TSTP Solution File: SWW298+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW298+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n025.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 12:22:53 EDT 2023
% Result : Theorem 40.13s 11.36s
% Output : Refutation 41.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1465
% Syntax : Number of formulae : 2747 ( 773 unt; 185 typ; 0 def)
% Number of atoms : 6906 (2179 equ; 0 cnn)
% Maximal formula atoms : 26 ( 2 avg)
% Number of connectives : 62637 ( 634 ~; 169 |; 860 &;57659 @)
% ( 295 <=>;3020 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 413 ( 413 >; 0 *; 0 +; 0 <<)
% Number of symbols : 187 ( 185 usr; 19 con; 0-6 aty)
% Number of variables : 8737 ( 0 ^;8524 !; 213 ?;8737 :)
% Comments :
%------------------------------------------------------------------------------
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_member_type,type,
c_member: $i > $i ).
thf(tc_Hoare__Mirabelle_Otriple_type,type,
tc_Hoare__Mirabelle_Otriple: $i > $i ).
thf(t_a_type,type,
t_a: $i ).
thf(v_ts_type,type,
v_ts: $i ).
thf(c_Hoare__Mirabelle_Otriple__valid_type,type,
c_Hoare__Mirabelle_Otriple__valid: $i > $i > $i > $o ).
thf(v_n_type,type,
v_n: $i ).
thf(c_List_Odrop_type,type,
c_List_Odrop: $i > $i ).
thf(c_List_Oappend_type,type,
c_List_Oappend: $i > $i ).
thf(c_Groups_Ominus__class_Ominus_type,type,
c_Groups_Ominus__class_Ominus: $i > $i ).
thf(tc_Nat_Onat_type,type,
tc_Nat_Onat: $i ).
thf(c_Nat_Osize__class_Osize_type,type,
c_Nat_Osize__class_Osize: $i > $i ).
thf(tc_List_Olist_type,type,
tc_List_Olist: $i > $i ).
thf(tc_prod_type,type,
tc_prod: $i > $i > $i ).
thf(c_Product__Type_OPair_type,type,
c_Product__Type_OPair: $i > $i > $i ).
thf(c_List_Olistrel_type,type,
c_List_Olistrel: $i > $i > $i ).
thf(c_List_Ofoldl_type,type,
c_List_Ofoldl: $i > $i > $i > $i > $i ).
thf(c_List_Olist_ONil_type,type,
c_List_Olist_ONil: $i > $i ).
thf(c_Groups_Otimes__class_Otimes_type,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
thf(c_Groups_Ozero__class_Ozero_type,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
thf(c_Relation_Osym_type,type,
c_Relation_Osym: $i > $i > $o ).
thf(c_Orderings_Oord__class_Oless__eq_type,type,
c_Orderings_Oord__class_Oless__eq: $i > $i ).
thf(tc_Int_Oint_type,type,
tc_Int_Oint: $i ).
thf(c_Orderings_Oord__class_Oless_type,type,
c_Orderings_Oord__class_Oless: $i > $i ).
thf(c_Groups_Oplus__class_Oplus_type,type,
c_Groups_Oplus__class_Oplus: $i > $i ).
thf(c_Groups_Oone__class_Oone_type,type,
c_Groups_Oone__class_Oone: $i > $i ).
thf(c_List_Otake_type,type,
c_List_Otake: $i > $i ).
thf(c_List_Olist_OCons_type,type,
c_List_Olist_OCons: $i > $i ).
thf(c_List_Olexord_type,type,
c_List_Olexord: $i > $i > $i ).
thf(c_List_Ofilter_type,type,
c_List_Ofilter: $i > $i > $i ).
thf(c_List_Omap_type,type,
c_List_Omap: $i > $i > $i ).
thf(c_Fun_Ocomp_type,type,
c_Fun_Ocomp: $i > $i > $i > $i > $i ).
thf(tc_HOL_Obool_type,type,
tc_HOL_Obool: $i ).
thf(c_Nat_OSuc_type,type,
c_Nat_OSuc: $i ).
thf(c_List_OtakeWhile_type,type,
c_List_OtakeWhile: $i > $i > $i > $i ).
thf(c_List_Onth_type,type,
c_List_Onth: $i > $i ).
thf(c_Wellfounded_Oacyclic_type,type,
c_Wellfounded_Oacyclic: $i > $i > $o ).
thf(c_Set_OCollect_type,type,
c_Set_OCollect: $i > $i ).
thf(c_Product__Type_Oprod_Oprod__case_type,type,
c_Product__Type_Oprod_Oprod__case: $i > $i > $i > $i ).
thf(c_Predicate_Oconversep_type,type,
c_Predicate_Oconversep: $i > $i > $i > $i ).
thf(c_Divides_Odiv__class_Omod_type,type,
c_Divides_Odiv__class_Omod: $i > $i > $i > $i ).
thf(c_Divides_Odiv__class_Odiv_type,type,
c_Divides_Odiv__class_Odiv: $i > $i ).
thf(c_List_OdropWhile_type,type,
c_List_OdropWhile: $i > $i > $i > $i ).
thf(c_COMBK_type,type,
c_COMBK: $i > $i > $i ).
thf(c_Rings_Odvd__class_Odvd_type,type,
c_Rings_Odvd__class_Odvd: $i > $i ).
thf(c_List_Oremdups_type,type,
c_List_Oremdups: $i > $i > $i ).
thf(c_List_Olistrel1_type,type,
c_List_Olistrel1: $i > $i > $i ).
thf(c_fTrue_type,type,
c_fTrue: $i ).
thf(c_List_Oset_type,type,
c_List_Oset: $i > $i ).
thf(c_List_Odistinct_type,type,
c_List_Odistinct: $i > $i ).
thf(c_Finite__Set_Ocard_type,type,
c_Finite__Set_Ocard: $i > $i ).
thf(c_Predicate_Osymp_type,type,
c_Predicate_Osymp: $i > $i > $o ).
thf(c_Finite__Set_Ofinite_type,type,
c_Finite__Set_Ofinite: $i > $i ).
thf(c_SetInterval_Oord__class_OatLeastAtMost_type,type,
c_SetInterval_Oord__class_OatLeastAtMost: $i > $i > $i > $i ).
thf(c_Int_Onumber__class_Onumber__of_type,type,
c_Int_Onumber__class_Onumber__of: $i > $i ).
thf(class_Nat_Osize_type,type,
class_Nat_Osize: $i > $o ).
thf(c_Relation_Otrans_type,type,
c_Relation_Otrans: $i > $i > $o ).
thf(c_Wellfounded_Owf_type,type,
c_Wellfounded_Owf: $i > $i > $o ).
thf(c_Wellfounded_Omeasure_type,type,
c_Wellfounded_Omeasure: $i > $i ).
thf(c_Transitive__Closure_Ortrancl_type,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
thf(c_SetInterval_Oord__class_OatLeastLessThan_type,type,
c_SetInterval_Oord__class_OatLeastLessThan: $i > $i > $i ).
thf(c_SetInterval_Oord__class_OgreaterThanLessThan_type,type,
c_SetInterval_Oord__class_OgreaterThanLessThan: $i > $i > $i > $i ).
thf(c_List_Ozip_type,type,
c_List_Ozip: $i > $i > $i ).
thf(c_fequal_type,type,
c_fequal: $i ).
thf(c_List_Obutlast_type,type,
c_List_Obutlast: $i > $i > $i ).
thf(c_List_Olist__ex_type,type,
c_List_Olist__ex: $i > $i > $i > $o ).
thf(c_List_Oupt_type,type,
c_List_Oupt: $i > $i > $i ).
thf(c_fFalse_type,type,
c_fFalse: $i ).
thf(c_Predicate_Otransp_type,type,
c_Predicate_Otransp: $i > $i > $o ).
thf(c_List_Olist__all_type,type,
c_List_Olist__all: $i > $i > $i > $o ).
thf(class_Enum_Oenum_type,type,
class_Enum_Oenum: $i > $o ).
thf(c_FunDef_Opair__less_type,type,
c_FunDef_Opair__less: $i ).
thf(c_Wellfounded_OwfP_type,type,
c_Wellfounded_OwfP: $i > $i > $o ).
thf(c_SetInterval_Oord__class_OgreaterThanAtMost_type,type,
c_SetInterval_Oord__class_OgreaterThanAtMost: $i > $i > $i > $i ).
thf(c_Wellfounded_Omlex__prod_type,type,
c_Wellfounded_Omlex__prod: $i > $i > $i > $i ).
thf(c_Relation_Orel__comp_type,type,
c_Relation_Orel__comp: $i > $i > $i > $i ).
thf(c_Relation_Orefl__on_type,type,
c_Relation_Orefl__on: $i > $i > $i > $o ).
thf(c_Relation_Oconverse_type,type,
c_Relation_Oconverse: $i > $i > $i ).
thf(c_Relation_Ototal__on_type,type,
c_Relation_Ototal__on: $i > $i > $i > $o ).
thf(c_Transitive__Closure_Otrancl_type,type,
c_Transitive__Closure_Otrancl: $i > $i > $i ).
thf(c_Relation_Oinv__image_type,type,
c_Relation_Oinv__image: $i > $i > $i ).
thf(c_Relation_OId__on_type,type,
c_Relation_OId__on: $i > $i > $i ).
thf(c_Finite__Set_Ofolding__image__simple_type,type,
c_Finite__Set_Ofolding__image__simple: $i > $i > $i > $i > $i > $i > $o ).
thf(c_Finite__Set_Ofold__image_type,type,
c_Finite__Set_Ofold__image: $i > $i > $i > $i ).
thf(c_Relation_ORange_type,type,
c_Relation_ORange: $i > $i > $i ).
thf(c_Relation_ODomain_type,type,
c_Relation_ODomain: $i > $i > $i ).
thf(c_Relation_Oantisym_type,type,
c_Relation_Oantisym: $i > $i > $o ).
thf(c_Relation_OId_type,type,
c_Relation_OId: $i > $i ).
thf(c_List_Olistsp_type,type,
c_List_Olistsp: $i > $i > $i ).
thf(c_List_Osublist_type,type,
c_List_Osublist: $i > $i > $i > $i ).
thf(c_Finite__Set_Ofun__left__comm_type,type,
c_Finite__Set_Ofun__left__comm: $i > $i > $i > $o ).
thf(c_Finite__Set_Ofold_type,type,
c_Finite__Set_Ofold: $i > $i > $i > $i ).
thf(c_Set_Oinsert_type,type,
c_Set_Oinsert: $i > $i ).
thf(c_SetInterval_Oord__class_OatMost_type,type,
c_SetInterval_Oord__class_OatMost: $i > $i ).
thf(c_Wellfounded_Opred__nat_type,type,
c_Wellfounded_Opred__nat: $i ).
thf(c_Fun_Oinj__on_type,type,
c_Fun_Oinj__on: $i > $i > $i > $i > $o ).
thf(c_Set_Oimage_type,type,
c_Set_Oimage: $i > $i > $i > $i ).
thf(c_Product__Type_Omap__pair_type,type,
c_Product__Type_Omap__pair: $i > $i > $i > $i > $i > $i > $i ).
thf(c_List_Oinsert_type,type,
c_List_Oinsert: $i > $i > $i > $i ).
thf(c_Fun_Ofun__upd_type,type,
c_Fun_Ofun__upd: $i > $i > $i > $i > $i > $i ).
thf(c_Divides_Odivmod__nat__rel_type,type,
c_Divides_Odivmod__nat__rel: $i > $i > $i ).
thf(c_Finite__Set_Ofold__graph_type,type,
c_Finite__Set_Ofold__graph: $i > $i > $i > $i > $i > $i ).
thf(c_Equiv__Relations_Oequiv_type,type,
c_Equiv__Relations_Oequiv: $i > $i > $i > $o ).
thf(c_Finite__Set_Ofolding__one_type,type,
c_Finite__Set_Ofolding__one: $i > $i > $i > $o ).
thf(class_Orderings_Owellorder_type,type,
class_Orderings_Owellorder: $i > $o ).
thf(c_Wellfounded_Oacc_type,type,
c_Wellfounded_Oacc: $i > $i > $i ).
thf(c_Wellfounded_Olex__prod_type,type,
c_Wellfounded_Olex__prod: $i > $i > $i > $i > $i ).
thf(c_List_OremoveAll_type,type,
c_List_OremoveAll: $i > $i > $i ).
thf(c_Relation_OField_type,type,
c_Relation_OField: $i > $i ).
thf(c_SetInterval_Oord__class_OlessThan_type,type,
c_SetInterval_Oord__class_OlessThan: $i > $i ).
thf(c_List_Oremove1_type,type,
c_List_Oremove1: $i > $i > $i > $i ).
thf(c_List_Olistrelp_type,type,
c_List_Olistrelp: $i > $i > $i > $i > $o ).
thf(c_Divides_Odivmod__nat_type,type,
c_Divides_Odivmod__nat: $i > $i > $i ).
thf(c_List_Olist__ex1_type,type,
c_List_Olist__ex1: $i > $i > $i > $o ).
thf(c_Set_Ovimage_type,type,
c_Set_Ovimage: $i > $i > $i > $i ).
thf(c_Wellfounded_Oaccp_type,type,
c_Wellfounded_Oaccp: $i > $i > $i ).
thf(c_Nitpick_Onat__gcd__rel_type,type,
c_Nitpick_Onat__gcd__rel: $i ).
thf(c_Relation_Osingle__valued_type,type,
c_Relation_Osingle__valued: $i > $i > $i > $o ).
thf(c_Nitpick_Opair__box_Opair__box__size_type,type,
c_Nitpick_Opair__box_Opair__box__size: $i > $i > $i > $i > $i > $i ).
thf(c_Nitpick_Opair__box_OPairBox_type,type,
c_Nitpick_Opair__box_OPairBox: $i > $i > $i > $i > $i ).
thf(c_Relation_OImage_type,type,
c_Relation_OImage: $i > $i > $i > $i ).
thf(c_Predicate_Opred__comp_type,type,
c_Predicate_Opred__comp: $i > $i > $i > $i > $i > $i ).
thf(c_Finite__Set_Ofold1_type,type,
c_Finite__Set_Ofold1: $i > $i > $i ).
thf(c_HOL_OThe_type,type,
c_HOL_OThe: $i > $i > $i ).
thf(c_Finite__Set_Ofold1Set_type,type,
c_Finite__Set_Ofold1Set: $i > $i > $i > $i ).
thf(c_Equiv__Relations_Ocongruent2_type,type,
c_Equiv__Relations_Ocongruent2: $i > $i > $i > $i > $i > $i > $o ).
thf(c_Equiv__Relations_Opart__equivp_type,type,
c_Equiv__Relations_Opart__equivp: $i > $i > $o ).
thf(c_Finite__Set_Ofolding__image__simple__idem_type,type,
c_Finite__Set_Ofolding__image__simple__idem: $i > $i > $i > $i > $i > $i > $o ).
thf(c_Equiv__Relations_Oequivp_type,type,
c_Equiv__Relations_Oequivp: $i > $i > $o ).
thf(c_Predicate_Oreflp_type,type,
c_Predicate_Oreflp: $i > $i > $o ).
thf(c_Fun_Othe__inv__into_type,type,
c_Fun_Othe__inv__into: $i > $i > $i > $i > $i ).
thf(c_List_Omember_type,type,
c_List_Omember: $i > $i ).
thf(c_Recdef_Osame__fst_type,type,
c_Recdef_Osame__fst: $i > $i > $i > $i > $i ).
thf(c_Product__Type_OSigma_type,type,
c_Product__Type_OSigma: $i > $i > $i ).
thf(c_FunDef_Oin__rel_type,type,
c_FunDef_Oin__rel: $i > $i > $i > $i ).
thf(c_Equiv__Relations_Ocongruent_type,type,
c_Equiv__Relations_Ocongruent: $i > $i > $i > $i > $o ).
thf(c_Orderings_Oord__class_OLeast_type,type,
c_Orderings_Oord__class_OLeast: $i > $i > $i ).
thf(c_New__Random__Sequence_Opos__empty_type,type,
c_New__Random__Sequence_Opos__empty: $i > $i > $i > $i > $i ).
thf(c_New__DSequence_Opos__empty_type,type,
c_New__DSequence_Opos__empty: $i > $i ).
thf(c_Big__Operators_Ocomm__monoid__big_type,type,
c_Big__Operators_Ocomm__monoid__big: $i > $i > $i > $i > $i > $o ).
thf(c_Finite__Set_Ofolding__one__idem_type,type,
c_Finite__Set_Ofolding__one__idem: $i > $i > $i > $o ).
thf(c_Hilbert__Choice_OEps_type,type,
c_Hilbert__Choice_OEps: $i > $i > $i ).
thf(c_Predicate_ORangeP_type,type,
c_Predicate_ORangeP: $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OatLeast_type,type,
c_SetInterval_Oord_OatLeast: $i > $i > $i > $i ).
thf(c_Hilbert__Choice_Oinv__into_type,type,
c_Hilbert__Choice_Oinv__into: $i > $i > $i > $i > $i ).
thf(c_Typedef_Otype__definition_type,type,
c_Typedef_Otype__definition: $i > $i > $i > $i > $i > $o ).
thf(c_SetInterval_Oord_OatLeastLessThan_type,type,
c_SetInterval_Oord_OatLeastLessThan: $i > $i > $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OlessThan_type,type,
c_SetInterval_Oord_OlessThan: $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OatMost_type,type,
c_SetInterval_Oord_OatMost: $i > $i > $i > $i ).
thf(c_fNot_type,type,
c_fNot: $i ).
thf(c_SetInterval_Oord_OatLeastAtMost_type,type,
c_SetInterval_Oord_OatLeastAtMost: $i > $i > $i > $i > $i ).
thf(c_fimplies_type,type,
c_fimplies: $i ).
thf(c_Predicate_OPowp_type,type,
c_Predicate_OPowp: $i > $i > $i ).
thf(c_Nitpick_Opair__box_Opair__box__rec_type,type,
c_Nitpick_Opair__box_Opair__box__rec: $i > $i > $i > $i > $i > $i ).
thf(c_New__Random__Sequence_Oneg__single_type,type,
c_New__Random__Sequence_Oneg__single: $i > $i ).
thf(c_New__DSequence_Oneg__single_type,type,
c_New__DSequence_Oneg__single: $i > $i > $i ).
thf(c_FunDef_Oreduction__pair_type,type,
c_FunDef_Oreduction__pair: $i > $i > $o ).
thf(c_FunDef_Orp__inv__image_type,type,
c_FunDef_Orp__inv__image: $i > $i > $i ).
thf(c_SetInterval_Oord_OgreaterThanLessThan_type,type,
c_SetInterval_Oord_OgreaterThanLessThan: $i > $i > $i > $i > $i ).
thf(c_Lazy__Sequence_Ohb__single_type,type,
c_Lazy__Sequence_Ohb__single: $i > $i > $i ).
thf(c_New__DSequence_Opos__single_type,type,
c_New__DSequence_Opos__single: $i > $i > $i ).
thf(c_Lazy__Sequence_Osingle_type,type,
c_Lazy__Sequence_Osingle: $i > $i ).
thf(c_fdisj_type,type,
c_fdisj: $i ).
thf(c_New__Random__Sequence_Opos__union_type,type,
c_New__Random__Sequence_Opos__union: $i > $i > $i > $i > $i > $i > $i ).
thf(c_New__DSequence_Opos__union_type,type,
c_New__DSequence_Opos__union: $i > $i > $i > $i ).
thf(c_FunDef_OTHE__default_type,type,
c_FunDef_OTHE__default: $i > $i > $i > $i ).
thf(c_Nitpick_Opair__box_Opair__box__case_type,type,
c_Nitpick_Opair__box_Opair__box__case: $i > $i > $i > $i > $i > $i ).
thf(c_fconj_type,type,
c_fconj: $i ).
thf(c_SetInterval_Oord_OgreaterThanAtMost_type,type,
c_SetInterval_Oord_OgreaterThanAtMost: $i > $i > $i > $i > $i > $i ).
thf(c_New__Random__Sequence_Opos__single_type,type,
c_New__Random__Sequence_Opos__single: $i > $i ).
thf(c_Relation_Oirrefl_type,type,
c_Relation_Oirrefl: $i > $i > $o ).
thf(c_Enum_Oenum__class_Oenum__all_type,type,
c_Enum_Oenum__class_Oenum__all: $i > $i ).
thf(c_New__Random__Sequence_Opos__not__random__dseq_type,type,
c_New__Random__Sequence_Opos__not__random__dseq: $i > $i > $i > $i > $i ).
thf(c_New__DSequence_Opos__not__seq_type,type,
c_New__DSequence_Opos__not__seq: $i > $i ).
thf(c_Product__Type_Oprod_Oprod__rec_type,type,
c_Product__Type_Oprod_Oprod__rec: $i > $i > $i > $i > $i > $i ).
thf(c_Enum_Oenum__class_Oenum__ex_type,type,
c_Enum_Oenum__class_Oenum__ex: $i > $i ).
thf(c_SetInterval_Oord_OgreaterThan_type,type,
c_SetInterval_Oord_OgreaterThan: $i > $i > $i > $i ).
thf(c_Predicate_ODomainP_type,type,
c_Predicate_ODomainP: $i > $i > $i > $i ).
thf(c_Lazy__Sequence_Oempty_type,type,
c_Lazy__Sequence_Oempty: $i > $i ).
thf(c_Big__Operators_Osemilattice__big_type,type,
c_Big__Operators_Osemilattice__big: $i > $i > $i > $o ).
thf(c_Int_ORep__Integ_type,type,
c_Int_ORep__Integ: $i ).
thf(c_Lazy__Sequence_Oappend_type,type,
c_Lazy__Sequence_Oappend: $i > $i > $i > $i ).
thf(c_Nitpick_Orefl_H_type,type,
c_Nitpick_Orefl_H: $i > $i > $o ).
thf(c_Hoare__Mirabelle_Ohoare__valids_type,type,
c_Hoare__Mirabelle_Ohoare__valids: $i > $i > $i > $o ).
thf(1001,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C ) ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ F @ E ) @ B ) @ A ) ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ D ) @ ( hAPP @ ( c_List_Oset @ F ) @ B ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ C ) @ ( hAPP @ ( c_List_Oset @ E ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__zipE) ).
thf(5385,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C ) ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ F @ E ) @ B ) @ A ) ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ D ) @ ( hAPP @ ( c_List_Oset @ F ) @ B ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ C ) @ ( hAPP @ ( c_List_Oset @ E ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(698,axiom,
! [A: $i,B: $i] :
( ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) )
<=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__nat__less__eq) ).
thf(4188,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) ) )
& ( ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(62,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__nonpos__pos__le0) ).
thf(1501,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( 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)],[62]) ).
thf(792,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ B )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__div__geq) ).
thf(4560,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ B )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(204,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) )
| ( B = A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__linear) ).
thf(2094,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) )
| ( B = A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(1046,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Ozip @ F @ E ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ F @ E ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__Cons__Cons) ).
thf(5561,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Ozip @ F @ E ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ F @ E ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).
thf(251,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ A ) @ B ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__antisym) ).
thf(2295,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ A ) @ B ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(1272,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ ( hAPP @ D @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ C ) @ ( hAPP @ ( c_Set_Ovimage @ A @ E @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimageI2) ).
thf(6530,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ ( hAPP @ D @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ C ) @ ( hAPP @ ( c_Set_Ovimage @ A @ E @ D ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1272]) ).
thf(198,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__drop) ).
thf(2072,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(264,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__mult__distrib) ).
thf(2412,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(1253,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__downward) ).
thf(6431,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1253]) ).
thf(1173,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__Collect__eq) ).
thf(6074,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ A @ B ) ) )
& ( ( hBOOL @ ( hAPP @ A @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173]) ).
thf(1157,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_New__DSequence_Oneg__single @ C @ B ) @ A )
= ( c_Lazy__Sequence_Ohb__single @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Oneg__single__def) ).
thf(6014,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_New__DSequence_Oneg__single @ C @ B ) @ A )
= ( c_Lazy__Sequence_Ohb__single @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).
thf(335,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel2) ).
thf(2744,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[335]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ B ) @ A ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ B ) @ D ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ B ) @ A ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__append) ).
thf(1369,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ B ) @ A ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ B ) @ D ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ B ) @ A ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(211,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( c_List_Ofilter @ C @ B ) @ A ) ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__filter__le) ).
thf(2109,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( c_List_Ofilter @ C @ B ) @ A ) ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(1054,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ D @ C )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__eq) ).
thf(5593,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ D @ C )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).
thf(187,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ F ) ) @ E )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) )
=> ( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ F ) ) @ B )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Ozip @ F @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ F ) @ E ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ ( tc_prod @ F @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ F @ D ) @ E ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ F @ D ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__append) ).
