_Bseq__def, fact_complex_Orecs, fact_real__of__nat__inject, fact_reals__Archimedean3, fact_norm__triangle__ineq2, arity_Int__Oint__Groups_Omonoid__add, fact_expi__add, fact_add__Suc__shift, fact_complex__add__def, fact_less__SucI, fact_Suc__not__Zero, fact_real__of__nat__add, fact_ln__gt__zero__iff, fact_xt1_I7_J, fact_order__trans, arity_Complex__Ocomplex__Groups_Ozero, arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add, fact_not__square__less__zero, fact_Suc__lessI, fact_add__Suc__right, fact_less__bin__lemma, arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add, arity_Int__Oint__Rings_Olinordered__ring__strict, fact_mult_Odiff__right, fact_zdiv__mono2__neg__lemma, fact_cmod__unit__one, fact_ln__one, fact_natfloor__mono, fact_ln__ge__zero__iff, arity_Complex__Ocomplex__Rings_Ocomm__semiring__0, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, fact_mult__left_Oconvergent, arity_Int__Oint__Orderings_Opreorder, fact_divide__self, fact_nonzero__power__divide
% 54.44/13.30 % No. of inferences in proof: 2534
% 54.44/13.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 12765 ms resp. 12137 ms w/o parsing
% 55.59/13.71 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 55.83/13.72 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------