thf(2031,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ F ) ) @ E )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) )
=> ( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ F ) ) @ B )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Ozip @ F @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ F ) @ E ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ ( tc_prod @ F @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ F @ D ) @ E ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ F @ D ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(503,axiom,
! [A: $i,B: $i] :
( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__imp__le) ).
thf(3399,plain,
! [A: $i,B: $i] :
( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(179,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__one__le__iff__zero__less) ).
thf(1995,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[179]) ).
thf(246,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__add1__eq) ).
thf(2263,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) )
| ( B = A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) )
| ( B = A ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[246]) ).
thf(875,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Otrans @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ B ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transD) ).
thf(4899,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Otrans @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ B ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( c_List_OtakeWhile @ C @ B @ A ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ ( c_List_OtakeWhile @ C @ B @ A ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__nth) ).
thf(1559,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( c_List_OtakeWhile @ C @ B @ A ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ ( c_List_OtakeWhile @ C @ B @ A ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(834,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Otrans @ B @ A )
<=> ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ D ) ) @ A ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ D ) @ E ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ E ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__def) ).
thf(4729,plain,
! [A: $i,B: $i] :
( ( ( c_Relation_Otrans @ B @ A )
=> ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ D ) ) @ A ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ D ) @ E ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ E ) ) @ A ) ) ) ) )
& ( ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ D ) ) @ A ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ D ) @ E ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ E ) ) @ A ) ) ) )
=> ( c_Relation_Otrans @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(654,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ I @ H @ G @ F ) @ E )
= ( hAPP @ ( c_Fun_Ocomp @ D @ H @ G @ C ) @ B ) )
=> ( ( hAPP @ F @ ( hAPP @ E @ A ) )
= ( hAPP @ C @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__eq__dest) ).
thf(4022,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ I @ H @ G @ F ) @ E )
= ( hAPP @ ( c_Fun_Ocomp @ D @ H @ G @ C ) @ B ) )
=> ( ( hAPP @ F @ ( hAPP @ E @ A ) )
= ( hAPP @ C @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(115,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( c_List_OtakeWhile @ C @ B @ A ) ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__takeWhile__le) ).
thf(1729,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( c_List_OtakeWhile @ C @ B @ A ) ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(379,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofun__left__comm @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ ( hAPP @ ( hAPP @ D @ B ) @ A ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__insert2) ).
thf(2921,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofun__left__comm @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ ( hAPP @ ( hAPP @ D @ B ) @ A ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(722,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Osingle__valued @ E @ D @ C )
=> ( ( c_Relation_Osingle__valued @ D @ B @ A )
=> ( c_Relation_Osingle__valued @ E @ B @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ E @ D @ B ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__rel__comp) ).
thf(4290,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Osingle__valued @ E @ D @ C )
=> ( ( c_Relation_Osingle__valued @ D @ B @ A )
=> ( c_Relation_Osingle__valued @ E @ B @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ E @ D @ B ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(579,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ B @ B ) ) @ A ) )
=> ( ( c_Wellfounded_Oacyclic @ B @ A )
=> ( c_Wellfounded_Owf @ B @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__acyclic__wf__converse) ).
thf(3698,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ B @ B ) ) @ A ) )
=> ( ( c_Wellfounded_Oacyclic @ B @ A )
=> ( c_Wellfounded_Owf @ B @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(1003,axiom,
! [A: $i,B: $i] :
( ( c_HOL_OThe @ B @ ( hAPP @ c_fequal @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__sym__eq__trivial) ).
thf(5390,plain,
! [A: $i,B: $i] :
( ( c_HOL_OThe @ B @ ( hAPP @ c_fequal @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(1221,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__absorb) ).
thf(6285,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1221]) ).
thf(545,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Oacyclic @ B @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) )
<=> ( c_Wellfounded_Oacyclic @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclic__converse) ).
thf(3566,plain,
! [A: $i,B: $i] :
( ( ( c_Wellfounded_Oacyclic @ B @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) )
=> ( c_Wellfounded_Oacyclic @ B @ A ) )
& ( ( c_Wellfounded_Oacyclic @ B @ A )
=> ( c_Wellfounded_Oacyclic @ B @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(904,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc_OaccI) ).
thf(5028,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(934,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ D @ E ) )
=> ( c_Wellfounded_Owf @ C @ ( hAPP @ B @ E ) ) )
=> ( c_Wellfounded_Owf @ ( tc_prod @ A @ C ) @ ( c_Recdef_Osame__fst @ A @ C @ D @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__same__fst) ).
thf(5131,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ D @ E ) )
=> ( c_Wellfounded_Owf @ C @ ( hAPP @ B @ E ) ) )
=> ( c_Wellfounded_Owf @ ( tc_prod @ A @ C ) @ ( c_Recdef_Osame__fst @ A @ C @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(74,axiom,
( ( hAPP @ ( c_Nat_Osize__class_Osize @ tc_HOL_Obool ) @ c_fTrue )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bool_Osize_I3_J) ).
thf(1549,plain,
( ( hAPP @ ( c_Nat_Osize__class_Osize @ tc_HOL_Obool ) @ c_fTrue )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(1170,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_New__Random__Sequence_Opos__union @ F @ E @ D @ C @ B @ A )
= ( c_New__DSequence_Opos__union @ F @ ( hAPP @ ( hAPP @ ( hAPP @ E @ C ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( hAPP @ D @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__union__def) ).
thf(6057,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_New__Random__Sequence_Opos__union @ F @ E @ D @ C @ B @ A )
= ( c_New__DSequence_Opos__union @ F @ ( hAPP @ ( hAPP @ ( hAPP @ E @ C ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( hAPP @ D @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170]) ).
thf(1160,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Predicate_Osymp @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sympE) ).
thf(6022,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Predicate_Osymp @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).
thf(1193,axiom,
~ ( hBOOL @ c_fFalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fFalse__1) ).
thf(6162,plain,
~ ( hBOOL @ c_fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193]) ).
thf(611,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) )
<=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__nat__less) ).
thf(3813,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) )
=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) )
& ( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) )
=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(540,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ D ) @ C ) ) @ ( c_List_Olexord @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ C ) @ A ) ) @ ( c_List_Olexord @ E @ B ) ) )
=> ( ( c_Relation_Otrans @ E @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ D ) @ A ) ) @ ( c_List_Olexord @ E @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__trans) ).
thf(3549,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ D ) @ C ) ) @ ( c_List_Olexord @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ C ) @ A ) ) @ ( c_List_Olexord @ E @ B ) ) )
=> ( ( c_Relation_Otrans @ E @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ D ) @ A ) ) @ ( c_List_Olexord @ E @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(1125,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ B @ A ) @ ( c_Divides_Odivmod__nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel__divmod__nat) ).
thf(5878,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ B @ A ) @ ( c_Divides_Odivmod__nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).
thf(206,axiom,
hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_int__0__less__1) ).
thf(2099,plain,
hBOOL @ ( hAPP @ ( 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)],[206]) ).
thf(356,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ A ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ A ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ D ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bset_I8_J) ).
thf(2837,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ A ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ A ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ D ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(804,axiom,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Otrancl @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ B @ B @ B ) @ A ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__unfold__left) ).
thf(4614,plain,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Otrancl @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ B @ B @ B ) @ A ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(1158,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Predicate_Otransp @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpE) ).
thf(6017,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Predicate_Otransp @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).
thf(1060,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofolding__one @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) )
=> ( ( hAPP @ B @ A )
= ( hAPP @ ( c_Finite__Set_Ofold1 @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one_Oeq__fold) ).
thf(5614,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofolding__one @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) )
=> ( ( hAPP @ B @ A )
= ( hAPP @ ( c_Finite__Set_Ofold1 @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).
thf(1260,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Hoare__Mirabelle_Ohoare__valids @ C @ B @ A )
<=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ C ) ) @ E ) @ B ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ C @ D @ E ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ C ) ) @ E ) @ A ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ C @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hoare__valids__def) ).
thf(6480,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__valids @ C @ B @ A )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ C ) ) @ E ) @ B ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ C @ D @ E ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ C ) ) @ E ) @ A ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ C @ D @ E ) ) ) )
& ( ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ C ) ) @ E ) @ B ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ C @ D @ E ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ C ) ) @ E ) @ A ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ C @ D @ E ) ) )
=> ( c_Hoare__Mirabelle_Ohoare__valids @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1260]) ).
thf(771,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_List_Ofilter @ B @ A ) @ ( c_List_Olist_ONil @ B ) )
= ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter_Osimps_I1_J) ).
thf(4479,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_List_Ofilter @ B @ A ) @ ( c_List_Olist_ONil @ B ) )
= ( c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(147,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib) ).
thf(1855,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(200,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ A ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonneg1__imp__zdiv__pos__iff) ).
thf(2077,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ A ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ A ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(658,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ B ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ A ) ) )
=> ( ( c_List_Oupt @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ tc_Nat_Onat ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ B ) ) @ ( c_List_Oupt @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ B ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ A ) ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ B ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ A ) ) )
=> ( ( c_List_Oupt @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ A ) )
= ( c_List_Olist_ONil @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__rec__number__of) ).
thf(4043,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ B ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ A ) ) )
=> ( ( c_List_Oupt @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ tc_Nat_Onat ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ B ) ) @ ( c_List_Oupt @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ B ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ A ) ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ B ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ A ) ) )
=> ( ( c_List_Oupt @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ A ) )
= ( c_List_Olist_ONil @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(537,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__geq) ).
thf(3534,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(398,axiom,
! [A: $i] : ( c_Relation_Osym @ A @ ( c_Relation_OId @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sym__Id) ).
thf(2976,plain,
! [A: $i] : ( c_Relation_Osym @ A @ ( c_Relation_OId @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(742,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ) @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff__inverse2) ).
thf(4376,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(386,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).
thf(2940,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__pos__lemma) ).
thf(1406,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[39]) ).
thf(209,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__assoc) ).
thf(2104,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)],[209]) ).
thf(943,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_OwfP @ B @ ( c_FunDef_Oin__rel @ B @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__in__rel) ).
thf(5168,plain,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_OwfP @ B @ ( c_FunDef_Oin__rel @ B @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(707,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ E ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ B ) ) @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ E ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ B ) ) @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__append2) ).
thf(4226,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ E ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ B ) ) @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ E ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ B ) ) @ C ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(776,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diffs0__imp__equal) ).
thf(4500,plain,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(667,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_le__iff__add) ).
thf(4075,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(153,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ C ) @ A ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ B ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__take) ).
thf(1882,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ C ) @ A ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ B ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(728,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ C @ C @ B ) @ ( c_Relation_OId @ C ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__O__R) ).
thf(4311,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ C @ C @ B ) @ ( c_Relation_OId @ C ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(594,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__mono) ).
thf(3762,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__div__less__self) ).
thf(1443,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(508,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ E ) @ D )
= C )
=> ( ( B
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ F ) @ D ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ E ) @ B )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ F ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__eq__appendI) ).
thf(3417,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ E ) @ D )
= C )
=> ( ( B
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ F ) @ D ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ E ) @ B )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ F ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(961,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__into__trancl1) ).
thf(5242,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(475,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc1) ).
thf(3285,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(518,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ B ) @ A ) )
<=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ D ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ B ) ) )
=> ( ( D
= ( hAPP @ ( hAPP @ ( c_List_Otake @ E ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ D ) ) @ B ) )
& ( C
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ E ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ D ) ) @ B ) ) @ A ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ D ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ B ) ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_List_Otake @ E ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ B ) ) @ D )
= B )
& ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ E ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ B ) ) @ D ) ) @ C )
= A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__eq__append__conv__if) ).
thf(3460,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ D ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ B ) ) )
=> ( ( D
= ( hAPP @ ( hAPP @ ( c_List_Otake @ E ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ D ) ) @ B ) )
& ( C
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ E ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ D ) ) @ B ) ) @ A ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ D ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ B ) ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_List_Otake @ E ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ B ) ) @ D )
= B )
& ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ E ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ B ) ) @ D ) ) @ C )
= A ) ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ D ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ B ) ) )
=> ( ( D
= ( hAPP @ ( hAPP @ ( c_List_Otake @ E ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ D ) ) @ B ) )
& ( C
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ E ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ D ) ) @ B ) ) @ A ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ D ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ B ) ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_List_Otake @ E ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ B ) ) @ D )
= B )
& ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ E ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ B ) ) @ D ) ) @ C )
= A ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(389,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ B ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ A ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ D ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_aset_I8_J) ).
thf(2947,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ B ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ A ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ D ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(166,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ C ) @ ( c_List_Obutlast @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__butlast) ).
thf(1939,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ C ) @ ( c_List_Obutlast @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(854,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__inject) ).
thf(4807,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmod__right) ).
thf(1544,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(314,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( 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 ) )
= ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__div__cancel1) ).
thf(2676,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( 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 ) )
= ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(1228,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Opart__equivp @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_part__equivp__transp) ).
thf(6338,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Opart__equivp @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1228]) ).
thf(1150,axiom,
! [A: $i,B: $i] :
( ? [C: $i] : ( hBOOL @ ( hAPP @ B @ C ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Hilbert__Choice_OEps @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tfl__some) ).
thf(5982,plain,
! [A: $i,B: $i] :
( ? [C: $i] : ( hBOOL @ ( hAPP @ B @ C ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Hilbert__Choice_OEps @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).
thf(968,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_List_Olist @ E ) @ ( c_List_Olistrel1 @ E @ B ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ A ) @ C ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_List_Olist @ E ) @ ( c_List_Olistrel1 @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__listrel1__ConsI1) ).
thf(5265,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_List_Olist @ E ) @ ( c_List_Olistrel1 @ E @ B ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ A ) @ C ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_List_Olist @ E ) @ ( c_List_Olistrel1 @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(703,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ A )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__image) ).
thf(4215,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ A )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(1037,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessI) ).
thf(5529,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(888,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Oacyclic @ B @ A )
<=> ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ C ) ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclic__def) ).
thf(4973,plain,
! [A: $i,B: $i] :
( ( ( c_Wellfounded_Oacyclic @ B @ A )
=> ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ C ) ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ) )
& ( ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ C ) ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) )
=> ( c_Wellfounded_Oacyclic @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(750,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel) ).
thf(4408,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(1163,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ B ) @ ( c_SetInterval_Oord_OatLeast @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_OatLeast__iff) ).
thf(6031,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ B ) @ ( c_SetInterval_Oord_OatLeast @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ B ) @ ( c_SetInterval_Oord_OatLeast @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).
thf(782,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Orefl__on @ C @ B @ A )
=> ( ( c_Relation_Osym @ C @ A )
=> ( ( c_Relation_Otrans @ C @ A )
=> ( c_Equiv__Relations_Oequiv @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivI) ).
thf(4532,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Orefl__on @ C @ B @ A )
=> ( ( c_Relation_Osym @ C @ A )
=> ( ( c_Relation_Otrans @ C @ A )
=> ( c_Equiv__Relations_Oequiv @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(675,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Owf @ D @ C )
=> ( c_Wellfounded_Owf @ B @ ( hAPP @ ( hAPP @ ( c_Relation_Oinv__image @ D @ B ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__inv__image) ).
thf(4105,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Owf @ D @ C )
=> ( c_Wellfounded_Owf @ B @ ( hAPP @ ( hAPP @ ( c_Relation_Oinv__image @ D @ B ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(1266,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Set_Ovimage @ E @ C @ B ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__eq) ).
thf(6505,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Set_Ovimage @ E @ C @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ D ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ D ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Set_Ovimage @ E @ C @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1266]) ).
thf(589,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__assoc) ).
thf(3745,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(797,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ C ) @ A ) ) ) @ c_FunDef_Opair__less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__lessI2) ).
thf(4575,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ C ) @ A ) ) ) @ c_FunDef_Opair__less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(1096,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
<=> ? [D: $i,E: $i] :
( A
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__conv__decomp) ).
thf(5755,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ? [D: $i,E: $i] :
( A
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ E ) ) ) )
& ( ? [D: $i,E: $i] :
( A
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).
thf(673,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__less__dividend) ).
thf(4097,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(655,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( c_List_OdropWhile @ B @ D @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ C ) @ A ) )
= ( c_List_OdropWhile @ B @ D @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( c_List_OdropWhile @ B @ D @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile_Osimps_I2_J) ).
thf(4026,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( c_List_OdropWhile @ B @ D @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ C ) @ A ) )
= ( c_List_OdropWhile @ B @ D @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( c_List_OdropWhile @ B @ D @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(259,axiom,
! [A: $i,B: $i] :
( ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ tc_Int_Oint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastPlusOneAtMost__greaterThanAtMost__int) ).
thf(2316,plain,
! [A: $i,B: $i] :
( ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ tc_Int_Oint @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(983,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ C ) ) )
=> ( c_Fun_Oinj__on @ F @ E @ ( c_Fun_Ofun__upd @ F @ E @ D @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__fun__updI) ).
thf(5316,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ C ) ) )
=> ( c_Fun_Oinj__on @ F @ E @ ( c_Fun_Ofun__upd @ F @ E @ D @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(1082,axiom,
! [A: $i,B: $i] :
( ( B = A )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oeq__iff) ).
thf(5701,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).
thf(601,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__pred) ).
thf(3781,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(577,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ B ) )
=> ( ( c_List_Oremove1 @ C @ A @ ( c_List_Oremdups @ C @ B ) )
= ( c_List_Oremdups @ C @ ( c_List_Oremove1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remove1__remdups) ).
thf(3693,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ B ) )
=> ( ( c_List_Oremove1 @ C @ A @ ( c_List_Oremdups @ C @ B ) )
= ( c_List_Oremdups @ C @ ( c_List_Oremove1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(941,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ C ) @ ( hAPP @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SigmaD2) ).
thf(5163,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ C ) @ ( hAPP @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(890,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__1__left) ).
thf(4980,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(949,axiom,
class_Nat_Osize @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Nat_Osize) ).
thf(5192,plain,
class_Nat_Osize @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(472,axiom,
! [A: $i,B: $i,C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ B ) @ ( c_List_Olist_ONil @ C ) ) ) @ ( c_List_Olistrel1 @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__listrel1__Nil) ).
thf(3276,plain,
! [A: $i,B: $i,C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ B ) @ ( c_List_Olist_ONil @ C ) ) ) @ ( c_List_Olistrel1 @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(113,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__le__cancel1) ).
thf(1705,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(410,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__is__0__eq) ).
thf(3017,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( 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)],[410]) ).
thf(1145,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_New__Random__Sequence_Oneg__single @ E ) @ D ) @ C ) @ B ) @ A )
= ( c_New__DSequence_Oneg__single @ E @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__single__def) ).
thf(5967,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_New__Random__Sequence_Oneg__single @ E ) @ D ) @ C ) @ B ) @ A )
= ( c_New__DSequence_Oneg__single @ E @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).
thf(1041,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Owellorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ ( c_Orderings_Oord__class_OLeast @ C @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__Least) ).
thf(5550,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Owellorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ ( c_Orderings_Oord__class_OLeast @ C @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(45,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0) ).
thf(1426,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)],[45]) ).
thf(535,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__mono) ).
thf(3530,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(1241,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ D @ C ) @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel__unique) ).
thf(6391,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ D @ C ) @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1241]) ).
thf(88,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Int_Oint ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__atLeastAtMost__int) ).
thf(1608,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Int_Oint ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(749,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Otrans @ B @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) )
<=> ( c_Relation_Otrans @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__converse) ).
thf(4403,plain,
! [A: $i,B: $i] :
( ( ( c_Relation_Otrans @ B @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) )
=> ( c_Relation_Otrans @ B @ A ) )
& ( ( c_Relation_Otrans @ B @ A )
=> ( c_Relation_Otrans @ B @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(491,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ E @ D )
= C )
=> ( ( c_Fun_Ofun__upd @ B @ A @ E @ D @ C )
= E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__idem) ).
thf(3365,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ E @ D )
= C )
=> ( ( c_Fun_Ofun__upd @ B @ A @ E @ D @ C )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(333,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__mod__bound) ).
thf(2740,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(677,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Set_Ovimage @ F @ E @ ( hAPP @ ( c_Fun_Ocomp @ D @ E @ F @ C ) @ B ) ) @ A )
= ( hAPP @ ( c_Set_Ovimage @ F @ D @ B ) @ ( hAPP @ ( c_Set_Ovimage @ D @ E @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__compose) ).
thf(4110,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Set_Ovimage @ F @ E @ ( hAPP @ ( c_Fun_Ocomp @ D @ E @ F @ C ) @ B ) ) @ A )
= ( hAPP @ ( c_Set_Ovimage @ F @ D @ B ) @ ( hAPP @ ( c_Set_Ovimage @ D @ E @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(705,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Omap @ F @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ F ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ E ) @ ( hAPP @ ( c_Fun_Ocomp @ F @ E @ C @ D ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__map) ).
thf(4220,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Omap @ F @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ F ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ E ) @ ( hAPP @ ( c_Fun_Ocomp @ F @ E @ C @ D ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(966,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__into__rtrancl) ).
thf(5257,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(272,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__mono) ).
thf(2434,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[272]) ).
thf(151,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ B ) @ B ) ) @ ( c_List_Olistrel @ C @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__rtrancl__refl) ).
thf(1872,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ B ) @ B ) ) @ ( c_List_Olistrel @ C @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ C ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ B ) ) @ C ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__add__mult__distrib) ).
thf(1342,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)],[18]) ).
thf(724,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ ( tc_prod @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ D @ B ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__zipI1) ).
thf(4294,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ ( tc_prod @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ D @ B ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(374,axiom,
! [A: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__1) ).
thf(2901,plain,
! [A: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(481,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__Cons) ).
thf(3313,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(1066,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ A ) @ ( c_Relation_OId @ B ) ) )
=> ~ ! [C: $i] :
( A
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IdE) ).
thf(5636,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ A ) @ ( c_Relation_OId @ B ) ) )
=> ~ ! [C: $i] :
( A
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).
thf(358,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__eq__diff__pred) ).
thf(2844,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(562,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= ( hAPP @ B @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__other) ).
thf(3629,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= ( hAPP @ B @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(1091,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B ) ) )
=> ( ( hAPP @ C @ ( hAPP @ ( c_Fun_Othe__inv__into @ E @ D @ B @ C ) @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_f__the__inv__into__f) ).
thf(5740,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B ) ) )
=> ( ( hAPP @ C @ ( hAPP @ ( c_Fun_Othe__inv__into @ E @ D @ B @ C ) @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).
thf(526,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Omap @ F @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ F ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ E ) @ ( hAPP @ ( c_Fun_Ocomp @ F @ E @ C @ D ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_List_Omap_Ocompositionality) ).
thf(3502,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Omap @ F @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ F ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ E ) @ ( hAPP @ ( c_Fun_Ocomp @ F @ E @ C @ D ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(423,axiom,
! [A: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ ( c_Relation_OId @ A ) )
= ( c_Relation_OId @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__Id) ).
thf(3088,plain,
! [A: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ ( c_Relation_OId @ A ) )
= ( c_Relation_OId @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(1155,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequivp @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__transp) ).
thf(6009,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequivp @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).
thf(1132,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Typedef_Otype__definition @ F @ E @ D @ C @ B )
=> ( ( hAPP @ C @ ( hAPP @ D @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_ORep__inverse) ).
thf(5903,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Typedef_Otype__definition @ F @ E @ D @ C @ B )
=> ( ( hAPP @ C @ ( hAPP @ D @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).
thf(197,axiom,
! [A: $i,B: $i] :
( ( c_Predicate_Otransp @ B @ A )
<=> ( c_Relation_Otrans @ B @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ B @ tc_HOL_Obool ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transp__def) ).
thf(2067,plain,
! [A: $i,B: $i] :
( ( ( c_Predicate_Otransp @ B @ A )
=> ( c_Relation_Otrans @ B @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ B @ tc_HOL_Obool ) @ A ) ) ) )
& ( ( c_Relation_Otrans @ B @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ B @ tc_HOL_Obool ) @ A ) ) )
=> ( c_Predicate_Otransp @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__simps_I3_J) ).
thf(1482,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(745,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ E @ D ) ) @ ( hAPP @ E @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ D ) @ C ) ) @ ( c_Wellfounded_Omlex__prod @ B @ E @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mlex__less) ).
thf(4386,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ E @ D ) ) @ ( hAPP @ E @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ D ) @ C ) ) @ ( c_Wellfounded_Omlex__prod @ B @ E @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(485,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_less__diff__conv) ).
thf(3335,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(1185,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Nitpick_Opair__box_Opair__box__case @ F @ E @ D @ C @ ( c_Nitpick_Opair__box_OPairBox @ F @ E @ B @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__box_Osimps_I2_J) ).
thf(6138,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Nitpick_Opair__box_Opair__box__case @ F @ E @ D @ C @ ( c_Nitpick_Opair__box_OPairBox @ F @ E @ B @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185]) ).
thf(120,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__imp__zdiv__nonneg__iff) ).
thf(1746,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(428,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Relation_ORange @ C @ B ) @ ( hAPP @ ( c_Relation_Oconverse @ B @ C ) @ A ) )
= ( hAPP @ ( c_Relation_ODomain @ B @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__converse) ).
thf(3103,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Relation_ORange @ C @ B ) @ ( hAPP @ ( c_Relation_Oconverse @ B @ C ) @ A ) )
= ( hAPP @ ( c_Relation_ODomain @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(1208,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ c_fequal @ A ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__mem) ).
thf(6236,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ c_fequal @ A ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ c_fequal @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1208]) ).
thf(140,axiom,
! [A: $i,B: $i] :
( ( c_List_Obutlast @ B @ A )
= ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast__conv__take) ).
thf(1835,plain,
! [A: $i,B: $i] :
( ( c_List_Obutlast @ B @ A )
= ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(396,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__le__mono) ).
thf(2972,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(964,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_List_Obutlast @ C @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ B ) @ ( c_List_Obutlast @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast__drop) ).
thf(5252,plain,
! [A: $i,B: $i,C: $i] :
( ( c_List_Obutlast @ C @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ B ) @ ( c_List_Obutlast @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(1149,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OatMost @ D @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OatMost__iff) ).
thf(5977,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OatMost @ D @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ C ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ B @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OatMost @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).
thf(161,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ E ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ B ) @ E ) ) ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) )
=> ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ B ) @ D ) ) ) )
=> ( ( c_List_OtakeWhile @ C @ A @ B )
= ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__eq__take__P__nth) ).
thf(1914,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ E ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ B ) @ E ) ) ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) )
=> ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ B ) @ D ) ) ) )
=> ( ( c_List_OtakeWhile @ C @ A @ B )
= ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ D ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(1004,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__Suc__Cons) ).
thf(5393,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(339,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ A ) @ B ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__same__eq) ).
thf(2763,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ A ) @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(1029,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ B ) )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__insert__disjoint) ).
thf(5486,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ B ) )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(129,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__imp__zdiv__nonneg__iff) ).
thf(1782,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(402,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ F @ E @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_prod_Osimps_I2_J) ).
thf(2985,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ F @ E @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(933,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
<=> ? [D: $i,E: $i] :
( ( A
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ E ) ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__conv__decomp__last) ).
thf(5123,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ? [D: $i,E: $i] :
( ( A
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ E ) ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ E ) ) ) ) )
& ( ? [D: $i,E: $i] :
( ( A
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ E ) ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ E ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(464,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( c_List_Olist_ONil @ B ) )
=> ( ( c_List_Obutlast @ B @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ A ) @ C ) )
= ( c_List_Olist_ONil @ B ) ) )
& ( ( C
!= ( c_List_Olist_ONil @ B ) )
=> ( ( c_List_Obutlast @ B @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ A ) @ ( c_List_Obutlast @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast_Osimps_I2_J) ).
thf(3249,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( c_List_Olist_ONil @ B ) )
=> ( ( c_List_Obutlast @ B @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ A ) @ C ) )
= ( c_List_Olist_ONil @ B ) ) )
& ( ( C
!= ( c_List_Olist_ONil @ B ) )
=> ( ( c_List_Obutlast @ B @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ A ) @ ( c_List_Obutlast @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__le__nonneg__dividend) ).
thf(1441,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(1240,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Omap @ E @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ E @ D ) @ A ) @ B ) )
<=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ ( hAPP @ ( c_List_Oset @ E ) @ B ) ) )
=> ( ( hAPP @ C @ F )
= ( hAPP @ A @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__eq__conv) ).
thf(6381,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Omap @ E @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ E @ D ) @ A ) @ B ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ ( hAPP @ ( c_List_Oset @ E ) @ B ) ) )
=> ( ( hAPP @ C @ F )
= ( hAPP @ A @ F ) ) ) )
& ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ ( hAPP @ ( c_List_Oset @ E ) @ B ) ) )
=> ( ( hAPP @ C @ F )
= ( hAPP @ A @ F ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Omap @ E @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ E @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1240]) ).
thf(182,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Omap @ tc_Nat_Onat @ B ) @ ( hAPP @ ( c_List_Onth @ B ) @ A ) ) @ ( c_List_Oupt @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__nth) ).
thf(2010,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Omap @ tc_Nat_Onat @ B ) @ ( hAPP @ ( c_List_Onth @ B ) @ A ) ) @ ( c_List_Oupt @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(852,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ I @ H ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ I @ H ) @ G ) @ F ) ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ ( hAPP @ B @ G ) ) @ ( hAPP @ A @ F ) ) ) @ ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ I @ H ) @ ( tc_prod @ D @ C ) @ ( c_Product__Type_Omap__pair @ I @ D @ H @ C @ B @ A ) ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair__imageI) ).
thf(4803,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ I @ H ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ I @ H ) @ G ) @ F ) ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ ( hAPP @ B @ G ) ) @ ( hAPP @ A @ F ) ) ) @ ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ I @ H ) @ ( tc_prod @ D @ C ) @ ( c_Product__Type_Omap__pair @ I @ D @ H @ C @ B @ A ) ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(681,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olist_ONil @ C ) ) @ B ) ) @ ( c_List_Olexord @ C @ A ) ) )
<=> ? [D: $i,E: $i] :
( B
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ D ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__Nil__left) ).
thf(4124,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olist_ONil @ C ) ) @ B ) ) @ ( c_List_Olexord @ C @ A ) ) )
=> ? [D: $i,E: $i] :
( B
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ D ) @ E ) ) )
& ( ? [D: $i,E: $i] :
( B
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ D ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olist_ONil @ C ) ) @ B ) ) @ ( c_List_Olexord @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(583,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__assoc2) ).
thf(3730,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) @ A )
= ( hAPP @ ( hAPP @ ( 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)],[583]) ).
thf(1086,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ B ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ B ) )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__insert__if) ).
thf(5723,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ B ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ B ) )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).
thf(913,axiom,
! [A: $i,B: $i] :
( ( ( class_Enum_Oenum @ B )
& ( class_Enum_Oenum @ A ) )
=> ( class_Enum_Oenum @ ( tc_prod @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_prod__Enum_Oenum) ).
thf(5056,plain,
! [A: $i,B: $i] :
( ( ( class_Enum_Oenum @ B )
& ( class_Enum_Oenum @ A ) )
=> ( class_Enum_Oenum @ ( tc_prod @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ C ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ B ) @ D ) @ A ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__drop) ).
thf(1386,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ C ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ B ) @ D ) @ A ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(474,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( C
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ A ) @ ( c_List_Olist_ONil @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__Nil__appendI) ).
thf(3281,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( C
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ A ) @ ( c_List_Olist_ONil @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(731,axiom,
! [A: $i] :
( ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A )
= ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__Suc__le__raw) ).
thf(4322,plain,
! [A: $i] :
( ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A )
= ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(353,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add1) ).
thf(2819,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[353]) ).
thf(1095,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
<=> ~ ? [C: $i] :
! [D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ ( hAPP @ C @ ( hAPP @ c_Nat_OSuc @ D ) ) ) @ ( hAPP @ C @ D ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__iff__no__infinite__down__chain) ).
thf(5750,plain,
! [A: $i,B: $i] :
( ( ( c_Wellfounded_Owf @ B @ A )
=> ~ ? [C: $i] :
! [D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ ( hAPP @ C @ ( hAPP @ c_Nat_OSuc @ D ) ) ) @ ( hAPP @ C @ D ) ) ) @ A ) ) )
& ( ~ ? [C: $i] :
! [D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ ( hAPP @ C @ ( hAPP @ c_Nat_OSuc @ D ) ) ) @ ( hAPP @ C @ D ) ) ) @ A ) )
=> ( c_Wellfounded_Owf @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ C ) @ B ) ) @ ( c_List_Olistrel1 @ D @ A ) ) )
=> ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1__eq__len) ).
thf(1518,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ C ) @ B ) ) @ ( c_List_Olistrel1 @ D @ A ) ) )
=> ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(112,axiom,
! [A: $i,B: $i] : ( c_Wellfounded_Owf @ B @ ( hAPP @ ( c_Wellfounded_Omeasure @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__measure) ).
thf(1703,plain,
! [A: $i,B: $i] : ( c_Wellfounded_Owf @ B @ ( hAPP @ ( c_Wellfounded_Omeasure @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(902,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mono) ).
thf(5024,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(992,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Fun_Oinj__on @ G @ F @ E @ ( hAPP @ ( c_Set_Oimage @ D @ G @ C ) @ B ) )
=> ( ( c_Fun_Oinj__on @ D @ G @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ ( hAPP @ ( c_Set_Oimage @ G @ F @ E ) @ ( hAPP @ ( c_Set_Oimage @ D @ G @ C ) @ B ) ) ) )
=> ( ( hAPP @ ( c_Fun_Othe__inv__into @ D @ F @ B @ ( hAPP @ ( c_Fun_Ocomp @ G @ F @ D @ E ) @ C ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ G @ D @ F @ ( c_Fun_Othe__inv__into @ D @ G @ B @ C ) ) @ ( c_Fun_Othe__inv__into @ G @ F @ ( hAPP @ ( c_Set_Oimage @ D @ G @ C ) @ B ) @ E ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__inv__into__comp) ).
thf(5352,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Fun_Oinj__on @ G @ F @ E @ ( hAPP @ ( c_Set_Oimage @ D @ G @ C ) @ B ) )
=> ( ( c_Fun_Oinj__on @ D @ G @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ ( hAPP @ ( c_Set_Oimage @ G @ F @ E ) @ ( hAPP @ ( c_Set_Oimage @ D @ G @ C ) @ B ) ) ) )
=> ( ( hAPP @ ( c_Fun_Othe__inv__into @ D @ F @ B @ ( hAPP @ ( c_Fun_Ocomp @ G @ F @ D @ E ) @ C ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ G @ D @ F @ ( c_Fun_Othe__inv__into @ D @ G @ B @ C ) ) @ ( c_Fun_Othe__inv__into @ G @ F @ ( hAPP @ ( c_Set_Oimage @ D @ G @ C ) @ B ) @ E ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(811,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__le__mono2) ).
thf(4637,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(785,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__diffD1) ).
thf(4539,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(688,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ A ) @ C ) )
<=> ( A
= ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__append__conv2) ).
thf(4151,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ A ) @ C ) )
=> ( A
= ( c_List_Olist_ONil @ B ) ) )
& ( ( A
= ( c_List_Olist_ONil @ B ) )
=> ( C
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(524,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr__implies__not0) ).
thf(3495,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( 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)],[524]) ).
thf(1251,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ B ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__takeD) ).
thf(6423,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ B ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1251]) ).
thf(612,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD1) ).
thf(3821,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(286,axiom,
hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
thf(2501,plain,
hBOOL @ ( hAPP @ ( 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)],[286]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_List_Ofilter @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ E ) @ B ) @ ( hAPP @ ( c_List_Ofilter @ C @ ( hAPP @ ( c_Fun_Ocomp @ E @ tc_HOL_Obool @ C @ D ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__map) ).
thf(1330,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_List_Ofilter @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ E ) @ B ) @ ( hAPP @ ( c_List_Ofilter @ C @ ( hAPP @ ( c_Fun_Ocomp @ E @ tc_HOL_Obool @ C @ D ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(438,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ F ) @ E ) @ D )
= C )
=> ( ( B
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ F ) @ D ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ F ) @ E ) @ B )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ F ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__eq__appendI) ).
thf(3148,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ F ) @ E ) @ D )
= C )
=> ( ( B
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ F ) @ D ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ F ) @ E ) @ B )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ F ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(520,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__less__eq__dividend) ).
thf(3485,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(599,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono) ).
thf(3776,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[599]) ).
thf(316,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono1) ).
thf(2682,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(505,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD2) ).
thf(3410,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( c_List_OdropWhile @ C @ B @ A ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ ( c_List_OdropWhile @ C @ B @ A ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( c_List_OtakeWhile @ C @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile__nth) ).
thf(1832,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( c_List_OdropWhile @ C @ B @ A ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ ( c_List_OdropWhile @ C @ B @ A ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( c_List_OtakeWhile @ C @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(609,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc0) ).
thf(3803,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(757,axiom,
! [A: $i,B: $i] :
( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ tc_Nat_Onat @ B @ A )
= ( hAPP @ ( c_List_Oset @ tc_Nat_Onat ) @ ( c_List_Oupt @ ( hAPP @ c_Nat_OSuc @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_greaterThanAtMost__upt) ).
thf(4428,plain,
! [A: $i,B: $i] :
( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ tc_Nat_Onat @ B @ A )
= ( hAPP @ ( c_List_Oset @ tc_Nat_Onat ) @ ( c_List_Oupt @ ( hAPP @ c_Nat_OSuc @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(1098,axiom,
! [A: $i,B: $i] :
( ( c_Hilbert__Choice_OEps @ B @ ( hAPP @ c_fequal @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_some__sym__eq__trivial) ).
thf(5765,plain,
! [A: $i,B: $i] :
( ( c_Hilbert__Choice_OEps @ B @ ( hAPP @ c_fequal @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).
thf(467,axiom,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__Suc__eq__Suc__mod) ).
thf(3263,plain,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(761,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ? [B: $i] :
( A
= ( hAPP @ c_Nat_OSuc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0__implies__Suc) ).
thf(4439,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ? [B: $i] :
( A
= ( hAPP @ c_Nat_OSuc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(644,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
thf(3976,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[644]) ).
thf(377,axiom,
! [A: $i,B: $i] :
( ( B != A )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
thf(2916,plain,
! [A: $i,B: $i] :
( ( B != A )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(780,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Oantisym @ B @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) )
<=> ( c_Relation_Oantisym @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisym__converse) ).
thf(4524,plain,
! [A: $i,B: $i] :
( ( ( c_Relation_Oantisym @ B @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) )
=> ( c_Relation_Oantisym @ B @ A ) )
& ( ( c_Relation_Oantisym @ B @ A )
=> ( c_Relation_Oantisym @ B @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(352,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
<=> ( c_Wellfounded_Owf @ B @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ B @ B @ B ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__comp__self) ).
thf(2814,plain,
! [A: $i,B: $i] :
( ( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_Owf @ B @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ B @ B @ B ) @ A ) @ A ) ) )
& ( ( c_Wellfounded_Owf @ B @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ B @ B @ B ) @ A ) @ A ) )
=> ( c_Wellfounded_Owf @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(793,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ ( c_List_OtakeWhile @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__takeWhile) ).
thf(4563,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ ( c_List_OtakeWhile @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(176,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__bin__lemma) ).
thf(1985,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(104,axiom,
! [A: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ tc_Nat_Onat ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__size) ).
thf(1660,plain,
! [A: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ tc_Nat_Onat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(1127,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ ( c_List_Osublist @ D @ B @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__sublistD) ).
thf(5883,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ ( c_List_Osublist @ D @ B @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).
thf(124,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ B ) @ ( c_List_Olist_ONil @ C ) ) ) @ ( c_List_Olistrel @ C @ A ) ) )
=> ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__Nil2) ).
thf(1760,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ B ) @ ( c_List_Olist_ONil @ C ) ) ) @ ( c_List_Olistrel @ C @ A ) ) )
=> ( B
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(436,axiom,
! [A: $i,B: $i] :
( ( B != A )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
thf(3131,plain,
! [A: $i,B: $i] :
( ( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(1217,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ A ) ) ) )
=> ( ( C = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__ConsD) ).
thf(6274,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ A ) ) ) )
=> ( ( C = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1217]) ).
thf(826,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__le) ).
thf(4692,plain,
! [A: $i,B: $i] :
( ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ( B != A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ( B != A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(576,axiom,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).
thf(3689,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(539,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= ( c_List_Olist_ONil @ C ) ) )
& ( ( ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__Cons__number__of) ).
thf(3542,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= ( c_List_Olist_ONil @ C ) ) )
& ( ( ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(1226,axiom,
! [A: $i,B: $i] :
( ( c_Equiv__Relations_Oequivp @ B @ A )
<=> ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
<=> ( ( hAPP @ A @ C )
= ( hAPP @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__def) ).
thf(6315,plain,
! [A: $i,B: $i] :
( ( ( c_Equiv__Relations_Oequivp @ B @ A )
=> ! [C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
=> ( ( hAPP @ A @ C )
= ( hAPP @ A @ D ) ) )
& ( ( ( hAPP @ A @ C )
= ( hAPP @ A @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ D ) ) ) ) )
& ( ! [C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
=> ( ( hAPP @ A @ C )
= ( hAPP @ A @ D ) ) )
& ( ( ( hAPP @ A @ C )
= ( hAPP @ A @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ D ) ) ) )
=> ( c_Equiv__Relations_Oequivp @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1226]) ).
thf(736,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A )
!= ( c_List_Olist_ONil @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osimps_I3_J) ).
thf(4349,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A )
!= ( c_List_Olist_ONil @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(947,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_Oconverse @ D @ E ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ E ) @ B ) @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converseD) ).
thf(5182,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_Oconverse @ D @ E ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ E ) @ B ) @ C ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(1067,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ E @ E @ D @ C @ B ) @ A ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ E @ D @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1Set_Ointros) ).
thf(5640,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ E @ E @ D @ C @ B ) @ A ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ E @ D @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).
thf(1083,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Owellorder @ C )
=> ( ( hBOOL @ ( hAPP @ B @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ ( c_Orderings_Oord__class_OLeast @ C @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Least__le) ).
thf(5712,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Owellorder @ C )
=> ( ( hBOOL @ ( hAPP @ B @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ ( c_Orderings_Oord__class_OLeast @ C @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).
thf(1270,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Typedef_Otype__definition @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( ( ( hAPP @ D @ B )
= ( hAPP @ D @ A ) )
<=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_OAbs__inject) ).
thf(6519,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Typedef_Otype__definition @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( ( ( ( hAPP @ D @ B )
= ( hAPP @ D @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ D @ B )
= ( hAPP @ D @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1270]) ).
thf(178,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ C @ A ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zadd1__eq) ).
thf(1992,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ C @ A ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(974,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oorder__trans) ).
thf(5289,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(958,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ C @ B ) ) @ ( hAPP @ ( c_Relation_Oconverse @ B @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ B @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__converse) ).
thf(5231,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ C @ B ) ) @ ( hAPP @ ( c_Relation_Oconverse @ B @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ B @ C ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ B @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ C @ B ) ) @ ( hAPP @ ( c_Relation_Oconverse @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(1212,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_New__Random__Sequence_Opos__not__random__dseq @ D @ C @ B @ A )
= ( c_New__DSequence_Opos__not__seq @ ( hAPP @ ( hAPP @ ( hAPP @ D @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__not__random__dseq__def) ).
thf(6253,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_New__Random__Sequence_Opos__not__random__dseq @ D @ C @ B @ A )
= ( c_New__DSequence_Opos__not__seq @ ( hAPP @ ( hAPP @ ( hAPP @ D @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1212]) ).
thf(565,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G != F )
=> ( ( c_Fun_Ofun__upd @ E @ D @ ( c_Fun_Ofun__upd @ E @ D @ C @ G @ B ) @ F @ A )
= ( c_Fun_Ofun__upd @ E @ D @ ( c_Fun_Ofun__upd @ E @ D @ C @ F @ A ) @ G @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__twist) ).
thf(3638,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G != F )
=> ( ( c_Fun_Ofun__upd @ E @ D @ ( c_Fun_Ofun__upd @ E @ D @ C @ G @ B ) @ F @ A )
= ( c_Fun_Ofun__upd @ E @ D @ ( c_Fun_Ofun__upd @ E @ D @ C @ F @ A ) @ G @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(193,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__all) ).
thf(2049,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(1190,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ F @ D @ C @ B @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ D @ E ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OgreaterThanAtMost__iff) ).
thf(6149,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ F @ D @ C @ B @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ D @ E ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ D @ E ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ F @ D @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__reduce) ).
thf(1741,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(1093,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Orefl__on @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__onD2) ).
thf(5746,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Orefl__on @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).
thf(715,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ B @ B @ B ) @ A ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ B @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_r__comp__rtrancl__eq) ).
thf(4265,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ B @ B @ B ) @ A ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ B @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(1161,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_New__DSequence_Opos__single @ C @ B ) @ A )
= ( hAPP @ ( c_Lazy__Sequence_Osingle @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Opos__single__def) ).
thf(6025,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_New__DSequence_Opos__single @ C @ B ) @ A )
= ( hAPP @ ( c_Lazy__Sequence_Osingle @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).
thf(921,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_Relation_ORange @ B @ D ) @ A ) ) )
<=> ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ D ) @ E ) @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__iff) ).
thf(5077,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_Relation_ORange @ B @ D ) @ A ) ) )
=> ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ D ) @ E ) @ C ) ) @ A ) ) )
& ( ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ D ) @ E ) @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_Relation_ORange @ B @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(1061,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ C ) ) )
=> ( ( B = A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oord__less__eq__trans) ).
thf(5617,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ C ) ) )
=> ( ( B = A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).
thf(887,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ D ) @ B ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ A ) )
& ( c_Fun_Oinj__on @ C @ D @ B @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__map) ).
thf(4967,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ D ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ A ) )
& ( c_Fun_Oinj__on @ C @ D @ B @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ A ) )
& ( c_Fun_Oinj__on @ C @ D @ B @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ D ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(1107,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ B @ B ) ) @ A ) )
=> ( ( c_Wellfounded_Oacyclic @ B @ A )
=> ( c_Wellfounded_Owf @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__acyclic__wf) ).
thf(5792,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ B @ B ) ) @ A ) )
=> ( ( c_Wellfounded_Oacyclic @ B @ A )
=> ( c_Wellfounded_Owf @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).
thf(326,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0) ).
thf(2713,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)],[326]) ).
thf(531,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__atLeastLessThan) ).
thf(3517,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(993,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leD) ).
thf(5355,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(498,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Otrans @ D @ C )
=> ( c_Relation_Otrans @ B @ ( hAPP @ ( hAPP @ ( c_Relation_Oinv__image @ D @ B ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__inv__image) ).
thf(3385,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Otrans @ D @ C )
=> ( c_Relation_Otrans @ B @ ( hAPP @ ( hAPP @ ( c_Relation_Oinv__image @ D @ B ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(737,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__ge__0__finite) ).
thf(4353,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(1122,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( hBOOL @ ( hAPP @ C @ D ) )
<=> ! [D: $i,E: $i] : ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ A ) @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__paired__All) ).
thf(5866,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] : ( hBOOL @ ( hAPP @ C @ D ) )
=> ! [D: $i,E: $i] : ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ A ) @ D ) @ E ) ) ) )
& ( ! [D: $i,E: $i] : ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ A ) @ D ) @ E ) ) )
=> ! [D: $i] : ( hBOOL @ ( hAPP @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).
thf(868,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( c_List_Oremove1 @ B @ C @ ( hAPP @ ( c_List_Ofilter @ B @ D ) @ A ) )
= ( hAPP @ ( c_List_Ofilter @ B @ D ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remove1__filter__not) ).
thf(4862,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( c_List_Oremove1 @ B @ C @ ( hAPP @ ( c_List_Ofilter @ B @ D ) @ A ) )
= ( hAPP @ ( c_List_Ofilter @ B @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(805,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) @ ( hAPP @ c_Nat_OSuc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__Suc) ).
thf(4617,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) @ ( hAPP @ c_Nat_OSuc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(1034,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Predicate_Oconversep @ E @ D @ ( c_Predicate_Opred__comp @ E @ C @ D @ B @ A ) )
= ( c_Predicate_Opred__comp @ D @ C @ E @ ( c_Predicate_Oconversep @ C @ D @ A ) @ ( c_Predicate_Oconversep @ E @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__pred__comp) ).
thf(5521,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Predicate_Oconversep @ E @ D @ ( c_Predicate_Opred__comp @ E @ C @ D @ B @ A ) )
= ( c_Predicate_Opred__comp @ D @ C @ E @ ( c_Predicate_Oconversep @ C @ D @ A ) @ ( c_Predicate_Oconversep @ E @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(952,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ B @ B ) ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ B @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__trancl) ).
thf(5199,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ B @ B ) ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ B @ B ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ B @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ B @ B ) ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(695,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ ( c_List_Oremove1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__remove1) ).
thf(4179,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ ( c_List_Oremove1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(950,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Relation_OImage @ C @ E @ B ) @ A ) ) )
=> ~ ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ E ) @ F ) @ D ) ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ImageE) ).
thf(5193,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Relation_OImage @ C @ E @ B ) @ A ) ) )
=> ~ ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ E ) @ F ) @ D ) ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(1239,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ B ) @ ( hAPP @ ( c_Set_OCollect @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_CollectI) ).
thf(6379,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ B ) @ ( hAPP @ ( c_Set_OCollect @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1239]) ).
thf(775,axiom,
! [A: $i,B: $i] :
( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= A ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__if) ).
thf(4492,plain,
! [A: $i,B: $i] :
( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= A ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(882,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__eq) ).
thf(4928,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(1137,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( ( ( hAPP @ D @ B )
= ( hAPP @ D @ A ) )
<=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__iff) ).
thf(5925,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( ( ( ( hAPP @ D @ B )
= ( hAPP @ D @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ D @ B )
= ( hAPP @ D @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).
thf(717,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__mono2) ).
thf(4270,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(789,axiom,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ A )
= ( hAPP @ ( c_List_Oset @ tc_Nat_Onat ) @ ( c_List_Oupt @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeast__upt) ).
thf(4551,plain,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ A )
= ( hAPP @ ( c_List_Oset @ tc_Nat_Onat ) @ ( c_List_Oupt @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ( A
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Onth @ B ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ B ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_id__take__nth__drop) ).
thf(1568,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ( A
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Onth @ B ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ B ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(1114,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ F @ C @ E ) @ B ) @ A ) ) )
=> ~ ! [G: $i,H: $i,I: $i] :
( ( D
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ G ) @ I ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ C ) @ G ) @ H ) ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ E ) @ H ) @ I ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__compE) ).
thf(5829,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ F @ C @ E ) @ B ) @ A ) ) )
=> ~ ! [G: $i,H: $i,I: $i] :
( ( D
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ G ) @ I ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ C ) @ G ) @ H ) ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ E ) @ H ) @ I ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).
thf(291,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( 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 ) @ B ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ D ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__lemma) ).
thf(2520,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( 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 ) @ B ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ D ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(744,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) )
<=> ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_le__diff__conv2) ).
thf(4383,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( 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 @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(253,axiom,
( ( hAPP @ ( c_Nat_Osize__class_Osize @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osize_I3_J) ).
thf(2301,plain,
( ( hAPP @ ( c_Nat_Osize__class_Osize @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(181,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ B ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__neg__neg__trivial) ).
thf(2007,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ B ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(1105,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__into__rtrancl) ).
thf(5787,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
thf(1154,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ A ) )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp_Osimps) ).
thf(6002,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ A ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ D ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).
thf(898,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_Owf @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__trancl) ).
thf(5013,plain,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_Owf @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(712,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__lessD1) ).
thf(4258,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(95,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__function__closures_I2_J) ).
thf(1632,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(649,axiom,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
thf(4001,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(988,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__imp__not__eq2) ).
thf(5333,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(236,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__mod__bound) ).
thf(2236,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(1247,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ B ) @ A ) )
| ~ ( hBOOL @ B )
| ( hBOOL @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fimplies__3) ).
thf(6410,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ B ) @ A ) )
| ~ ( hBOOL @ B )
| ( hBOOL @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1247]) ).
thf(833,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( c_Fun_Oinj__on @ D @ B @ A @ C )
<=> ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ ( hAPP @ ( c_Set_Oimage @ D @ B @ A ) @ C ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__iff__eq__card) ).
thf(4724,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( ( c_Fun_Oinj__on @ D @ B @ A @ C )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ ( hAPP @ ( c_Set_Oimage @ D @ B @ A ) @ C ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ C ) ) )
& ( ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ ( hAPP @ ( c_Set_Oimage @ D @ B @ A ) @ C ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ C ) )
=> ( c_Fun_Oinj__on @ D @ B @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(175,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ A ) ) )
<=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ A ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ B ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__iff__zmod__eq__0__number__of) ).
thf(1978,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ A ) ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ A ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ B ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ A ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ B ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(477,axiom,
! [A: $i] : ( c_Relation_Otrans @ A @ ( c_Relation_OId @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__Id) ).
thf(3290,plain,
! [A: $i] : ( c_Relation_Otrans @ A @ ( c_Relation_OId @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(1192,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ B @ ( hAPP @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__code) ).
thf(6157,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ B @ ( hAPP @ C @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ B @ ( hAPP @ C @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1192]) ).
thf(439,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__linear) ).
thf(3152,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(967,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).
thf(5259,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(622,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ B ) @ ( c_List_Oremdups @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__remdups) ).
thf(3851,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ B ) @ ( c_List_Oremdups @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(1115,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( ( c_List_Oremdups @ C @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= ( c_List_Oremdups @ C @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( ( c_List_Oremdups @ C @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ ( c_List_Oremdups @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remdups_Osimps_I2_J) ).
thf(5834,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( ( c_List_Oremdups @ C @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= ( c_List_Oremdups @ C @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( ( c_List_Oremdups @ C @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ ( c_List_Oremdups @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).
thf(1214,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_List_OtakeWhile @ C @ B @ A )
= A )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__eq__all__conv) ).
thf(6259,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( c_List_OtakeWhile @ C @ B @ A )
= A )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ B @ D ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ B @ D ) ) )
=> ( ( c_List_OtakeWhile @ C @ B @ A )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1214]) ).
thf(1143,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ C @ B ) @ A ) )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Powp__def) ).
thf(5957,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ C @ B ) @ A ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ B @ D ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ B @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).
thf(41,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olist_ONil @ B ) ) @ ( c_List_Olist_ONil @ B ) ) ) @ ( c_List_Olistrel @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel_ONil) ).
thf(1415,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olist_ONil @ B ) ) @ ( c_List_Olist_ONil @ B ) ) ) @ ( c_List_Olistrel @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(1014,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ ( hAPP @ ( c_Set_Oimage @ D @ B @ A ) @ C ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ C ) )
=> ( c_Fun_Oinj__on @ D @ B @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__card__imp__inj__on) ).
thf(5433,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ ( hAPP @ ( c_Set_Oimage @ D @ B @ A ) @ C ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ C ) )
=> ( c_Fun_Oinj__on @ D @ B @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(1130,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ E @ B ) @ A ) ) )
<=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ A ) )
& ( D
= ( hAPP @ B @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__iff) ).
thf(5892,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ E @ B ) @ A ) ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ A ) )
& ( D
= ( hAPP @ B @ F ) ) ) )
& ( ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ A ) )
& ( D
= ( hAPP @ B @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ E @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).
thf(346,axiom,
! [A: $i,B: $i] :
( ( c_List_OdropWhile @ B @ A @ ( c_List_Olist_ONil @ B ) )
= ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile_Osimps_I1_J) ).
thf(2794,plain,
! [A: $i,B: $i] :
( ( c_List_OdropWhile @ B @ A @ ( c_List_Olist_ONil @ B ) )
= ( c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(630,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_List_Oupt @ B @ A )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ tc_Nat_Onat ) @ B ) @ ( c_List_Oupt @ ( hAPP @ c_Nat_OSuc @ B ) @ A ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_List_Oupt @ B @ A )
= ( c_List_Olist_ONil @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__rec) ).
thf(3887,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_List_Oupt @ B @ A )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ tc_Nat_Onat ) @ B ) @ ( c_List_Oupt @ ( hAPP @ c_Nat_OSuc @ B ) @ A ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_List_Oupt @ B @ A )
= ( c_List_Olist_ONil @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(642,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ A ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ A ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ D ) @ C ) ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_aset_I6_J) ).
thf(3966,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ A ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ A ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ D ) @ C ) ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(453,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( 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 @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_nat__less__cases) ).
thf(3199,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( 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 @ ( 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)],[453]) ).
thf(1207,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ B ) @ A ) )
<=> ( ( C = A )
| ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__code) ).
thf(6227,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ B ) @ A ) )
=> ( ( C = A )
| ( hBOOL @ ( hAPP @ B @ A ) ) ) )
& ( ( ( C = A )
| ( hBOOL @ ( hAPP @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1207]) ).
thf(160,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__pos__pos__trivial) ).
thf(1911,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(801,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( c_List_Olist_ONil @ B ) )
=> ( ( c_List_Obutlast @ B @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ A ) @ C ) )
= ( c_List_Obutlast @ B @ A ) ) )
& ( ( C
!= ( c_List_Olist_ONil @ B ) )
=> ( ( c_List_Obutlast @ B @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ A ) @ ( c_List_Obutlast @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast__append) ).
thf(4600,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( c_List_Olist_ONil @ B ) )
=> ( ( c_List_Obutlast @ B @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ A ) @ C ) )
= ( c_List_Obutlast @ B @ A ) ) )
& ( ( C
!= ( c_List_Olist_ONil @ B ) )
=> ( ( c_List_Obutlast @ B @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ A ) @ ( c_List_Obutlast @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(1184,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Equiv__Relations_Opart__equivp @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_part__equivp__symp) ).
thf(6135,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Equiv__Relations_Opart__equivp @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__add__iff2) ).
thf(1682,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( 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)],[108]) ).
thf(1079,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ A ) )
<=> ? [B: $i] :
! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded__le) ).
thf(5680,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ A ) )
=> ? [B: $i] :
! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) ) ) )
& ( ? [B: $i] :
! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).
thf(148,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add1__zle__eq) ).
thf(1858,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[148]) ).
thf(1224,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ B ) @ A ) )
| ( hBOOL @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__2) ).
thf(6300,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ B ) @ A ) )
| ( hBOOL @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1224]) ).
thf(659,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ C ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__diff__iff) ).
thf(4050,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ C ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(513,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ ( tc_prod @ B @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ B @ D ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__zipI2) ).
thf(3438,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ ( tc_prod @ B @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ B @ D ) @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(1197,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_CollectD) ).
thf(6187,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197]) ).
thf(1070,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ole__imp__less__or__eq) ).
thf(5650,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
| ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).
thf(243,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Onth @ B ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ B ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Odrop @ B ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__drop_H) ).
thf(2254,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Onth @ B ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ B ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Odrop @ B ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(106,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self__is__m) ).
thf(1677,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( 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)],[106]) ).
thf(188,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( 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 ) @ B ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ D ) ) ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult2__lemma__aux3) ).
thf(2034,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( 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 ) @ B ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ D ) ) ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(1278,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__mem__trans) ).
thf(6559,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1278]) ).
thf(1258,axiom,
! [A: $i,B: $i] :
( ( c_Equiv__Relations_Opart__equivp @ B @ A )
<=> ( ? [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ C ) )
& ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ A @ D ) @ D ) )
& ( ( hAPP @ A @ C )
= ( hAPP @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_part__equivp__def) ).
thf(6451,plain,
! [A: $i,B: $i] :
( ( ( c_Equiv__Relations_Opart__equivp @ B @ A )
=> ( ? [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ C ) )
& ! [C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ A @ D ) @ D ) )
& ( ( hAPP @ A @ C )
= ( hAPP @ A @ D ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ A @ D ) @ D ) )
& ( ( hAPP @ A @ C )
= ( hAPP @ A @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ D ) ) ) ) ) )
& ( ( ? [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ C ) )
& ! [C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ A @ D ) @ D ) )
& ( ( hAPP @ A @ C )
= ( hAPP @ A @ D ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ A @ D ) @ D ) )
& ( ( hAPP @ A @ C )
= ( hAPP @ A @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ D ) ) ) ) )
=> ( c_Equiv__Relations_Opart__equivp @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1258]) ).
thf(418,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
thf(3068,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)],[418]) ).
thf(656,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( c_List_Oremove1 @ C @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( c_List_Oremove1 @ C @ B @ A ) )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__remove1) ).
thf(4033,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( c_List_Oremove1 @ C @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( c_List_Oremove1 @ C @ B @ A ) )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(527,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Odiff__diff__eq) ).
thf(3505,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(1117,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ B ) @ A ) )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__1) ).
thf(5846,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ B ) @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Oacyclic @ B @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ B @ tc_HOL_Obool ) @ ( c_Predicate_Oconversep @ B @ B @ A ) ) ) )
<=> ( c_Wellfounded_Oacyclic @ B @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ B @ tc_HOL_Obool ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclicP__converse) ).
thf(1345,plain,
! [A: $i,B: $i] :
( ( ( c_Wellfounded_Oacyclic @ B @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ B @ tc_HOL_Obool ) @ ( c_Predicate_Oconversep @ B @ B @ A ) ) ) )
=> ( c_Wellfounded_Oacyclic @ B @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ B @ tc_HOL_Obool ) @ A ) ) ) )
& ( ( c_Wellfounded_Oacyclic @ B @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ B @ tc_HOL_Obool ) @ A ) ) )
=> ( c_Wellfounded_Oacyclic @ B @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ B @ tc_HOL_Obool ) @ ( c_Predicate_Oconversep @ B @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1030,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Relation_ODomain @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ ( hAPP @ ( c_Relation_ODomain @ E @ D ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__insert) ).
thf(5489,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Relation_ODomain @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ ( hAPP @ ( c_Relation_ODomain @ E @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(336,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ E ) @ D ) )
=> ( ( hAPP @ ( hAPP @ ( 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 ) )
= ( hAPP @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__add__eq2) ).
thf(2750,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ E ) @ D ) )
=> ( ( hAPP @ ( hAPP @ ( 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 ) )
= ( hAPP @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(458,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ C ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__iff) ).
thf(3226,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(448,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ E @ C @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ D @ C @ E ) @ ( hAPP @ ( c_Relation_Oconverse @ C @ D ) @ A ) ) @ ( hAPP @ ( c_Relation_Oconverse @ E @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rel__comp) ).
thf(3184,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ E @ C @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ D @ C @ E ) @ ( hAPP @ ( c_Relation_Oconverse @ C @ D ) @ A ) ) @ ( hAPP @ ( c_Relation_Oconverse @ E @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(495,axiom,
! [A: $i] :
( ( class_Orderings_Owellorder @ A )
=> ( c_Wellfounded_Owf @ A @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ A @ A ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ A @ A @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf) ).
thf(3378,plain,
! [A: $i] :
( ( class_Orderings_Owellorder @ A )
=> ( c_Wellfounded_Owf @ A @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ A @ A ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ A @ A @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(909,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Oset @ C ) @ ( c_List_Oinsert @ C @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_List_Oset__insert) ).
thf(5045,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Oset @ C ) @ ( c_List_Oinsert @ C @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(1050,axiom,
! [A: $i,B: $i] :
( ( c_Equiv__Relations_Oequivp @ B @ A )
<=> ( ( c_Predicate_Oreflp @ B @ A )
& ( c_Predicate_Osymp @ B @ A )
& ( c_Predicate_Otransp @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__reflp__symp__transp) ).
thf(5572,plain,
! [A: $i,B: $i] :
( ( ( c_Equiv__Relations_Oequivp @ B @ A )
=> ( ( c_Predicate_Oreflp @ B @ A )
& ( c_Predicate_Osymp @ B @ A )
& ( c_Predicate_Otransp @ B @ A ) ) )
& ( ( ( c_Predicate_Oreflp @ B @ A )
& ( c_Predicate_Osymp @ B @ A )
& ( c_Predicate_Otransp @ B @ A ) )
=> ( c_Equiv__Relations_Oequivp @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).
thf(538,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ B ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ D ) @ C ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bset_I6_J) ).
thf(3537,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ B ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ D ) @ C ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(1101,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
<=> ? [D: $i] :
( ? [E: $i] :
( A
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ E ) ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__conv__decomp__first) ).
thf(5773,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ? [D: $i] :
( ? [E: $i] :
( A
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ E ) ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ D ) ) ) ) )
& ( ? [D: $i] :
( ? [E: $i] :
( A
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ E ) ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ D ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).
thf(926,axiom,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__idemp) ).
thf(5096,plain,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(509,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Ozip @ C @ B ) @ ( c_List_Olist_ONil @ C ) ) @ A )
= ( c_List_Olist_ONil @ ( tc_prod @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__Nil) ).
thf(3421,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Ozip @ C @ B ) @ ( c_List_Olist_ONil @ C ) ) @ A )
= ( c_List_Olist_ONil @ ( tc_prod @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono1__neg) ).
thf(1447,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(998,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__Cons__self2) ).
thf(5370,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(740,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).
thf(4364,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(1231,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Big__Operators_Ocomm__monoid__big @ G @ F @ E @ D @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hAPP @ ( hAPP @ C @ A ) @ B )
= D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__monoid__big_Oinfinite) ).
thf(6347,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Big__Operators_Ocomm__monoid__big @ G @ F @ E @ D @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hAPP @ ( hAPP @ C @ A ) @ B )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1231]) ).
thf(657,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_List_Oset @ tc_Nat_Onat ) @ ( c_List_Oupt @ B @ A ) )
= ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__upt) ).
thf(4040,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_List_Oset @ tc_Nat_Onat ) @ ( c_List_Oupt @ B @ A ) )
= ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(350,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ D ) @ C ) ) @ ( c_List_Olistrel1 @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ A ) @ C ) ) ) @ ( c_List_Olistrel1 @ E @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1I2) ).
thf(2809,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ D ) @ C ) ) @ ( c_List_Olistrel1 @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ A ) @ C ) ) ) @ ( c_List_Olistrel1 @ E @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(348,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ 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_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ C @ A ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__add1__eq) ).
thf(2804,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ 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_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ C @ A ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(1073,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Osingle__valued @ E @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ A ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__confluent) ).
thf(5665,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Osingle__valued @ E @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ A ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).
thf(1063,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ D ) @ C )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__eq) ).
thf(5629,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ D ) @ C )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).
thf(778,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Osym @ B @ A )
=> ( c_Relation_Osym @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sym__trancl) ).
thf(4519,plain,
! [A: $i,B: $i] :
( ( c_Relation_Osym @ B @ A )
=> ( c_Relation_Osym @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(86,axiom,
! [A: $i,B: $i] :
( ( c_Predicate_Osymp @ B @ A )
<=> ( c_Relation_Osym @ B @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ B @ tc_HOL_Obool ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_symp__def) ).
thf(1600,plain,
! [A: $i,B: $i] :
( ( ( c_Predicate_Osymp @ B @ A )
=> ( c_Relation_Osym @ B @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ B @ tc_HOL_Obool ) @ A ) ) ) )
& ( ( c_Relation_Osym @ B @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ B @ tc_HOL_Obool ) @ A ) ) )
=> ( c_Predicate_Osymp @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(828,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ tc_Nat_Onat @ c_Nat_OSuc ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ B @ A ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__Suc__atLeastAtMost) ).
thf(4707,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ tc_Nat_Onat @ c_Nat_OSuc ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ B @ A ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(743,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Equiv__Relations_Oequiv @ C @ B @ A )
=> ~ ( ( c_Relation_Orefl__on @ C @ B @ A )
=> ( ( c_Relation_Osym @ C @ A )
=> ~ ( c_Relation_Otrans @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivE) ).
thf(4379,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Equiv__Relations_Oequiv @ C @ B @ A )
=> ~ ( ( c_Relation_Orefl__on @ C @ B @ A )
=> ( ( c_Relation_Osym @ C @ A )
=> ~ ( c_Relation_Otrans @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(110,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib) ).
thf(1697,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)],[110]) ).
thf(544,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
thf(3559,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)],[544]) ).
thf(553,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__insert__le) ).
thf(3606,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(225,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Onth @ B ) @ A ) @ C ) ) @ ( c_List_Olist_ONil @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__Suc__conv__app__nth) ).
thf(2154,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Onth @ B ) @ A ) @ C ) ) @ ( c_List_Olist_ONil @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(1179,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ D ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) )
=> ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityCE) ).
thf(6103,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ D ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) )
=> ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux2) ).
thf(1521,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[67]) ).
thf(986,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatMost @ tc_Nat_Onat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__atMost) ).
thf(5328,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatMost @ tc_Nat_Onat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(808,axiom,
! [A: $i,B: $i] :
( ( B
!= ( c_List_Olist_ONil @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ A ) @ ( c_List_Obutlast @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__butlast) ).
thf(4628,plain,
! [A: $i,B: $i] :
( ( B
!= ( c_List_Olist_ONil @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ A ) @ ( c_List_Obutlast @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(328,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ C @ B ) ) @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__distrib) ).
thf(2718,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ C @ B ) ) @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(1146,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ ( c_List_OtakeWhile @ D @ B @ A ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ A ) ) )
& ( hBOOL @ ( hAPP @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__takeWhileD) ).
thf(5970,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ ( c_List_OtakeWhile @ D @ B @ A ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ A ) ) )
& ( hBOOL @ ( hAPP @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).
thf(230,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ C ) )
<=> ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ D ) @ B ) ) ) ) )
=> ( ? [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) )
<=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ C ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_periodic__finite__ex) ).
thf(2205,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ! [C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ A @ C ) )
=> ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ D ) @ B ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ D ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) )
=> ( ( ? [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ C ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) ) )
& ( ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ C ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) )
=> ? [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(174,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mod__equality_H) ).
thf(1975,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(668,axiom,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).
thf(4082,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(459,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ ( c_List_OtakeWhile @ C @ B @ A ) ) @ ( c_List_OdropWhile @ C @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__dropWhile__id) ).
thf(3229,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ ( c_List_OtakeWhile @ C @ B @ A ) ) @ ( c_List_OdropWhile @ C @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(408,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_List_Olist_ONil @ C )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osimps_I2_J) ).
thf(3011,plain,
! [A: $i,B: $i,C: $i] :
( ( c_List_Olist_ONil @ C )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(1159,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ G @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( hAPP @ B @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ A @ E ) @ ( tc_prod @ A @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ A @ E ) @ ( tc_prod @ A @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ A @ E ) @ F ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ A @ E ) @ F ) @ C ) ) ) @ ( c_Recdef_Osame__fst @ A @ E @ G @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_same__fstI) ).
thf(6020,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ G @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( hAPP @ B @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ A @ E ) @ ( tc_prod @ A @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ A @ E ) @ ( tc_prod @ A @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ A @ E ) @ F ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ A @ E ) @ F ) @ C ) ) ) @ ( c_Recdef_Osame__fst @ A @ E @ G @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).
thf(919,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( hAPP @ ( c_List_OremoveAll @ B @ C ) @ ( hAPP @ ( c_List_Ofilter @ B @ D ) @ A ) )
= ( hAPP @ ( c_List_Ofilter @ B @ D ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_removeAll__filter__not) ).
thf(5070,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( hAPP @ ( c_List_OremoveAll @ B @ C ) @ ( hAPP @ ( c_List_Ofilter @ B @ D ) @ A ) )
= ( hAPP @ ( c_List_Ofilter @ B @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(975,axiom,
! [A: $i,B: $i,C: $i] :
( C
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__Cons__self) ).
thf(5291,plain,
! [A: $i,B: $i,C: $i] :
( C
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(332,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( 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 @ ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__add__iff2) ).
thf(2737,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ E ) @ D ) )
=> ( ( ( hBOOL @ ( hAPP @ ( 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 @ ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[332]) ).
thf(877,axiom,
! [A: $i,B: $i] : ( class_Nat_Osize @ ( tc_prod @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_prod__Nat_Osize) ).
thf(4910,plain,
! [A: $i,B: $i] : ( class_Nat_Osize @ ( tc_prod @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(661,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
thf(4059,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[661]) ).
thf(977,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ ( hAPP @ ( c_Relation_Oconverse @ D @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__converseI) ).
thf(5298,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ ( hAPP @ ( c_Relation_Oconverse @ D @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(149,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_List_Olist__ex @ C @ B @ A )
<=> ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) )
& ( hBOOL @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex__length) ).
thf(1863,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_List_Olist__ex @ C @ B @ A )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) )
& ( hBOOL @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ A ) @ D ) ) ) ) )
& ( ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) )
& ( hBOOL @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ A ) @ D ) ) ) )
=> ( c_List_Olist__ex @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(1220,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( ( hAPP @ D @ B )
!= ( hAPP @ D @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__contraD) ).
thf(6282,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( ( hAPP @ D @ B )
!= ( hAPP @ D @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1220]) ).
thf(101,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__imp__zdiv__pos__iff) ).
thf(1651,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(945,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Oset @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_List_Oset_Osimps_I2_J) ).
thf(5174,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Oset @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(426,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ( ( c_List_Obutlast @ B @ ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast__take) ).
thf(3097,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ( ( c_List_Obutlast @ B @ ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(1103,axiom,
! [A: $i] : ( c_Equiv__Relations_Oequivp @ A @ c_fequal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_identity__equivp) ).
thf(5783,plain,
! [A: $i] : ( c_Equiv__Relations_Oequivp @ A @ c_fequal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).
thf(548,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Relation_ODomain @ C @ B ) @ ( hAPP @ ( c_Relation_Oconverse @ B @ C ) @ A ) )
= ( hAPP @ ( c_Relation_ORange @ B @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__converse) ).
thf(3591,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Relation_ODomain @ C @ B ) @ ( hAPP @ ( c_Relation_Oconverse @ B @ C ) @ A ) )
= ( hAPP @ ( c_Relation_ORange @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(306,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel1) ).
thf(2574,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[306]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Odrop @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ E ) @ C ) @ D )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__via__drop) ).
thf(1438,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Odrop @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ E ) @ C ) @ D )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(564,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__Suc) ).
thf(3635,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(1018,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Set_Oimage @ D @ B @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__imageI) ).
thf(5443,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Set_Oimage @ D @ B @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(1211,axiom,
! [A: $i,B: $i] :
( ( class_Enum_Oenum @ B )
=> ( ! [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) )
<=> ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__all @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__code) ).
thf(6250,plain,
! [A: $i,B: $i] :
( ( class_Enum_Oenum @ B )
=> ( ( ! [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__all @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__all @ B ) @ A ) )
=> ! [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1211]) ).
thf(791,axiom,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ tc_Nat_Onat @ c_Nat_OSuc ) @ ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessThan__Suc__eq__insert__0) ).
thf(4557,plain,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ tc_Nat_Onat @ c_Nat_OSuc ) @ ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(192,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_List_Olist @ B ) ) @ A ) )
=> ? [C: $i] :
! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ B ) ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ D ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__maxlen) ).
thf(2047,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_List_Olist @ B ) ) @ A ) )
=> ? [C: $i] :
! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ B ) ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ D ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(932,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Oacyclic @ D @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ A ) )
<=> ( ( c_Wellfounded_Oacyclic @ D @ A )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclic__insert) ).
thf(5117,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Wellfounded_Oacyclic @ D @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ A ) )
=> ( ( c_Wellfounded_Oacyclic @ D @ A )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ) )
& ( ( ( c_Wellfounded_Oacyclic @ D @ A )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) )
=> ( c_Wellfounded_Oacyclic @ D @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( 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 @ ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__add__iff2) ).
thf(1311,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ E ) @ D ) )
=> ( ( ( hBOOL @ ( hAPP @ ( 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 @ ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[10]) ).
thf(596,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_Divides_Odivmod__nat @ A @ B )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ) @ B ) ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__step) ).
thf(3767,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_Divides_Odivmod__nat @ A @ B )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ) @ B ) ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(694,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Osym @ B @ A )
<=> ( ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sym__conv__converse__eq) ).
thf(4172,plain,
! [A: $i,B: $i] :
( ( ( c_Relation_Osym @ B @ A )
=> ( ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A )
= A ) )
& ( ( ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A )
= A )
=> ( c_Relation_Osym @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(180,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ B ) @ A )
= ( c_List_Olist_ONil @ C ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__eq__Nil) ).
thf(2000,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ B ) @ A )
= ( c_List_Olist_ONil @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ B ) @ A )
= ( c_List_Olist_ONil @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(881,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__antisym) ).
thf(4925,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(1176,axiom,
hBOOL @ c_fTrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fTrue__1) ).
thf(6092,plain,
hBOOL @ c_fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176]) ).
thf(606,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less) ).
thf(3795,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(415,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( 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 @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ D ) ) ) )
& ( hBOOL @ ( hAPP @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__div_H) ).
thf(3037,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( 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 @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( hAPP @ 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 @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ D ) ) ) )
& ( hBOOL @ ( hAPP @ C @ D ) ) ) )
=> ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(1201,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ B @ ( c_Hilbert__Choice_OEps @ A @ B ) ) )
<=> ? [C: $i] : ( hBOOL @ ( hAPP @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_some__eq__ex) ).
thf(6200,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ B @ ( c_Hilbert__Choice_OEps @ A @ B ) ) )
=> ? [C: $i] : ( hBOOL @ ( hAPP @ B @ C ) ) )
& ( ? [C: $i] : ( hBOOL @ ( hAPP @ B @ C ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Hilbert__Choice_OEps @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1201]) ).
thf(313,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ E ) @ D ) )
=> ( ( hAPP @ ( hAPP @ ( 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 ) )
= ( hAPP @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__add__eq1) ).
thf(2673,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ E ) @ D ) )
=> ( ( hAPP @ ( hAPP @ ( 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 ) )
= ( hAPP @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(156,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_zless__imp__add1__zle) ).
thf(1900,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[156]) ).
thf(1230,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ F @ E )
= D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ E ) @ ( hAPP @ ( c_Set_Ovimage @ A @ C @ F ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimageI) ).
thf(6343,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ F @ E )
= D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ E ) @ ( hAPP @ ( c_Set_Ovimage @ A @ C @ F ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1230]) ).
thf(297,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__function__closures_I1_J) ).
thf(2541,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(223,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ ( c_List_Oremdups @ B @ A ) ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__remdups__leq) ).
thf(2147,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ ( c_List_Oremdups @ B @ A ) ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(555,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Relation_OField @ B ) @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) )
= ( hAPP @ ( c_Relation_OField @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Field__converse) ).
thf(3610,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Relation_OField @ B ) @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) )
= ( hAPP @ ( c_Relation_OField @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(440,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ ( hAPP @ ( c_List_Oset @ D ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ B @ E ) ) )
=> ( ( c_List_OdropWhile @ D @ B @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ A ) )
= ( c_List_OdropWhile @ D @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile__append2) ).
thf(3154,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ ( hAPP @ ( c_List_Oset @ D ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ B @ E ) ) )
=> ( ( c_List_OdropWhile @ D @ B @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ A ) )
= ( c_List_OdropWhile @ D @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono1) ).
thf(1619,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[91]) ).
thf(530,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_List_Oupt @ A @ B )
= ( c_List_Olist_ONil @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__conv__Nil) ).
thf(3514,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_List_Oupt @ A @ B )
= ( c_List_Olist_ONil @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(767,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__drop) ).
thf(4466,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(1059,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ ( hAPP @ C @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__insert) ).
thf(5611,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ ( hAPP @ C @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).
thf(1174,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) )
<=> ( ( C = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__iff) ).
thf(6079,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) )
=> ( ( C = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) )
& ( ( ( C = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).
thf(615,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ C ) @ A ) )
<=> ( A
= ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__append__conv) ).
thf(3827,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ C ) @ A ) )
=> ( A
= ( c_List_Olist_ONil @ B ) ) )
& ( ( A
= ( c_List_Olist_ONil @ B ) )
=> ( C
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(1181,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_CollectE) ).
thf(6122,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1181]) ).
thf(270,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ ( hAPP @ ( c_List_Oset @ B ) @ A ) )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__distinct) ).
thf(2428,plain,
! [A: $i,B: $i] :
( ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ ( hAPP @ ( c_List_Oset @ B ) @ A ) )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(241,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_zmult__zless__mono2) ).
thf(2249,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[241]) ).
thf(552,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ ( c_List_Olist_ONil @ B ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__Nil) ).
thf(3603,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ ( c_List_Olist_ONil @ B ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(625,axiom,
! [A: $i,B: $i] :
( ( ( c_List_Oremdups @ B @ A )
= A )
<=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remdups__id__iff__distinct) ).
thf(3867,plain,
! [A: $i,B: $i] :
( ( ( ( c_List_Oremdups @ B @ A )
= A )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ B ) @ A ) )
=> ( ( c_List_Oremdups @ B @ A )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(895,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Finite__Set_Ofun__left__comm @ G @ F @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ F @ E @ D @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ C ) @ B ) ) @ A ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ C ) @ B ) )
=> ~ ! [H: $i] :
( ( A
= ( hAPP @ ( hAPP @ E @ C ) @ H ) )
=> ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ F @ E @ D @ B ) @ H ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__graph__insertE) ).
thf(5002,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Finite__Set_Ofun__left__comm @ G @ F @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ F @ E @ D @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ C ) @ B ) ) @ A ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ C ) @ B ) )
=> ~ ! [H: $i] :
( ( A
= ( hAPP @ ( hAPP @ E @ C ) @ H ) )
=> ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ F @ E @ D @ B ) @ H ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zmult1__eq) ).
thf(1355,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(248,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel1) ).
thf(2277,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[248]) ).
thf(1108,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Owf @ D @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ A ) )
<=> ( ( c_Wellfounded_Owf @ D @ A )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__insert) ).
thf(5794,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Wellfounded_Owf @ D @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ A ) )
=> ( ( c_Wellfounded_Owf @ D @ A )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ) )
& ( ( ( c_Wellfounded_Owf @ D @ A )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) )
=> ( c_Wellfounded_Owf @ D @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).
thf(759,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Relation_ODomain @ B @ B ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) )
= ( hAPP @ ( c_Relation_ODomain @ B @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__domain) ).
thf(4434,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Relation_ODomain @ B @ B ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) )
= ( hAPP @ ( c_Relation_ODomain @ B @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(872,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Omap @ D @ C ) @ B ) @ ( c_List_Obutlast @ D @ A ) )
= ( c_List_Obutlast @ C @ ( hAPP @ ( hAPP @ ( c_List_Omap @ D @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__butlast) ).
thf(4878,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Omap @ D @ C ) @ B ) @ ( c_List_Obutlast @ D @ A ) )
= ( c_List_Obutlast @ C @ ( hAPP @ ( hAPP @ ( c_List_Omap @ D @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(1051,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_OwfP @ C @ B )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__wfPD) ).
thf(5579,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_OwfP @ C @ B )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(894,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
<=> ( ( C = B )
| ( ( C != B )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__eq__or__trancl) ).
thf(4989,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ( ( C = B )
| ( ( C != B )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ) ) )
& ( ( ( C = B )
| ( ( C != B )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(991,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( B
= ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SucE) ).
thf(5349,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( B
= ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__append__length__plus) ).
thf(1751,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(1111,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D = C )
=> ( ( hAPP @ ( c_List_OremoveAll @ B @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ C ) @ A ) )
= ( hAPP @ ( c_List_OremoveAll @ B @ D ) @ A ) ) )
& ( ( D != C )
=> ( ( hAPP @ ( c_List_OremoveAll @ B @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ C ) @ ( hAPP @ ( c_List_OremoveAll @ B @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_removeAll_Osimps_I2_J) ).
thf(5815,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D = C )
=> ( ( hAPP @ ( c_List_OremoveAll @ B @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ C ) @ A ) )
= ( hAPP @ ( c_List_OremoveAll @ B @ D ) @ A ) ) )
& ( ( D != C )
=> ( ( hAPP @ ( c_List_OremoveAll @ B @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ C ) @ ( hAPP @ ( c_List_OremoveAll @ B @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).
thf(588,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ C ) @ ( hAPP @ ( c_List_Omap @ E @ D ) @ B ) ) @ ( hAPP @ ( c_List_Omap @ C @ E ) @ A ) )
= ( hAPP @ ( c_List_Omap @ C @ D ) @ ( hAPP @ ( c_Fun_Ocomp @ E @ D @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__comp__map) ).
thf(3742,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ C ) @ ( hAPP @ ( c_List_Omap @ E @ D ) @ B ) ) @ ( hAPP @ ( c_List_Omap @ C @ E ) @ A ) )
= ( hAPP @ ( c_List_Omap @ C @ D ) @ ( hAPP @ ( c_Fun_Ocomp @ E @ D @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(1280,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ B ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ ( c_List_Oremove1 @ D @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_notin__set__remove1) ).
thf(6565,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ B ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ ( c_List_Oremove1 @ D @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1280]) ).
thf(395,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_List_Oinsert @ C @ B @ ( c_List_Oremdups @ C @ A ) )
= ( c_List_Oremdups @ C @ ( c_List_Oinsert @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__remdups) ).
thf(2969,plain,
! [A: $i,B: $i,C: $i] :
( ( c_List_Oinsert @ C @ B @ ( c_List_Oremdups @ C @ A ) )
= ( c_List_Oremdups @ C @ ( c_List_Oinsert @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(996,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ A ) @ A ) ) @ ( c_Relation_OId @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IdI) ).
thf(5366,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ A ) @ A ) ) @ ( c_Relation_OId @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(592,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_List_Olist_ONil @ D )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ D ) @ B ) @ A ) )
<=> ( A
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nil__is__map__conv) ).
thf(3752,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( c_List_Olist_ONil @ D )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ D ) @ B ) @ A ) )
=> ( A
= ( c_List_Olist_ONil @ C ) ) )
& ( ( A
= ( c_List_Olist_ONil @ C ) )
=> ( ( c_List_Olist_ONil @ D )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(779,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ B )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__geq) ).
thf(4521,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ B )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(1026,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ A @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ C ) @ E ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ C ) @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SigmaI) ).
thf(5470,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ A @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ C ) @ E ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ C ) @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).
thf(385,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Omap @ E @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ E @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ E @ D ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__append) ).
thf(2937,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Omap @ E @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ E @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ E @ D ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(700,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ B ) @ A ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ A ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ D ) @ C ) ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_aset_I5_J) ).
thf(4204,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ B ) @ A ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ A ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ D ) @ C ) ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(629,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ C ) ) @ ( hAPP @ c_Nat_OSuc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq1) ).
thf(3884,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ C ) ) @ ( hAPP @ c_Nat_OSuc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(1263,axiom,
! [A: $i,B: $i] :
( ( class_Enum_Oenum @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__all @ B ) @ A ) )
<=> ! [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_enum__all) ).
thf(6496,plain,
! [A: $i,B: $i] :
( ( class_Enum_Oenum @ B )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__all @ B ) @ A ) )
=> ! [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) ) )
& ( ! [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__all @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1263]) ).
thf(1032,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
<=> ! [C: $i] :
( ? [D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ C ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ C ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ E ) @ D ) ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ E ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__eq__minimal) ).
thf(5507,plain,
! [A: $i,B: $i] :
( ( ( c_Wellfounded_Owf @ B @ A )
=> ! [C: $i] :
( ? [D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ C ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ C ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ E ) @ D ) ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ E ) @ C ) ) ) ) ) )
& ( ! [C: $i] :
( ? [D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ C ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ C ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ E ) @ D ) ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ E ) @ C ) ) ) ) )
=> ( c_Wellfounded_Owf @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).
thf(858,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ ( c_List_OdropWhile @ C @ B @ A ) ) ) )
=> ~ ( hBOOL @ ( hAPP @ B @ D ) ) )
=> ( ( c_List_OtakeWhile @ C @ B @ A )
= ( hAPP @ ( c_List_Ofilter @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__eq__filter) ).
thf(4821,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ ( c_List_OdropWhile @ C @ B @ A ) ) ) )
=> ~ ( hBOOL @ ( hAPP @ B @ D ) ) )
=> ( ( c_List_OtakeWhile @ C @ B @ A )
= ( hAPP @ ( c_List_Ofilter @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(1005,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oord__eq__le__trans) ).
thf(5396,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(818,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ C ) )
=> ! [E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ G ) @ B ) )
=> ( E
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ G ) @ F ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ E ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ E ) @ C ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bset_I9_J) ).
thf(4661,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ C ) )
=> ! [E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ G ) @ B ) )
=> ( E
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ G ) @ F ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ E ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ E ) @ C ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(294,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_pos__zmult__eq__1__iff) ).
thf(2528,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( 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)],[294]) ).
thf(600,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ A ) ) )
=> ( ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_expand__Suc) ).
thf(3778,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ A ) ) )
=> ( ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(184,axiom,
! [A: $i,B: $i] :
( ( c_List_Olistrel @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) )
= ( c_Transitive__Closure_Ortrancl @ ( tc_List_Olist @ B ) @ ( c_List_Olistrel1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__rtrancl__eq__rtrancl__listrel1) ).
thf(2015,plain,
! [A: $i,B: $i] :
( ( c_List_Olistrel @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) )
= ( c_Transitive__Closure_Ortrancl @ ( tc_List_Olist @ B ) @ ( c_List_Olistrel1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(610,axiom,
! [A: $i,B: $i] :
( ( c_List_OtakeWhile @ B @ A @ ( c_List_Olist_ONil @ B ) )
= ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile_Osimps_I1_J) ).
thf(3810,plain,
! [A: $i,B: $i] :
( ( c_List_OtakeWhile @ B @ A @ ( c_List_Olist_ONil @ B ) )
= ( c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(283,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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ C ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ A ) )
& ( hBOOL @ ( hAPP @ ( 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 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ D ) @ C )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__rel__div__eq) ).
thf(2477,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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ C ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ A ) )
& ( hBOOL @ ( hAPP @ ( 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 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ D ) @ C )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(504,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_COMBK @ tc_Nat_Onat @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__def) ).
thf(3403,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_COMBK @ tc_Nat_Onat @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(1081,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ole__less) ).
thf(5690,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
| ( B = A ) ) )
& ( ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
| ( B = A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).
thf(551,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__1) ).
thf(3600,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(631,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc) ).
thf(3894,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(1187,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ A ) @ v_ts ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ ( hAPP @ c_Nat_OSuc @ v_n ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(6143,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ A ) @ v_ts ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ ( hAPP @ c_Nat_OSuc @ v_n ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1187]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_List_Ofoldl @ D @ C @ B @ A ) @ ( c_List_Olist_ONil @ C ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldl__Nil) ).
thf(1291,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_List_Ofoldl @ D @ C @ B @ A ) @ ( c_List_Olist_ONil @ C ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(987,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__le__trans) ).
thf(5330,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(392,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__diff) ).
thf(2958,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__distrib2) ).
thf(1423,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(470,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Set_Oimage @ F @ E @ ( hAPP @ ( c_Fun_Ocomp @ D @ E @ F @ C ) @ B ) ) @ A )
= ( hAPP @ ( c_Set_Oimage @ D @ E @ C ) @ ( hAPP @ ( c_Set_Oimage @ F @ D @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__compose) ).
thf(3271,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Set_Oimage @ F @ E @ ( hAPP @ ( c_Fun_Ocomp @ D @ E @ F @ C ) @ B ) ) @ A )
= ( hAPP @ ( c_Set_Oimage @ D @ E @ C ) @ ( hAPP @ ( c_Set_Oimage @ F @ D @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(639,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ B ) @ A ) @ ( c_List_Olist_ONil @ C ) )
= ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map_Osimps_I1_J) ).
thf(3958,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ B ) @ A ) @ ( c_List_Olist_ONil @ C ) )
= ( c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(276,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_zadd__zless__mono) ).
thf(2445,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[276]) ).
thf(720,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_List_Oremdups @ D @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ D ) @ B ) @ ( c_List_Oremdups @ C @ A ) ) )
= ( c_List_Oremdups @ D @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ D ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remdups__map__remdups) ).
thf(4280,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_List_Oremdups @ D @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ D ) @ B ) @ ( c_List_Oremdups @ C @ A ) ) )
= ( c_List_Oremdups @ D @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ D ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(367,axiom,
! [A: $i] : ( c_Relation_Oantisym @ A @ ( c_Relation_OId @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisym__Id) ).
thf(2873,plain,
! [A: $i] : ( c_Relation_Oantisym @ A @ ( c_Relation_OId @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(1031,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Ototal__on @ C @ B @ A )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( D != E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ E ) ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ E ) @ D ) ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_total__on__def) ).
thf(5492,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Relation_Ototal__on @ C @ B @ A )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( D != E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ E ) ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ E ) @ D ) ) @ A ) ) ) ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( D != E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ E ) ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ E ) @ D ) ) @ A ) ) ) ) ) )
=> ( c_Relation_Ototal__on @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).
thf(469,axiom,
! [A: $i,B: $i] : ( c_Relation_Otrans @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__trancl) ).
thf(3269,plain,
! [A: $i,B: $i] : ( c_Relation_Otrans @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(558,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ C ) @ B ) ) @ ( c_List_Olistrel @ D @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_List_Olist @ D ) @ ( c_List_Olistrel1 @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__listrel1__if__listrel) ).
thf(3618,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ C ) @ B ) ) @ ( c_List_Olistrel @ D @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_List_Olist @ D ) @ ( c_List_Olistrel1 @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(1071,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
=> ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ E ) @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tranclD2) ).
thf(5655,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
=> ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ E ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).
thf(685,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( hAPP @ ( c_Product__Type_Omap__pair @ K @ J @ I @ H @ G @ F ) @ ( hAPP @ ( c_Product__Type_Omap__pair @ E @ K @ D @ I @ C @ B ) @ A ) )
= ( hAPP @ ( c_Product__Type_Omap__pair @ E @ J @ D @ H @ ( hAPP @ ( c_Fun_Ocomp @ K @ J @ E @ G ) @ C ) @ ( hAPP @ ( c_Fun_Ocomp @ I @ H @ D @ F ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair_Ocompositionality) ).
thf(4140,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( hAPP @ ( c_Product__Type_Omap__pair @ K @ J @ I @ H @ G @ F ) @ ( hAPP @ ( c_Product__Type_Omap__pair @ E @ K @ D @ I @ C @ B ) @ A ) )
= ( hAPP @ ( c_Product__Type_Omap__pair @ E @ J @ D @ H @ ( hAPP @ ( c_Fun_Ocomp @ K @ J @ E @ G ) @ C ) @ ( hAPP @ ( c_Fun_Ocomp @ I @ H @ D @ F ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(1025,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Oinv__image @ C @ F ) @ B ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ ( hAPP @ A @ E ) ) @ ( hAPP @ A @ D ) ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__inv__image) ).
thf(5465,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Oinv__image @ C @ F ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ ( hAPP @ A @ E ) ) @ ( hAPP @ A @ D ) ) ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ ( hAPP @ A @ E ) ) @ ( hAPP @ A @ D ) ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Oinv__image @ C @ F ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(802,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_List_Obutlast @ C @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ A ) @ ( c_List_Olist_ONil @ C ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast__snoc) ).
thf(4608,plain,
! [A: $i,B: $i,C: $i] :
( ( c_List_Obutlast @ C @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ A ) @ ( c_List_Olist_ONil @ C ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(262,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ! [D: $i] :
( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ E ) )
& ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ! [D: $i] :
( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ E ) )
& ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_split__zdiv) ).
thf(2332,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ! [D: $i] :
( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ E ) )
& ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ! [D: $i] :
( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ E ) )
& ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ! [D: $i] :
( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ E ) )
& ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ! [D: $i] :
( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ E ) )
& ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(1166,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ E @ D @ C ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep__iff) ).
thf(6043,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ E @ D @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ E @ D @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166]) ).
thf(841,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
<=> ( A
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__1__iff__1) ).
thf(4757,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
=> ( A
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( A
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(591,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff) ).
thf(3750,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( 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)],[591]) ).
thf(946,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ tc_Nat_Onat @ c_Wellfounded_Opred__nat ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__nat__trancl__eq__le) ).
thf(5177,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ tc_Nat_Onat @ c_Wellfounded_Opred__nat ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ tc_Nat_Onat @ c_Wellfounded_Opred__nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(543,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Odrop @ B ) @ A ) @ ( c_List_Olist_ONil @ B ) )
= ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__Nil) ).
thf(3556,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Odrop @ B ) @ A ) @ ( c_List_Olist_ONil @ B ) )
= ( c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(901,axiom,
! [A: $i] :
( ( c_Divides_Odivmod__nat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__zero) ).
thf(5021,plain,
! [A: $i] :
( ( c_Divides_Odivmod__nat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(1023,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_r__r__into__trancl) ).
thf(5460,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(907,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).
thf(5038,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(838,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__trans) ).
thf(4746,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(1048,axiom,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
thf(5566,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).
thf(1171,axiom,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( hBOOL @ ( hAPP @ C @ D ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ C @ E ) )
=> ( E = D ) ) )
=> ( ( c_FunDef_OTHE__default @ B @ A @ C )
= ( c_HOL_OThe @ B @ C ) ) )
& ( ~ ? [D: $i] :
( ( hBOOL @ ( hAPP @ C @ D ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ C @ E ) )
=> ( E = D ) ) )
=> ( ( c_FunDef_OTHE__default @ B @ A @ C )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_THE__default__def) ).
thf(6060,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( hBOOL @ ( hAPP @ C @ D ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ C @ E ) )
=> ( E = D ) ) )
=> ( ( c_FunDef_OTHE__default @ B @ A @ C )
= ( c_HOL_OThe @ B @ C ) ) )
& ( ~ ? [D: $i] :
( ( hBOOL @ ( hAPP @ C @ D ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ C @ E ) )
=> ( E = D ) ) )
=> ( ( c_FunDef_OTHE__default @ B @ A @ C )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).
thf(1195,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_List_Olist__ex1 @ C @ B @ A )
<=> ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
& ( hBOOL @ ( hAPP @ B @ D ) )
& ! [E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
& ( hBOOL @ ( hAPP @ B @ E ) ) )
=> ( E = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex1__iff__raw) ).
thf(6168,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_List_Olist__ex1 @ C @ B @ A )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
& ( hBOOL @ ( hAPP @ B @ D ) )
& ! [E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
& ( hBOOL @ ( hAPP @ B @ E ) ) )
=> ( E = D ) ) ) )
& ( ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
& ( hBOOL @ ( hAPP @ B @ D ) )
& ! [E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
& ( hBOOL @ ( hAPP @ B @ E ) ) )
=> ( E = D ) ) )
=> ( c_List_Olist__ex1 @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195]) ).
thf(1072,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oord__eq__less__trans) ).
thf(5658,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
thf(416,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).
thf(3050,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[416]) ).
thf(258,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ ( hAPP @ ( c_List_Oset @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ E ) ) )
=> ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ B ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ball__nth) ).
thf(2313,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ ( hAPP @ ( c_List_Oset @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ E ) ) )
=> ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ B ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(1120,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ B ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Hilbert__Choice_OEps @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_someI) ).
thf(5858,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ B ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Hilbert__Choice_OEps @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ C ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ C ) ) )
<=> ! [D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ E ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( A
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__neg__lemma) ).
thf(1634,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ C ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ C ) ) )
=> ! [D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ E ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( A
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ E ) ) ) )
& ( ! [D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ E ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( A
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ C ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(33,axiom,
! [A: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ A ) ) @ ( c_List_Olist_ONil @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osize_I3_J) ).
thf(1392,plain,
! [A: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ A ) ) @ ( c_List_Olist_ONil @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(602,axiom,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0I) ).
thf(3784,plain,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[602]) ).
thf(1084,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Omap @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Nat_OSuc ) @ ( c_List_Oupt @ B @ A ) )
= ( c_List_Oupt @ ( hAPP @ c_Nat_OSuc @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__Suc__upt) ).
thf(5714,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Omap @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Nat_OSuc ) @ ( c_List_Oupt @ B @ A ) )
= ( c_List_Oupt @ ( hAPP @ c_Nat_OSuc @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).
thf(970,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( ( hAPP @ c_Nat_OSuc @ B )
!= A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessI) ).
thf(5270,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( ( hAPP @ c_Nat_OSuc @ B )
!= A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(787,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofun__left__comm @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ F @ E @ D @ C @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ C ) @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__equality) ).
thf(4544,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofun__left__comm @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ F @ E @ D @ C @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ C ) @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ C @ B ) ) @ A ) @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ C ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmod__left) ).
thf(1498,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ C @ B ) ) @ A ) @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ C ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(865,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( c_List_Ofilter @ C @ B ) @ A )
= ( c_List_Olist_ONil @ C ) )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__empty__conv) ).
thf(4845,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( c_List_Ofilter @ C @ B ) @ A )
= ( c_List_Olist_ONil @ C ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ B @ D ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ B @ D ) ) )
=> ( ( hAPP @ ( c_List_Ofilter @ C @ B ) @ A )
= ( c_List_Olist_ONil @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(641,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__self__eq__0) ).
thf(3963,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(1080,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ E @ E @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Oeq__fold__idem_H) ).
thf(5687,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ E @ E @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).
thf(514,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_le__0__eq) ).
thf(3440,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( 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 @ ( 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)],[514]) ).
thf(37,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__refl) ).
thf(1402,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(1204,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ ( hAPP @ A @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ B @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_imageI) ).
thf(6215,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ ( hAPP @ A @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ B @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1204]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__pos__neg__trivial) ).
thf(1350,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(165,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ tc_Nat_Onat ) ) @ ( c_List_Oupt @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__upt) ).
thf(1936,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ tc_Nat_Onat ) ) @ ( c_List_Oupt @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(285,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ C ) ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ C ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zmod__equality) ).
thf(2498,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ C ) ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ C ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(557,axiom,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatMost @ tc_Nat_Onat ) @ A )
= ( hAPP @ ( c_List_Oset @ tc_Nat_Onat ) @ ( c_List_Oupt @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atMost__upto) ).
thf(3615,plain,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatMost @ tc_Nat_Onat ) @ A )
= ( hAPP @ ( c_List_Oset @ tc_Nat_Onat ) @ ( c_List_Oupt @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(71,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zdiv__trivial) ).
thf(1541,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(226,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
thf(2157,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[226]) ).
thf(1058,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__diff__nat) ).
thf(5609,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(519,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Otrans @ B @ A )
=> ( ( c_Transitive__Closure_Otrancl @ B @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__id) ).
thf(3482,plain,
! [A: $i,B: $i] :
( ( c_Relation_Otrans @ B @ A )
=> ( ( c_Transitive__Closure_Otrancl @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(912,axiom,
! [A: $i] :
( ( c_List_Omember @ A )
= ( c_List_Oset @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_member__set) ).
thf(5053,plain,
! [A: $i] :
( ( c_List_Omember @ A )
= ( c_List_Oset @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(937,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ B ) @ ( c_List_Obutlast @ C @ A ) )
= ( c_List_Obutlast @ C @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__butlast) ).
thf(5145,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ B ) @ ( c_List_Obutlast @ C @ A ) )
= ( c_List_Obutlast @ C @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(207,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__mult) ).
thf(2100,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(506,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).
thf(3413,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(131,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( 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 @ ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__add__iff1) ).
thf(1794,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ E ) @ D ) )
=> ( ( ( hBOOL @ ( hAPP @ ( 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 @ ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ B ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[131]) ).
thf(1076,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Wellfounded_Oacc @ D @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ A ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( c_Wellfounded_Oacc @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__downwards) ).
thf(5673,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Wellfounded_Oacc @ D @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ A ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( c_Wellfounded_Oacc @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).
thf(896,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__into__trancl2) ).
thf(5006,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(1013,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ F ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ D ) @ C ) ) ) @ ( c_Wellfounded_Olex__prod @ H @ G @ B @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ H @ H ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ H ) @ F ) @ D ) ) @ B ) )
| ( ( F = D )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ G @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ G ) @ E ) @ C ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__lex__prod) ).
thf(5423,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ F ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ D ) @ C ) ) ) @ ( c_Wellfounded_Olex__prod @ H @ G @ B @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ H @ H ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ H ) @ F ) @ D ) ) @ B ) )
| ( ( F = D )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ G @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ G ) @ E ) @ C ) ) @ A ) ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ H @ H ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ H ) @ F ) @ D ) ) @ B ) )
| ( ( F = D )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ G @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ G ) @ E ) @ C ) ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ F ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ D ) @ C ) ) ) @ ( c_Wellfounded_Olex__prod @ H @ G @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(133,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( 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 @ ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__add__iff1) ).
thf(1804,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ E ) @ D ) )
=> ( ( ( hBOOL @ ( hAPP @ ( 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 @ ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ B ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[133]) ).
thf(373,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ B ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ D @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__in__listsp__conv) ).
thf(2895,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ D @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ D @ C ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ D @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ D @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(710,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_List_Oupt @ B @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ tc_Nat_Onat ) @ ( c_List_Oupt @ B @ A ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ tc_Nat_Onat ) @ A ) @ ( c_List_Olist_ONil @ tc_Nat_Onat ) ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_List_Oupt @ B @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( c_List_Olist_ONil @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__Suc) ).
thf(4248,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_List_Oupt @ B @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ tc_Nat_Onat ) @ ( c_List_Oupt @ B @ A ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ tc_Nat_Onat ) @ A ) @ ( c_List_Olist_ONil @ tc_Nat_Onat ) ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_List_Oupt @ B @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( c_List_Olist_ONil @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(1199,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) )
=> ( ( C != B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertE) ).
thf(6195,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) )
=> ( ( C != B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1199]) ).
thf(1162,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ D @ A ) @ ( hAPP @ C @ B ) )
= ( hAPP @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Oin__idem) ).
thf(6028,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ D @ A ) @ ( hAPP @ C @ B ) )
= ( hAPP @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).
thf(330,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ B @ D ) )
=> ( hBOOL @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ D ) @ C ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ B @ D ) )
=> ( hBOOL @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_decr__mult__lemma) ).
thf(2724,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ B @ D ) )
=> ( hBOOL @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ D ) @ C ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ B @ D ) )
=> ( hBOOL @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(362,axiom,
! [A: $i,B: $i] : ( c_Relation_Orefl__on @ B @ A @ ( c_Relation_OId__on @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__Id__on) ).
thf(2858,plain,
! [A: $i,B: $i] : ( c_Relation_Orefl__on @ B @ A @ ( c_Relation_OId__on @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(563,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofun__left__comm @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ C ) )
=> ( ( hAPP @ ( hAPP @ D @ B ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ ( hAPP @ ( hAPP @ D @ B ) @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__fun__comm) ).
thf(3632,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofun__left__comm @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ C ) )
=> ( ( hAPP @ ( hAPP @ D @ B ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ ( hAPP @ ( hAPP @ D @ B ) @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(672,axiom,
! [A: $i,B: $i] : ( c_Relation_Osym @ B @ ( c_Relation_OId__on @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sym__Id__on) ).
thf(4095,plain,
! [A: $i,B: $i] : ( c_Relation_Osym @ B @ ( c_Relation_OId__on @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(432,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ? [E: $i,F: $i] :
( D
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ E ) @ F ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ B ) @ D ) ) ) @ ( c_List_Olexord @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__append__rightI) ).
thf(3119,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ? [E: $i,F: $i] :
( D
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ E ) @ F ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ B ) @ D ) ) ) @ ( c_List_Olexord @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(863,axiom,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatMost @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatMost @ tc_Nat_Onat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atMost__Suc) ).
thf(4840,plain,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatMost @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatMost @ tc_Nat_Onat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(421,axiom,
! [A: $i,B: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) )
= A )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( ( hAPP @ c_Nat_OSuc @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) )
!= A )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__Suc) ).
thf(3078,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) )
= A )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( ( hAPP @ c_Nat_OSuc @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) )
!= A )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(634,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ B ) @ A ) )
<=> ( ( ( B
= ( c_List_Olist_ONil @ E ) )
& ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ D ) @ C )
= A ) )
| ? [F: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ D ) @ F )
= B )
& ( C
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ F ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__eq__append__conv) ).
thf(3916,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ B ) @ A ) )
=> ( ( ( B
= ( c_List_Olist_ONil @ E ) )
& ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ D ) @ C )
= A ) )
| ? [F: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ D ) @ F )
= B )
& ( C
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ F ) @ A ) ) ) ) )
& ( ( ( ( B
= ( c_List_Olist_ONil @ E ) )
& ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ D ) @ C )
= A ) )
| ? [F: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ D ) @ F )
= B )
& ( C
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ F ) @ A ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(461,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( c_List_Osublist @ B @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ A ) @ ( c_List_Olist_ONil @ B ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ A ) @ ( c_List_Olist_ONil @ B ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( c_List_Osublist @ B @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ A ) @ ( c_List_Olist_ONil @ B ) ) @ C )
= ( c_List_Olist_ONil @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sublist__singleton) ).
thf(3237,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( c_List_Osublist @ B @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ A ) @ ( c_List_Olist_ONil @ B ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ A ) @ ( c_List_Olist_ONil @ B ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( c_List_Osublist @ B @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ A ) @ ( c_List_Olist_ONil @ B ) ) @ C )
= ( c_List_Olist_ONil @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__assoc) ).
thf(1397,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)],[35]) ).
thf(714,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Otrans @ D @ C )
=> ( ( c_Relation_Otrans @ B @ A )
=> ( c_Relation_Otrans @ ( tc_prod @ D @ B ) @ ( c_Wellfounded_Olex__prod @ D @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__lex__prod) ).
thf(4263,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Otrans @ D @ C )
=> ( ( c_Relation_Otrans @ B @ A )
=> ( c_Relation_Otrans @ ( tc_prod @ D @ B ) @ ( c_Wellfounded_Olex__prod @ D @ B @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(822,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ tc_Nat_Onat @ c_Wellfounded_Opred__nat ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq) ).
thf(4676,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ tc_Nat_Onat @ c_Wellfounded_Opred__nat ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ tc_Nat_Onat @ c_Wellfounded_Opred__nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__neg__lemma) ).
thf(1493,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[59]) ).
thf(905,axiom,
! [A: $i,B: $i] :
( ( c_Equiv__Relations_Opart__equivp @ B @ A )
=> ~ ( ? [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ C ) )
=> ( ( c_Predicate_Osymp @ B @ A )
=> ~ ( c_Predicate_Otransp @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_part__equivpE) ).
thf(5031,plain,
! [A: $i,B: $i] :
( ( c_Equiv__Relations_Opart__equivp @ B @ A )
=> ~ ( ? [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ C ) )
=> ( ( c_Predicate_Osymp @ B @ A )
=> ~ ( c_Predicate_Otransp @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zdiv__equality) ).
thf(1361,plain,
! [A: $i,B: $i] :
( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(167,axiom,
( ( hAPP @ ( c_Nat_Osize__class_Osize @ tc_HOL_Obool ) @ c_fFalse )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bool_Osize_I4_J) ).
thf(1942,plain,
( ( hAPP @ ( c_Nat_Osize__class_Osize @ tc_HOL_Obool ) @ c_fFalse )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(446,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__1) ).
thf(3179,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(1135,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OlessThan @ D @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OlessThan__iff) ).
thf(5915,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OlessThan @ D @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ C ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ B @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OlessThan @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).
thf(1092,axiom,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Otrancl @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__trancl__absorb) ).
thf(5743,plain,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Otrancl @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(989,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ A ) )
<=> ? [B: $i] :
! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded) ).
thf(5337,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ A ) )
=> ? [B: $i] :
! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) ) ) )
& ( ? [B: $i] :
! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(1053,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_Relation_ODomain @ D @ B ) @ A ) ) )
<=> ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ B ) @ C ) @ E ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__iff) ).
thf(5588,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_Relation_ODomain @ D @ B ) @ A ) ) )
=> ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ B ) @ C ) @ E ) ) @ A ) ) )
& ( ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ B ) @ C ) @ E ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_Relation_ODomain @ D @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(190,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) ) @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self4) ).
thf(2038,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) ) @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(1274,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Typedef_Otype__definition @ F @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ B ) )
=> ( ( hAPP @ D @ ( hAPP @ C @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_OAbs__inverse) ).
thf(6539,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Typedef_Otype__definition @ F @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ B ) )
=> ( ( hAPP @ D @ ( hAPP @ C @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1274]) ).
thf(763,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_List_Olist_ONil @ C )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ B ) @ A ) )
<=> ( ( B
= ( c_List_Olist_ONil @ C ) )
& ( A
= ( c_List_Olist_ONil @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nil__is__append__conv) ).
thf(4444,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( c_List_Olist_ONil @ C )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ B ) @ A ) )
=> ( ( B
= ( c_List_Olist_ONil @ C ) )
& ( A
= ( c_List_Olist_ONil @ C ) ) ) )
& ( ( ( B
= ( c_List_Olist_ONil @ C ) )
& ( A
= ( c_List_Olist_ONil @ C ) ) )
=> ( ( c_List_Olist_ONil @ C )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(1216,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Set_Ovimage @ E @ C @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimageD) ).
thf(6271,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Set_Ovimage @ E @ C @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1216]) ).
thf(636,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F = E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= A ) )
& ( ( F != E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= ( hAPP @ B @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__def) ).
thf(3935,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F = E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= A ) )
& ( ( F != E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= ( hAPP @ B @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(437,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Omap @ D @ C ) @ B ) @ A )
= ( c_List_Olist_ONil @ C ) )
<=> ( A
= ( c_List_Olist_ONil @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__is__Nil__conv) ).
thf(3141,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Omap @ D @ C ) @ B ) @ A )
= ( c_List_Olist_ONil @ C ) )
=> ( A
= ( c_List_Olist_ONil @ D ) ) )
& ( ( A
= ( c_List_Olist_ONil @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Omap @ D @ C ) @ B ) @ A )
= ( c_List_Olist_ONil @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(886,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( c_List_Ofilter @ E @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ B ) @ A ) )
<=> ? [F: $i,G: $i] :
( ( C
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ F ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ B ) @ G ) ) )
& ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ H ) @ ( hAPP @ ( c_List_Oset @ E ) @ F ) ) )
=> ~ ( hBOOL @ ( hAPP @ D @ H ) ) )
& ( hBOOL @ ( hAPP @ D @ B ) )
& ( A
= ( hAPP @ ( c_List_Ofilter @ E @ D ) @ G ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__eq__Cons__iff) ).
thf(4951,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( hAPP @ ( c_List_Ofilter @ E @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ B ) @ A ) )
=> ? [F: $i,G: $i] :
( ( C
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ F ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ B ) @ G ) ) )
& ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ H ) @ ( hAPP @ ( c_List_Oset @ E ) @ F ) ) )
=> ~ ( hBOOL @ ( hAPP @ D @ H ) ) )
& ( hBOOL @ ( hAPP @ D @ B ) )
& ( A
= ( hAPP @ ( c_List_Ofilter @ E @ D ) @ G ) ) ) )
& ( ? [F: $i,G: $i] :
( ( C
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ F ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ B ) @ G ) ) )
& ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ H ) @ ( hAPP @ ( c_List_Oset @ E ) @ F ) ) )
=> ~ ( hBOOL @ ( hAPP @ D @ H ) ) )
& ( hBOOL @ ( hAPP @ D @ B ) )
& ( A
= ( hAPP @ ( c_List_Ofilter @ E @ D ) @ G ) ) )
=> ( ( hAPP @ ( c_List_Ofilter @ E @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(369,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
thf(2877,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[369]) ).
thf(484,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__0) ).
thf(3326,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)],[484]) ).
thf(942,axiom,
! [A: $i] : ( c_Fun_Oinj__on @ tc_Nat_Onat @ tc_Nat_Onat @ c_Nat_OSuc @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__Suc) ).
thf(5166,plain,
! [A: $i] : ( c_Fun_Oinj__on @ tc_Nat_Onat @ tc_Nat_Onat @ c_Nat_OSuc @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(302,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono1) ).
thf(2561,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[302]) ).
thf(1180,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ D ) ) )
<=> ( c_List_Olist__all @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ball__set__list__all) ).
thf(6116,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ D ) ) )
=> ( c_List_Olist__all @ C @ A @ B ) )
& ( ( c_List_Olist__all @ C @ A @ B )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1180]) ).
thf(425,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Relation_ORange @ B @ B ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) )
= ( hAPP @ ( c_Relation_ORange @ B @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__range) ).
thf(3094,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Relation_ORange @ B @ B ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) )
= ( hAPP @ ( c_Relation_ORange @ B @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(692,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__cancel) ).
thf(4167,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(118,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ D ) @ C ) ) @ ( c_List_Olistrel @ E @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ C ) @ A ) ) @ ( c_List_Olistrel @ E @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ D ) @ A ) ) @ ( c_List_Olistrel @ E @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__rtrancl__trans) ).
thf(1739,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ D ) @ C ) ) @ ( c_List_Olistrel @ E @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ C ) @ A ) ) @ ( c_List_Olistrel @ E @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ D ) @ A ) ) @ ( c_List_Olistrel @ E @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(756,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__left) ).
thf(4425,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(365,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__self) ).
thf(2868,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(550,axiom,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).
thf(3596,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(754,axiom,
! [A: $i] : ( c_Relation_Osingle__valued @ A @ A @ ( c_Relation_OId @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__Id) ).
thf(4421,plain,
! [A: $i] : ( c_Relation_Osingle__valued @ A @ A @ ( c_Relation_OId @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(278,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Int_Oint @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThanPlusOne__atLeastAtMost__int) ).
thf(2455,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Int_Oint @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(840,axiom,
! [A: $i,B: $i] :
( ( c_Equiv__Relations_Opart__equivp @ B @ A )
<=> ( ? [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ C ) )
& ( c_Predicate_Osymp @ B @ A )
& ( c_Predicate_Otransp @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_part__equivp__refl__symp__transp) ).
thf(4750,plain,
! [A: $i,B: $i] :
( ( ( c_Equiv__Relations_Opart__equivp @ B @ A )
=> ( ? [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ C ) )
& ( c_Predicate_Osymp @ B @ A )
& ( c_Predicate_Otransp @ B @ A ) ) )
& ( ( ? [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ C ) )
& ( c_Predicate_Osymp @ B @ A )
& ( c_Predicate_Otransp @ B @ A ) )
=> ( c_Equiv__Relations_Opart__equivp @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(837,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ ( hAPP @ ( c_Relation_ORange @ E @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeI) ).
thf(4744,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ ( hAPP @ ( c_Relation_ORange @ E @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__mult__distrib2) ).
thf(1700,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(1194,axiom,
! [A: $i,B: $i] :
( ( B != A )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__2) ).
thf(6164,plain,
! [A: $i,B: $i] :
( ( B != A )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194]) ).
thf(1213,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Product__Type_Oprod_Oprod__rec @ F @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_prod_Orecs) ).
thf(6256,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Product__Type_Oprod_Oprod__rec @ F @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1213]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__mult__cancel) ).
thf(1810,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(90,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) ) )
& ( ( ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__Cons__number__of) ).
thf(1612,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) ) )
& ( ( ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(399,axiom,
! [A: $i,B: $i] : ( c_List_Olist__all @ B @ A @ ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all__simps_I2_J) ).
thf(2978,plain,
! [A: $i,B: $i] : ( c_List_Olist__all @ B @ A @ ( c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(807,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ B ) @ A )
= A )
<=> ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__self__conv2) ).
thf(4621,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ B ) @ A )
= A )
=> ( B
= ( c_List_Olist_ONil @ C ) ) )
& ( ( B
= ( c_List_Olist_ONil @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ B ) @ A )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(1178,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_List_Olist__ex @ C @ B @ A )
<=> ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
& ( hBOOL @ ( hAPP @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex__iff__raw) ).
thf(6097,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_List_Olist__ex @ C @ B @ A )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
& ( hBOOL @ ( hAPP @ B @ D ) ) ) )
& ( ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
& ( hBOOL @ ( hAPP @ B @ D ) ) )
=> ( c_List_Olist__ex @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178]) ).
thf(999,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SucI) ).
thf(5374,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(603,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__less) ).
thf(3787,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(312,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) )
<=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( hBOOL @ ( hAPP @ C @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ! [D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ E ) )
& ( hBOOL @ ( hAPP @ ( 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 @ E ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ! [D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ E ) )
& ( hBOOL @ ( hAPP @ ( 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 @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__zmod) ).
thf(2598,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( hBOOL @ ( hAPP @ C @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ! [D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ E ) )
& ( hBOOL @ ( hAPP @ ( 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 @ E ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ! [D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ E ) )
& ( hBOOL @ ( hAPP @ ( 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 @ E ) ) ) ) ) )
& ( ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( hBOOL @ ( hAPP @ C @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ! [D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ E ) )
& ( hBOOL @ ( hAPP @ ( 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 @ E ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ! [D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ E ) )
& ( hBOOL @ ( hAPP @ ( 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 @ E ) ) ) ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(489,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ C ) @ ( c_List_Olist_ONil @ E ) ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ A ) @ ( c_List_Olist_ONil @ E ) ) ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append1__eq__conv) ).
thf(3354,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ C ) @ ( c_List_Olist_ONil @ E ) ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ A ) @ ( c_List_Olist_ONil @ E ) ) ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ C ) @ ( c_List_Olist_ONil @ E ) ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ A ) @ ( c_List_Olist_ONil @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(935,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_OwfP @ B @ A )
<=> ! [C: $i] : ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfP__accp__iff) ).
thf(5134,plain,
! [A: $i,B: $i] :
( ( ( c_Wellfounded_OwfP @ B @ A )
=> ! [C: $i] : ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ B @ A ) @ C ) ) )
& ( ! [C: $i] : ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ B @ A ) @ C ) )
=> ( c_Wellfounded_OwfP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(307,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( c_Wellfounded_Owf @ C @ ( c_Wellfounded_Omlex__prod @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__mlex) ).
thf(2581,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( c_Wellfounded_Owf @ C @ ( c_Wellfounded_Omlex__prod @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(860,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Otake @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ D ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__map) ).
thf(4829,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Otake @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(169,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ D ) ) )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ B ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__set__conv__all__nth) ).
thf(1947,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ D ) ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ B ) @ D ) ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ B ) @ D ) ) ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(146,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ A ) @ B ) )
=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__antisym__nonneg) ).
thf(1852,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ A ) @ B ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
<=> ? [C: $i] :
( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__eq__0__iff) ).
thf(1429,plain,
! [A: $i,B: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ? [C: $i] :
( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) ) )
& ( ? [C: $i] :
( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(247,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_OwfP @ B @ A )
<=> ( c_Wellfounded_Owf @ B @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ B @ tc_HOL_Obool ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfP__def) ).
thf(2272,plain,
! [A: $i,B: $i] :
( ( ( c_Wellfounded_OwfP @ B @ A )
=> ( c_Wellfounded_Owf @ B @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ B @ tc_HOL_Obool ) @ A ) ) ) )
& ( ( c_Wellfounded_Owf @ B @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ B @ tc_HOL_Obool ) @ A ) ) )
=> ( c_Wellfounded_OwfP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(706,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_List_Ofilter @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ ( hAPP @ ( c_List_Ofilter @ D @ C ) @ B ) ) @ ( hAPP @ ( c_List_Ofilter @ D @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__append) ).
thf(4223,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_List_Ofilter @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ ( hAPP @ ( c_List_Ofilter @ D @ C ) @ B ) ) @ ( hAPP @ ( c_List_Ofilter @ D @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(916,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ C ) @ E ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_Relation_OImage @ F @ C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__ImageI) ).
thf(5063,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ C ) @ E ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_Relation_OImage @ F @ C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(1140,axiom,
! [A: $i] :
( ~ ~ ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ c_fNot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__2) ).
thf(5947,plain,
! [A: $i] :
( ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ c_fNot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).
thf(127,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1) ).
thf(1776,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)],[127]) ).
thf(971,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ B ) @ A ) ) )
=> ~ ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ B ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ G ) @ ( hAPP @ A @ F ) ) )
=> ( C
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ F ) @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SigmaE) ).
thf(5273,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ B ) @ A ) ) )
=> ~ ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ B ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ G ) @ ( hAPP @ A @ F ) ) )
=> ( C
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ F ) @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(569,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__assoc) ).
thf(3656,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( 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)],[569]) ).
thf(568,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).
thf(3654,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[568]) ).
thf(82,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__mod__sign) ).
thf(1588,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(295,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel) ).
thf(2536,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(434,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Ofun__upd @ D @ C @ B @ A @ ( hAPP @ B @ A ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__triv) ).
thf(3126,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Ofun__upd @ D @ C @ B @ A @ ( hAPP @ B @ A ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(1131,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ E @ B ) @ A ) ) )
=> ( ( hAPP @ B @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ C @ E @ A @ B ) @ D ) )
= D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_f__inv__into__f) ).
thf(5900,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ E @ B ) @ A ) ) )
=> ( ( hAPP @ B @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ C @ E @ A @ B ) @ D ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).
thf(597,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ B ) @ A ) )
=> ( ( c_List_Oremdups @ B @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__remdups__id) ).
thf(3770,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ B ) @ A ) )
=> ( ( c_List_Oremdups @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(1254,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_New__DSequence_Opos__union @ D @ C @ B ) @ A )
= ( c_Lazy__Sequence_Oappend @ D @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Opos__union__def) ).
thf(6433,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_New__DSequence_Opos__union @ D @ C @ B ) @ A )
= ( c_Lazy__Sequence_Oappend @ D @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1254]) ).
thf(239,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ A ) )
= ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__numeral__code_I9_J) ).
thf(2243,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ A ) )
= ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(1259,axiom,
! [A: $i,B: $i] :
( ( c_Nitpick_Orefl_H @ B @ A )
<=> ! [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Orefl_H__def) ).
thf(6475,plain,
! [A: $i,B: $i] :
( ( ( c_Nitpick_Orefl_H @ B @ A )
=> ! [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ C ) ) @ A ) ) )
& ( ! [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ C ) ) @ A ) )
=> ( c_Nitpick_Orefl_H @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1259]) ).
thf(1147,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_FunDef_Oreduction__pair @ D @ C )
=> ( c_FunDef_Oreduction__pair @ B @ ( hAPP @ ( hAPP @ ( c_FunDef_Orp__inv__image @ D @ B ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rp__inv__image__rp) ).
thf(5973,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_FunDef_Oreduction__pair @ D @ C )
=> ( c_FunDef_Oreduction__pair @ B @ ( hAPP @ ( hAPP @ ( c_FunDef_Orp__inv__image @ D @ B ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147]) ).
thf(772,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff__inverse) ).
thf(4482,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(304,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel1) ).
thf(2566,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( 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)],[304]) ).
thf(914,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Predicate_Oconversep @ C @ B @ ( c_Predicate_Oconversep @ B @ C @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep__conversep) ).
thf(5058,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Predicate_Oconversep @ C @ B @ ( c_Predicate_Oconversep @ B @ C @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(830,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Odrop @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ D ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__map) ).
thf(4717,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Odrop @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(152,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) ) @ D )
= B ) )
& ( ( D
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__Cons_H) ).
thf(1874,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) ) @ D )
= B ) )
& ( ( D
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(1112,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ ( c_Relation_OId__on @ C @ A ) ) )
=> ~ ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ A ) )
=> ( B
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__onE) ).
thf(5823,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ ( c_Relation_OId__on @ C @ A ) ) )
=> ~ ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ A ) )
=> ( B
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).
thf(980,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ A ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__not__refl) ).
thf(5305,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ A ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(194,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ C @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__eq__dvd__iff) ).
thf(2052,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ C @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ C ) @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ C ) @ A ) ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ C @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(320,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osize_I4_J) ).
thf(2697,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(430,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__cancel) ).
thf(3109,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(903,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ B @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Relation_OField @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Field) ).
thf(5026,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ B @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Relation_OField @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(406,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl3) ).
thf(3005,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(220,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ E @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ A @ tc_HOL_Obool ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ A ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splitI) ).
thf(2140,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ E @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ A @ tc_HOL_Obool ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ A ) @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(669,axiom,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( c_SetInterval_Oord__class_OatMost @ tc_Nat_Onat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessThan__Suc__atMost) ).
thf(4086,plain,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( c_SetInterval_Oord__class_OatMost @ tc_Nat_Onat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(1206,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_New__Random__Sequence_Opos__single @ E ) @ D ) @ C ) @ B ) @ A )
= ( c_New__DSequence_Opos__single @ E @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__single__def) ).
thf(6224,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_New__Random__Sequence_Opos__single @ E ) @ D ) @ C ) @ B ) @ A )
= ( c_New__DSequence_Opos__single @ E @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1206]) ).
thf(94,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__less__0) ).
thf(1627,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[94]) ).
thf(456,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ B ) @ A )
= ( c_List_Olist_ONil @ C ) )
<=> ( ( B
= ( c_List_Olist_ONil @ C ) )
& ( A
= ( c_List_Olist_ONil @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__is__Nil__conv) ).
thf(3215,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ B ) @ A )
= ( c_List_Olist_ONil @ C ) )
=> ( ( B
= ( c_List_Olist_ONil @ C ) )
& ( A
= ( c_List_Olist_ONil @ C ) ) ) )
& ( ( ( B
= ( c_List_Olist_ONil @ C ) )
& ( A
= ( c_List_Olist_ONil @ C ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ B ) @ A )
= ( c_List_Olist_ONil @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Suc) ).
thf(1333,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(616,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= B )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
thf(3834,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)],[616]) ).
thf(982,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oantisym__conv) ).
thf(5310,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(847,axiom,
! [A: $i,B: $i] :
( ? [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ B @ C ) @ C ) )
=> ( ( c_Predicate_Osymp @ A @ B )
=> ( ( c_Predicate_Otransp @ A @ B )
=> ( c_Equiv__Relations_Opart__equivp @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_part__equivpI) ).
thf(4782,plain,
! [A: $i,B: $i] :
( ? [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ B @ C ) @ C ) )
=> ( ( c_Predicate_Osymp @ A @ B )
=> ( ( c_Predicate_Otransp @ A @ B )
=> ( c_Equiv__Relations_Opart__equivp @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(444,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ C @ C @ C ) @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ B ) ) @ B )
= B )
=> ( ( ( hAPP @ ( c_Relation_ODomain @ C @ C ) @ B )
= A )
=> ( c_Equiv__Relations_Oequiv @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comp__equivI) ).
thf(3173,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ C @ C @ C ) @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ B ) ) @ B )
= B )
=> ( ( ( hAPP @ ( c_Relation_ODomain @ C @ C ) @ B )
= A )
=> ( c_Equiv__Relations_Oequiv @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(144,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ B @ D ) )
=> ( hBOOL @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ D ) @ C ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ B @ D ) )
=> ( hBOOL @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_incr__mult__lemma) ).
thf(1846,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ B @ D ) )
=> ( hBOOL @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ D ) @ C ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ B @ D ) )
=> ( hBOOL @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(1144,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Nitpick_Opair__box_Opair__box__rec @ F @ E @ D @ C @ ( c_Nitpick_Opair__box_OPairBox @ F @ E @ B @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__box_Orecs) ).
thf(5964,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Nitpick_Opair__box_Opair__box__rec @ F @ E @ D @ C @ ( c_Nitpick_Opair__box_OPairBox @ F @ E @ B @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).
thf(528,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ G @ F @ E ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ G @ D @ F ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ G @ D @ E ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ D @ F @ E ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_O__assoc) ).
thf(3508,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ G @ F @ E ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ G @ D @ F ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ G @ D @ E ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ D @ F @ E ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(269,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ C ) @ B ) ) ) @ ( c_List_Olistrel @ E @ A ) ) )
=> ~ ! [F: $i,G: $i] :
( ( D
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ F ) @ G ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ F ) @ C ) ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ G ) @ B ) ) @ ( c_List_Olistrel @ E @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__Cons2) ).
thf(2423,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ C ) @ B ) ) ) @ ( c_List_Olistrel @ E @ A ) ) )
=> ~ ! [F: $i,G: $i] :
( ( D
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ F ) @ G ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ F ) @ C ) ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ G ) @ B ) ) @ ( c_List_Olistrel @ E @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(796,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ B ) @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__take__drop__id) ).
thf(4572,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ B ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(944,axiom,
! [A: $i] :
( A
!= ( hAPP @ c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
thf(5170,plain,
! [A: $i] :
( A
!= ( hAPP @ c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(690,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ E @ D ) ) @ ( hAPP @ E @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ D ) @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ D ) @ C ) ) @ ( c_Wellfounded_Omlex__prod @ B @ E @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mlex__leq) ).
thf(4163,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ E @ D ) ) @ ( hAPP @ E @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ D ) @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ D ) @ C ) ) @ ( c_Wellfounded_Omlex__prod @ B @ E @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(516,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__drop) ).
thf(3454,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(687,axiom,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_not__add__less1) ).
thf(4148,plain,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( 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)],[687]) ).
thf(930,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oantisym) ).
thf(5112,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(1044,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ F ) @ E ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ G @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ C ) @ E ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ H @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ C ) @ F ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ H @ G @ C ) @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__compI) ).
thf(5557,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ F ) @ E ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ G @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ C ) @ E ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ H @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ C ) @ F ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ H @ G @ C ) @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).
thf(697,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofun__left__comm @ E @ D @ C )
=> ( ( hAPP @ ( c_Fun_Ocomp @ D @ D @ D @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ D @ D @ D @ ( hAPP @ C @ A ) ) @ ( hAPP @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofun__comp__comm) ).
thf(4184,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofun__left__comm @ E @ D @ C )
=> ( ( hAPP @ ( c_Fun_Ocomp @ D @ D @ D @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ D @ D @ D @ ( hAPP @ C @ A ) ) @ ( hAPP @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(322,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Int_Oint ) @ ( c_SetInterval_Oord__class_OgreaterThanLessThan @ tc_Int_Oint @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__greaterThanLessThan__int) ).
thf(2702,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Int_Oint ) @ ( c_SetInterval_Oord__class_OgreaterThanLessThan @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(299,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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ C ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ A ) )
& ( hBOOL @ ( hAPP @ ( 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_Omod @ tc_Int_Oint @ D @ C )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__rel__mod__eq) ).
thf(2546,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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ C ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ A ) )
& ( hBOOL @ ( hAPP @ ( 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_Omod @ tc_Int_Oint @ D @ C )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(128,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ B ) @ A ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ ( hAPP @ ( c_List_Oset @ B ) @ A ) )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__card) ).
thf(1779,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ B ) @ A ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ ( hAPP @ ( c_List_Oset @ B ) @ A ) )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(1007,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__rtrancl__trancl) ).
thf(5402,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(473,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ B ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ A @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ ( hAPP @ ( c_List_Ofilter @ D @ A ) @ B ) ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__filter__less) ).
thf(3279,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ B ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ A @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ ( hAPP @ ( c_List_Ofilter @ D @ A ) @ B ) ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(702,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less0) ).
thf(4212,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( 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)],[702]) ).
thf(648,axiom,
! [A: $i,B: $i] : ( c_Relation_Otrans @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__rtrancl) ).
thf(3999,plain,
! [A: $i,B: $i] : ( c_Relation_Otrans @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(393,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__0) ).
thf(2963,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(1090,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ B ) @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ D ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ C ) @ ( hAPP @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SigmaE2) ).
thf(5737,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ B ) @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ D ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ C ) @ ( hAPP @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).
thf(105,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
<=> ( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ A ) ) @ C )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ A ) ) @ B ) )
& ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ A ) ) @ C ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ A ) @ C ) @ D )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ A ) @ B ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__eq__iff__nth__eq) ).
thf(1663,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C = B )
=> ( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ A ) ) @ C )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ A ) ) @ B ) )
& ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ A ) ) @ C ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ A ) @ C ) @ D )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ A ) @ B ) @ D ) ) ) ) )
& ( ( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ A ) ) @ C )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ A ) ) @ B ) )
& ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ A ) ) @ C ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ A ) @ C ) @ D )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ A ) @ B ) @ D ) ) ) )
=> ( C = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(450,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ F @ E @ D @ C ) @ B ) @ A )
= ( hAPP @ C @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__apply) ).
thf(3190,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ F @ E @ D @ C ) @ B ) @ A )
= ( hAPP @ C @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(228,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
<=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__1__iff) ).
thf(2189,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)],[228]) ).
thf(1244,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( C
= ( hAPP @ B @ E ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ C ) @ ( hAPP @ ( c_Set_Oimage @ F @ A @ B ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__image__eqI) ).
thf(6400,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( C
= ( hAPP @ B @ E ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ C ) @ ( hAPP @ ( c_Set_Oimage @ F @ A @ B ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1244]) ).
thf(618,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ ( c_SetInterval_Oord__class_OgreaterThanLessThan @ tc_Nat_Onat @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__greaterThanLessThan) ).
thf(3841,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ ( c_SetInterval_Oord__class_OgreaterThanLessThan @ tc_Nat_Onat @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(976,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_List_Oset @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ D ) @ B ) @ A ) )
= ( hAPP @ ( c_Set_Oimage @ C @ D @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__map) ).
thf(5295,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_List_Oset @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ D ) @ B ) @ A ) )
= ( hAPP @ ( c_Set_Oimage @ C @ D @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(650,axiom,
! [A: $i] :
( ( c_List_Oremdups @ A @ ( c_List_Olist_ONil @ A ) )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remdups_Osimps_I1_J) ).
thf(4004,plain,
! [A: $i] :
( ( c_List_Oremdups @ A @ ( c_List_Olist_ONil @ A ) )
= ( c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(727,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_COMBK @ tc_Nat_Onat @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card_Oeq__fold__g) ).
thf(4308,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_COMBK @ tc_Nat_Onat @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ B ) @ ( c_List_Olist_ONil @ C ) ) ) @ ( c_List_Olexord @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__Nil__right) ).
thf(1510,plain,
! [A: $i,B: $i,C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ B ) @ ( c_List_Olist_ONil @ C ) ) ) @ ( c_List_Olexord @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(301,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__number__of__int__code) ).
thf(2556,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(309,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__div__cancel) ).
thf(2585,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(972,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Relation_OId__on @ D @ A ) ) )
<=> ( ( C = B )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__on__iff) ).
thf(5278,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Relation_OId__on @ D @ A ) ) )
=> ( ( C = B )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) )
& ( ( ( C = B )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Relation_OId__on @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(523,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F = E )
=> ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ B ) @ A ) @ F )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ B ) @ A ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__weak__cong) ).
thf(3491,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F = E )
=> ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ B ) @ A ) @ F )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ B ) @ A ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(752,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= B ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__if) ).
thf(4412,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= B ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
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/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__commute) ).
thf(1927,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(910,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( hAPP @ ( c_List_Oset @ F ) @ D ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Omap @ F @ C ) @ ( c_Fun_Ofun__upd @ F @ C @ B @ E @ A ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ F @ C ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__fun__upd) ).
thf(5048,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( hAPP @ ( c_List_Oset @ F ) @ D ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Omap @ F @ C ) @ ( c_Fun_Ofun__upd @ F @ C @ B @ E @ A ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ F @ C ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(1209,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Oirrefl @ B @ A )
<=> ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_irrefl__def) ).
thf(6243,plain,
! [A: $i,B: $i] :
( ( ( c_Relation_Oirrefl @ B @ A )
=> ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ C ) ) @ A ) ) )
& ( ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ C ) ) @ A ) )
=> ( c_Relation_Oirrefl @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1209]) ).
thf(575,axiom,
! [A: $i,B: $i] :
( ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ B @ A )
= ( hAPP @ ( c_List_Oset @ tc_Nat_Onat ) @ ( c_List_Oupt @ B @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastAtMost__upt) ).
thf(3686,plain,
! [A: $i,B: $i] :
( ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ B @ A )
= ( hAPP @ ( c_List_Oset @ tc_Nat_Onat ) @ ( c_List_Oupt @ B @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(487,axiom,
! [A: $i,B: $i] :
( ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) )
<=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__nat__less) ).
thf(3343,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) ) )
& ( ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(214,axiom,
( ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint )
!= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0__neq__1) ).
thf(2121,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)],[214]) ).
thf(222,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1) ).
thf(2144,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)],[222]) ).
thf(1236,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( ( hAPP @ D @ B )
= A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hAPP @ ( c_Fun_Othe__inv__into @ F @ E @ C @ D ) @ A )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__inv__into__f__eq) ).
thf(6368,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( ( hAPP @ D @ B )
= A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hAPP @ ( c_Fun_Othe__inv__into @ F @ E @ C @ D ) @ A )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1236]) ).
thf(99,axiom,
class_Nat_Osize @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Nat_Osize) ).
thf(1648,plain,
class_Nat_Osize @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(1028,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ tc_Nat_Onat @ c_Nat_OSuc ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ A ) )
= ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__Suc__atLeastLessThan) ).
thf(5483,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ tc_Nat_Onat @ c_Nat_OSuc ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ A ) )
= ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(879,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__take) ).
thf(4919,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(682,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono) ).
thf(4131,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[682]) ).
thf(1035,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) )
=> ~ ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__acc__down) ).
thf(5524,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) )
=> ~ ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(769,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
thf(4470,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( 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)],[769]) ).
thf(123,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__mult__iff) ).
thf(1754,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(375,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__zeroE) ).
thf(2904,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( 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)],[375]) ).
thf(107,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Otrans @ B @ A )
=> ( c_Relation_Otrans @ ( tc_List_Olist @ B ) @ ( c_List_Olexord @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__transI) ).
thf(1680,plain,
! [A: $i,B: $i] :
( ( c_Relation_Otrans @ B @ A )
=> ( c_Relation_Otrans @ ( tc_List_Olist @ B ) @ ( c_List_Olexord @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(224,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B )
!= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neq__if__length__neq) ).
thf(2149,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B )
!= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(1097,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( hAPP @ ( c_List_Oset @ E ) @ A ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Omap @ E @ D ) @ C ) @ ( hAPP @ ( c_List_OremoveAll @ E @ B ) @ A ) )
= ( hAPP @ ( c_List_OremoveAll @ D @ ( hAPP @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ E @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__removeAll__inj__on) ).
thf(5762,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( hAPP @ ( c_List_Oset @ E ) @ A ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Omap @ E @ D ) @ C ) @ ( hAPP @ ( c_List_OremoveAll @ E @ B ) @ A ) )
= ( hAPP @ ( c_List_OremoveAll @ D @ ( hAPP @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ E @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).
thf(465,axiom,
! [A: $i,B: $i] :
( ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) @ A )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastSucAtMost__greaterThanAtMost) ).
thf(3257,plain,
! [A: $i,B: $i] :
( ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) @ A )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(1020,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_List_Oset @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__set) ).
thf(5451,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_List_Oset @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).
thf(586,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ ( hAPP @ ( c_List_Ofilter @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__filter) ).
thf(3738,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ ( hAPP @ ( c_List_Ofilter @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(186,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ D ) @ B ) @ A ) )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__map) ).
thf(2028,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ D ) @ B ) @ A ) )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(735,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( hAPP @ c_Nat_OSuc @ B ) ) ) ) )
<=> ( B
= ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__div__lemma) ).
thf(4340,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( ( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( hAPP @ c_Nat_OSuc @ B ) ) ) ) )
=> ( B
= ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ C ) ) )
& ( ( B
= ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( hAPP @ c_Nat_OSuc @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(494,axiom,
! [A: $i] :
( ( c_List_Obutlast @ A @ ( c_List_Olist_ONil @ A ) )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast_Osimps_I1_J) ).
thf(3375,plain,
! [A: $i] :
( ( c_List_Obutlast @ A @ ( c_List_Olist_ONil @ A ) )
= ( c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(84,axiom,
! [A: $i,B: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__self__implies__10) ).
thf(1595,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)],[84]) ).
thf(533,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ B ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ D ) @ C ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bset_I5_J) ).
thf(3523,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ B ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ D ) @ C ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(777,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ B ) @ A ) )
<=> ( ( ( D
= ( c_List_Olist_ONil @ E ) )
& ( C
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ B ) @ A ) ) )
| ? [F: $i] :
( ( D
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ B ) @ F ) )
& ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ F ) @ C )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__eq__Cons__conv) ).
thf(4503,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ B ) @ A ) )
=> ( ( ( D
= ( c_List_Olist_ONil @ E ) )
& ( C
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ B ) @ A ) ) )
| ? [F: $i] :
( ( D
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ B ) @ F ) )
& ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ F ) @ C )
= A ) ) ) )
& ( ( ( ( D
= ( c_List_Olist_ONil @ E ) )
& ( C
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ B ) @ A ) ) )
| ? [F: $i] :
( ( D
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ B ) @ F ) )
& ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ F ) @ C )
= A ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(798,axiom,
! [A: $i,B: $i] :
( ( c_List_Oinsert @ B @ A @ ( c_List_Olist_ONil @ B ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ A ) @ ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__Nil) ).
thf(4577,plain,
! [A: $i,B: $i] :
( ( c_List_Oinsert @ B @ A @ ( c_List_Olist_ONil @ B ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ A ) @ ( c_List_Olist_ONil @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(1276,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hAPP @ B @ C )
= ( hAPP @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).
thf(6546,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hAPP @ B @ C )
= ( hAPP @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1276]) ).
thf(471,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Osym @ D @ C )
=> ( c_Relation_Osym @ B @ ( hAPP @ ( hAPP @ ( c_Relation_Oinv__image @ D @ B ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sym__inv__image) ).
thf(3274,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Osym @ D @ C )
=> ( c_Relation_Osym @ B @ ( hAPP @ ( hAPP @ ( c_Relation_Oinv__image @ D @ B ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(578,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( c_Fun_Oinj__on @ E @ B @ A @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ C ) )
=> ( c_Fun_Oinj__on @ F @ B @ ( hAPP @ ( c_Fun_Ocomp @ E @ B @ F @ A ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comp__inj__on) ).
thf(3696,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( c_Fun_Oinj__on @ E @ B @ A @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ C ) )
=> ( c_Fun_Oinj__on @ F @ B @ ( hAPP @ ( c_Fun_Ocomp @ E @ B @ F @ A ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(774,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Ofun__upd @ F @ E @ ( c_Fun_Ofun__upd @ F @ E @ D @ C @ B ) @ C @ A )
= ( c_Fun_Ofun__upd @ F @ E @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__upd) ).
thf(4489,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Ofun__upd @ F @ E @ ( c_Fun_Ofun__upd @ F @ E @ D @ C @ B ) @ C @ A )
= ( c_Fun_Ofun__upd @ F @ E @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(502,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card_Oinsert) ).
thf(3396,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(764,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__assoc2) ).
thf(4453,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(1006,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_Oconverse @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ ( hAPP @ ( c_Relation_Oconverse @ D @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__converseI) ).
thf(5400,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_Oconverse @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ ( hAPP @ ( c_Relation_Oconverse @ D @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(849,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ E @ D @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ B ) ) @ A ) )
<=> ? [F: $i,G: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ F ) @ G ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ E @ E @ D @ F @ G ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ G ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1Set_Oequations) ).
thf(4786,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ E @ D @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ B ) ) @ A ) )
=> ? [F: $i,G: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ F ) @ G ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ E @ E @ D @ F @ G ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ G ) ) ) )
& ( ? [F: $i,G: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ F ) @ G ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ E @ E @ D @ F @ G ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ G ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ E @ D @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(493,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
thf(3372,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(1262,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Predicate_Oreflp @ C @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reflpE) ).
thf(6493,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Predicate_Oreflp @ C @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1262]) ).
thf(918,axiom,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_List_Omember @ B ) @ ( c_List_Olist_ONil @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_member__rec_I2_J) ).
thf(5067,plain,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_List_Omember @ B ) @ ( c_List_Olist_ONil @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(585,axiom,
! [A: $i,B: $i] : ( c_List_Olistrelp @ B @ A @ ( c_List_Olist_ONil @ B ) @ ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrelp_Oequations_I1_J) ).
thf(3736,plain,
! [A: $i,B: $i] : ( c_List_Olistrelp @ B @ A @ ( c_List_Olist_ONil @ B ) @ ( c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(1151,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ E @ C @ B @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OgreaterThanLessThan__iff) ).
thf(5984,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ E @ C @ B @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ E @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).
thf(733,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
thf(4328,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( B = A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( B = A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(327,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ ( hAPP @ ( c_List_Oset @ B ) @ A ) ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__length) ).
thf(2716,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ ( hAPP @ ( c_List_Oset @ B ) @ A ) ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(1246,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( ( c_List_Oremove1 @ C @ B @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remove1__idem) ).
thf(6407,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( ( c_List_Oremove1 @ C @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1246]) ).
thf(884,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_List_Ofilter @ D @ C ) @ ( c_List_Oremove1 @ D @ B @ A ) )
= ( c_List_Oremove1 @ D @ B @ ( hAPP @ ( c_List_Ofilter @ D @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__remove1) ).
thf(4946,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_List_Ofilter @ D @ C ) @ ( c_List_Oremove1 @ D @ B @ A ) )
= ( c_List_Oremove1 @ D @ B @ ( hAPP @ ( c_List_Ofilter @ D @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( 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 ) @ B ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ D ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult2__lemma__aux4) ).
thf(1488,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( 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 ) @ B ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ D ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(355,axiom,
! [A: $i,B: $i] :
( ( ( c_List_Oupt @ B @ A )
= ( c_List_Olist_ONil @ tc_Nat_Onat ) )
<=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__eq__Nil__conv) ).
thf(2827,plain,
! [A: $i,B: $i] :
( ( ( ( c_List_Oupt @ B @ A )
= ( c_List_Olist_ONil @ tc_Nat_Onat ) )
=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ B ) ) ) )
& ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( ( c_List_Oupt @ B @ A )
= ( c_List_Olist_ONil @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(499,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofun__left__comm @ F @ E @ D )
=> ( ( hAPP @ ( hAPP @ D @ C ) @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
= ( hAPP @ ( hAPP @ D @ B ) @ ( hAPP @ ( hAPP @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofun__left__comm) ).
thf(3387,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofun__left__comm @ F @ E @ D )
=> ( ( hAPP @ ( hAPP @ D @ C ) @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
= ( hAPP @ ( hAPP @ D @ B ) @ ( hAPP @ ( hAPP @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(449,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
thf(3187,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(716,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__less) ).
thf(4268,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(1139,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ A )
<=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ A ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ A ) )
=> ( ( ( hAPP @ B @ E )
= ( hAPP @ B @ F ) )
=> ( E = F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__def) ).
thf(5933,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Fun_Oinj__on @ D @ C @ B @ A )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ A ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ A ) )
=> ( ( ( hAPP @ B @ E )
= ( hAPP @ B @ F ) )
=> ( E = F ) ) ) ) )
& ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ A ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ A ) )
=> ( ( ( hAPP @ B @ E )
= ( hAPP @ B @ F ) )
=> ( E = F ) ) ) )
=> ( c_Fun_Oinj__on @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139]) ).
thf(331,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) )
<=> ( ( C = A )
| ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel2) ).
thf(2727,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)],[331]) ).
thf(721,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_same__append__eq) ).
thf(4283,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ F @ E @ D @ ( hAPP @ ( c_COMBK @ E @ F ) @ C ) ) @ B ) @ A )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_K__record__comp) ).
thf(1389,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ F @ E @ D @ ( hAPP @ ( c_COMBK @ E @ F ) @ C ) ) @ B ) @ A )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(1267,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( ( hAPP @ D @ B )
= ( hAPP @ D @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__onD) ).
thf(6510,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( ( hAPP @ D @ B )
= ( hAPP @ D @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1267]) ).
thf(345,axiom,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Otrancl @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ B @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__unfold__right) ).
thf(2791,plain,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Otrancl @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ B @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(293,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ A ) )
= ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__numeral__code_I5_J) ).
thf(2525,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ A ) )
= ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(917,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rtrancl__into__rtrancl) ).
thf(5065,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(468,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Odrop @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__0) ).
thf(3266,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Odrop @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(289,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__mod__conj) ).
thf(2514,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(927,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oord__le__eq__trans) ).
thf(5099,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(1124,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ H @ G ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ E @ F ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ C @ B @ A @ H @ E ) @ G ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__comp_Ointros) ).
thf(5876,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ H @ G ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ E @ F ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ C @ B @ A @ H @ E ) @ G ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).
thf(404,axiom,
! [A: $i,B: $i] :
( ( ( c_List_Oremdups @ B @ A )
= ( c_List_Olist_ONil @ B ) )
<=> ( A
= ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remdups__eq__nil__iff) ).
thf(2991,plain,
! [A: $i,B: $i] :
( ( ( ( c_List_Oremdups @ B @ A )
= ( c_List_Olist_ONil @ B ) )
=> ( A
= ( c_List_Olist_ONil @ B ) ) )
& ( ( A
= ( c_List_Olist_ONil @ B ) )
=> ( ( c_List_Oremdups @ B @ A )
= ( c_List_Olist_ONil @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(773,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hBOOL @ ( hAPP @ B @ A ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ A ) )
& ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_ex__least__nat__less) ).
thf(4485,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hBOOL @ ( hAPP @ B @ A ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ A ) )
& ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( 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)],[773]) ).
thf(256,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( c_List_OtakeWhile @ C @ B @ A ) ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ A ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( c_List_OtakeWhile @ C @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__length__takeWhile) ).
thf(2308,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( c_List_OtakeWhile @ C @ B @ A ) ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ A ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( c_List_OtakeWhile @ C @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(1273,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_List_Olist__all @ C @ B @ A )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all__iff) ).
thf(6532,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_List_Olist__all @ C @ B @ A )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ B @ D ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ B @ D ) ) )
=> ( c_List_Olist__all @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1273]) ).
thf(704,axiom,
! [A: $i,B: $i] : ( c_Relation_Otrans @ B @ ( c_Relation_OId__on @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__Id__on) ).
thf(4218,plain,
! [A: $i,B: $i] : ( c_Relation_Otrans @ B @ ( c_Relation_OId__on @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(1225,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_List_Olist__ex1 @ C @ B @ A )
<=> ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
& ( hBOOL @ ( hAPP @ B @ D ) )
& ! [E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
& ( hBOOL @ ( hAPP @ B @ E ) ) )
=> ( E = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex1__iff) ).
thf(6302,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_List_Olist__ex1 @ C @ B @ A )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
& ( hBOOL @ ( hAPP @ B @ D ) )
& ! [E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
& ( hBOOL @ ( hAPP @ B @ E ) ) )
=> ( E = D ) ) ) )
& ( ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
& ( hBOOL @ ( hAPP @ B @ D ) )
& ! [E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
& ( hBOOL @ ( hAPP @ B @ E ) ) )
=> ( E = D ) ) )
=> ( c_List_Olist__ex1 @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1225]) ).
thf(521,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Wellfounded_Oacc @ D @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ D ) ) @ A ) @ ( c_Wellfounded_Oacc @ ( tc_List_Olist @ D ) @ ( c_List_Olistrel1 @ D @ B ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ C ) @ A ) ) @ ( c_Wellfounded_Oacc @ ( tc_List_Olist @ D ) @ ( c_List_Olistrel1 @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__acc__listrel1I) ).
thf(3487,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Wellfounded_Oacc @ D @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ D ) ) @ A ) @ ( c_Wellfounded_Oacc @ ( tc_List_Olist @ D ) @ ( c_List_Olistrel1 @ D @ B ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ C ) @ A ) ) @ ( c_Wellfounded_Oacc @ ( tc_List_Olist @ D ) @ ( c_List_Olistrel1 @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(580,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ C ) @ B ) ) ) @ ( c_List_Olistrel1 @ F @ A ) ) )
<=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ E ) @ C ) ) @ A ) )
& ( D = B ) )
| ( ( E = C )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) @ D ) @ B ) ) @ ( c_List_Olistrel1 @ F @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__listrel1__Cons) ).
thf(3700,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ C ) @ B ) ) ) @ ( c_List_Olistrel1 @ F @ A ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ E ) @ C ) ) @ A ) )
& ( D = B ) )
| ( ( E = C )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) @ D ) @ B ) ) @ ( c_List_Olistrel1 @ F @ A ) ) ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ E ) @ C ) ) @ A ) )
& ( D = B ) )
| ( ( E = C )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) @ D ) @ B ) ) @ ( c_List_Olistrel1 @ F @ A ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ C ) @ B ) ) ) @ ( c_List_Olistrel1 @ F @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(566,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ B ) @ A )
= ( c_List_Olist_ONil @ C ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( A
= ( c_List_Olist_ONil @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__eq__Nil) ).
thf(3641,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ B ) @ A )
= ( c_List_Olist_ONil @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( A
= ( c_List_Olist_ONil @ C ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( A
= ( c_List_Olist_ONil @ C ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ B ) @ A )
= ( c_List_Olist_ONil @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(1210,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ E @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ B @ A @ E ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeP_Ointros) ).
thf(6248,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ E @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ B @ A @ E ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1210]) ).
thf(1277,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( c_List_Ofilter @ C @ B ) @ A )
= A )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__id__conv) ).
thf(6549,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( c_List_Ofilter @ C @ B ) @ A )
= A )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ B @ D ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ B @ D ) ) )
=> ( ( hAPP @ ( c_List_Ofilter @ C @ B ) @ A )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1277]) ).
thf(424,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_List_Oset @ B ) @ ( c_List_Oremdups @ B @ A ) )
= ( hAPP @ ( c_List_Oset @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__remdups) ).
thf(3091,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_List_Oset @ B ) @ ( c_List_Oremdups @ B @ A ) )
= ( hAPP @ ( c_List_Oset @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(1237,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ E @ D @ C ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__rel__def) ).
thf(6372,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ E @ D @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) @ C ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ E @ D @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1237]) ).
thf(260,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ C ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2) ).
thf(2319,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(1065,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__lessThan) ).
thf(5634,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).
thf(784,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__take) ).
thf(4537,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(63,axiom,
! [A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
& ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DIVISION__BY__ZERO) ).
thf(1503,plain,
! [A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
& ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(889,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__asym_H) ).
thf(4978,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(598,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__mod__geq) ).
thf(3773,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(567,axiom,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeast0LessThan) ).
thf(3651,plain,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(674,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ C ) @ B ) ) @ ( c_List_Olistrel1 @ D @ A ) ) )
=> ~ ! [E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ E ) @ F ) ) @ A ) )
=> ! [G: $i,H: $i] :
( ( C
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ G ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ E ) @ H ) ) )
=> ( B
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ G ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ F ) @ H ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1E) ).
thf(4099,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ C ) @ B ) ) @ ( c_List_Olistrel1 @ D @ A ) ) )
=> ~ ! [E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ E ) @ F ) ) @ A ) )
=> ! [G: $i,H: $i] :
( ( C
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ G ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ E ) @ H ) ) )
=> ( B
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ G ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ F ) @ H ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(486,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ B )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__le) ).
thf(3340,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ B )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(549,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ C ) @ A ) ) ) @ ( c_List_Olistrel1 @ E @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1I1) ).
thf(3594,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ C ) @ A ) ) ) @ ( c_List_Olistrel1 @ E @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(938,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ole__less__trans) ).
thf(5148,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(842,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ C @ B ) )
& ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp_Oequations_I2_J) ).
thf(4764,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ C @ B ) )
& ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ D @ C ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ C @ B ) )
& ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ D @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(433,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hAPP @ ( c_Product__Type_Omap__pair @ H @ G @ F @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ F ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ E ) @ ( hAPP @ D @ B ) ) @ ( hAPP @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair__simp) ).
thf(3123,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hAPP @ ( c_Product__Type_Omap__pair @ H @ G @ F @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ F ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ E ) @ ( hAPP @ D @ B ) ) @ ( hAPP @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(275,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0__right) ).
thf(2442,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)],[275]) ).
thf(337,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D ) )
= B ) )
& ( ( ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__Cons__number__of) ).
thf(2753,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D ) )
= B ) )
& ( ( ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(536,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ ( hAPP @ ( c_List_OremoveAll @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__removeAll) ).
thf(3532,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ ( hAPP @ ( c_List_OremoveAll @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(1167,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fdisj__2) ).
thf(6048,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).
thf(1009,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ ( c_List_Obutlast @ D @ B ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ ( c_List_Obutlast @ D @ A ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ ( c_List_Obutlast @ D @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__butlast__appendI) ).
thf(5407,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ ( c_List_Obutlast @ D @ B ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ ( c_List_Obutlast @ D @ A ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ ( c_List_Obutlast @ D @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(525,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ D @ B ) @ A ) ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) )
=> ~ ( c_Fun_Oinj__on @ C @ D @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pigeonhole) ).
thf(3500,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ D @ B ) @ A ) ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) )
=> ~ ( c_Fun_Oinj__on @ C @ D @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(447,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__refl) ).
thf(3182,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(746,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__gr__0) ).
thf(4388,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[746]) ).
thf(329,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self3) ).
thf(2721,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(213,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__nonneg__neg__le0) ).
thf(2119,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( 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)],[213]) ).
thf(734,axiom,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_not__add__less2) ).
thf(4337,plain,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( 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)],[734]) ).
thf(315,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zmult1__eq) ).
thf(2679,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(827,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_List_Oremove1 @ D @ C @ ( c_List_Oremove1 @ D @ B @ A ) )
= ( c_List_Oremove1 @ D @ B @ ( c_List_Oremove1 @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remove1__commute) ).
thf(4704,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_List_Oremove1 @ D @ C @ ( c_List_Oremove1 @ D @ B @ A ) )
= ( c_List_Oremove1 @ D @ B @ ( c_List_Oremove1 @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(647,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__shift) ).
thf(3996,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(296,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__append) ).
thf(2538,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ ( c_List_Oremdups @ B @ A ) )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) )
<=> ( ( c_List_Oremdups @ B @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__remdups__eq) ).
thf(1408,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ ( c_List_Oremdups @ B @ A ) )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) )
=> ( ( c_List_Oremdups @ B @ A )
= A ) )
& ( ( ( c_List_Oremdups @ B @ A )
= A )
=> ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ ( c_List_Oremdups @ B @ A ) )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(1075,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SucI) ).
thf(5671,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).
thf(1,conjecture,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ A ) @ v_ts ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ v_n @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ A ) @ v_ts ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ v_n @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(1282,plain,
~ ! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ A ) @ v_ts ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ v_n @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(202,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ D @ C ) @ B ) @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBK__1) ).
thf(2084,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ D @ C ) @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(962,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Omap @ E @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ ( hAPP @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ E @ D ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map_Osimps_I2_J) ).
thf(5244,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Omap @ E @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ ( hAPP @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ E @ D ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(595,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ C ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ tc_Nat_Onat @ B ) @ A ) @ ( c_List_Oupt @ C @ D ) ) ) @ E )
= ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__map__upt) ).
thf(3764,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ C ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ tc_Nat_Onat @ B ) @ A ) @ ( c_List_Oupt @ C @ D ) ) ) @ E )
= ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(155,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) @ B ) )
<=> ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel1) ).
thf(1894,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) @ B ) )
=> ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
& ( ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(265,axiom,
c_Wellfounded_Owf @ tc_Nat_Onat @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__less) ).
thf(2415,plain,
c_Wellfounded_Owf @ tc_Nat_Onat @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(928,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
<=> ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__dvd__1__iff__1) ).
thf(5103,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
=> ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
& ( ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(985,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
=> ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ E ) ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ E ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tranclD) ).
thf(5325,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
=> ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ E ) ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ E ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(541,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).
thf(3551,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)],[541]) ).
thf(726,axiom,
! [A: $i,B: $i] :
( ( c_Divides_Odivmod__nat @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__div__mod) ).
thf(4305,plain,
! [A: $i,B: $i] :
( ( c_Divides_Odivmod__nat @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(1189,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ ( c_List_Obutlast @ C @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__butlastD) ).
thf(6147,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ ( c_List_Obutlast @ C @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189]) ).
thf(1205,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ D ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eqset__imp__iff) ).
thf(6217,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1205]) ).
thf(476,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ A )
= ( hAPP @ ( c_List_Oset @ tc_Nat_Onat ) @ ( c_List_Oupt @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__upt) ).
thf(3287,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ A )
= ( hAPP @ ( c_List_Oset @ tc_Nat_Onat ) @ ( c_List_Oupt @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ E ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ D @ B ) @ A ) @ C ) ) @ E )
= ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ C ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__map) ).
thf(1524,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ E ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ D @ B ) @ A ) @ C ) ) @ E )
= ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ C ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(979,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ E ) @ B ) @ C ) ) @ ( hAPP @ ( c_Relation_Oconverse @ E @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converseI) ).
thf(5303,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ E ) @ B ) @ C ) ) @ ( hAPP @ ( c_Relation_Oconverse @ E @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(1113,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ A )
=> ( c_Fun_Oinj__on @ C @ D @ ( c_Fun_Othe__inv__into @ D @ C @ A @ B ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__the__inv__into) ).
thf(5827,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ A )
=> ( c_Fun_Oinj__on @ C @ D @ ( c_Fun_Othe__inv__into @ D @ C @ A @ B ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).
thf(205,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__zmod) ).
thf(2097,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(1119,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ D @ C @ B ) @ A ) )
<=> ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ B @ E ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeP_Oequations) ).
thf(5853,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ D @ C @ B ) @ A ) )
=> ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ B @ E ) @ A ) ) )
& ( ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ B @ E ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ D @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).
thf(244,axiom,
c_Wellfounded_Owf @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_FunDef_Opair__less,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__pair__less) ).
thf(2257,plain,
c_Wellfounded_Owf @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_FunDef_Opair__less,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(164,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib2) ).
thf(1933,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(391,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( A
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__pred_H) ).
thf(2955,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( A
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(240,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ D ) ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__period) ).
thf(2246,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ E ) @ D ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ D ) ) ) @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ D ) ) ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(429,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Finite__Set_Ofun__left__comm @ G @ F @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ F @ E @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ F @ E @ D @ C ) @ A ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__graph__determ) ).
thf(3106,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Finite__Set_Ofun__left__comm @ G @ F @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ F @ E @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ F @ E @ D @ C ) @ A ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(1126,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Fun_Othe__inv__into @ E @ D @ B @ C ) @ ( hAPP @ C @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__inv__into__f__f) ).
thf(5880,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Fun_Othe__inv__into @ E @ D @ B @ C ) @ ( hAPP @ C @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).
thf(853,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( ( c_List_Olistrelp @ C @ F @ B @ A )
=> ( c_List_Olistrelp @ C @ F @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrelp_OCons) ).
thf(4805,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( ( c_List_Olistrelp @ C @ F @ B @ A )
=> ( c_List_Olistrelp @ C @ F @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(955,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__imp__not__eq) ).
thf(5222,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(666,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__trans) ).
thf(4073,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(1038,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Oantisym @ B @ A )
<=> ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ D ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ D ) @ C ) ) @ A ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisym__def) ).
thf(5531,plain,
! [A: $i,B: $i] :
( ( ( c_Relation_Oantisym @ B @ A )
=> ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ D ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ D ) @ C ) ) @ A ) )
=> ( C = D ) ) ) )
& ( ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ D ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ D ) @ C ) ) @ A ) )
=> ( C = D ) ) )
=> ( c_Relation_Oantisym @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(80,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ B ) @ A ) )
<=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ( ( C != D )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ B ) @ A ) @ C )
!= ( hAPP @ ( hAPP @ ( c_List_Onth @ B ) @ A ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__conv__nth) ).
thf(1571,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ B ) @ A ) )
=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ( ( C != D )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ B ) @ A ) @ C )
!= ( hAPP @ ( hAPP @ ( c_List_Onth @ B ) @ A ) @ D ) ) ) ) ) )
& ( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ( ( C != D )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ B ) @ A ) @ C )
!= ( hAPP @ ( hAPP @ ( c_List_Onth @ B ) @ A ) @ D ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ D ) @ C ) ) @ B ) ) @ ( c_List_Olistrel @ E @ A ) ) )
=> ~ ! [F: $i,G: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ F ) @ G ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ F ) ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ C ) @ G ) ) @ ( c_List_Olistrel @ E @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__Cons1) ).
thf(1376,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ D ) @ C ) ) @ B ) ) @ ( c_List_Olistrel @ E @ A ) ) )
=> ~ ! [F: $i,G: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ F ) @ G ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ F ) ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ C ) @ G ) ) @ ( c_List_Olistrel @ E @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(676,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__0) ).
thf(4107,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= ( c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(172,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ E ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ C ) @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( hAPP @ ( c_List_Oset @ D ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__nth__imp__all__set) ).
thf(1969,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ E ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ C ) @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( hAPP @ ( c_List_Oset @ D ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(969,axiom,
! [A: $i] :
( ( c_Predicate_Oconversep @ A @ A @ c_fequal )
= c_fequal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep__eq) ).
thf(5267,plain,
! [A: $i] :
( ( c_Predicate_Oconversep @ A @ A @ c_fequal )
= c_fequal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Osym @ B @ A )
=> ( c_Relation_Osym @ ( tc_List_Olist @ B ) @ ( c_List_Olistrel @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__sym) ).
thf(1307,plain,
! [A: $i,B: $i] :
( ( c_Relation_Osym @ B @ A )
=> ( c_Relation_Osym @ ( tc_List_Olist @ B ) @ ( c_List_Olistrel @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1042,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ C ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__trans) ).
thf(5552,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ C ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(906,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ A )
=> ( ( hAPP @ ( c_Set_Oimage @ C @ D @ ( c_Fun_Othe__inv__into @ D @ C @ A @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__inv__into__onto) ).
thf(5035,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ A )
=> ( ( hAPP @ ( c_Set_Oimage @ C @ D @ ( c_Fun_Othe__inv__into @ D @ C @ A @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(652,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ B ) @ A ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ A ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( D != B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ D ) @ C )
!= B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_aset_I4_J) ).
thf(4009,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ B ) @ A ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ A ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( D != B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ D ) @ C )
!= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(212,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( 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 ) )
=> ( ( hAPP @ ( hAPP @ ( 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 ) )
= ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__div__cancel__disj) ).
thf(2111,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( 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 ) )
=> ( ( hAPP @ ( hAPP @ ( 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 ) )
= ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(342,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ A ) @ ( c_List_Olist_ONil @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__Nil2) ).
thf(2780,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ A ) @ ( c_List_Olist_ONil @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(719,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__right) ).
thf(4277,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( 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)],[719]) ).
thf(696,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( c_List_Oupt @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ tc_Nat_Onat ) @ ( c_List_Oupt @ C @ B ) ) @ ( c_List_Oupt @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__add__eq__append) ).
thf(4181,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( c_List_Oupt @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ tc_Nat_Onat ) @ ( c_List_Oupt @ C @ B ) ) @ ( c_List_Oupt @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(1249,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ c_Int_ORep__Integ @ B )
= ( hAPP @ c_Int_ORep__Integ @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Rep__Integ__inject) ).
thf(6414,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ c_Int_ORep__Integ @ B )
= ( hAPP @ c_Int_ORep__Integ @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ c_Int_ORep__Integ @ B )
= ( hAPP @ c_Int_ORep__Integ @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1249]) ).
thf(725,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( c_List_OdropWhile @ E @ D @ C )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ B ) @ A ) )
<=> ( ( C
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ ( c_List_OtakeWhile @ E @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ B ) @ A ) ) )
& ~ ( hBOOL @ ( hAPP @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile__eq__Cons__conv) ).
thf(4296,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( c_List_OdropWhile @ E @ D @ C )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ B ) @ A ) )
=> ( ( C
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ ( c_List_OtakeWhile @ E @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ B ) @ A ) ) )
& ~ ( hBOOL @ ( hAPP @ D @ B ) ) ) )
& ( ( ( C
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ ( c_List_OtakeWhile @ E @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ B ) @ A ) ) )
& ~ ( hBOOL @ ( hAPP @ D @ B ) ) )
=> ( ( c_List_OdropWhile @ E @ D @ C )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(250,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) @ B ) )
<=> ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel2) ).
thf(2289,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) @ B ) )
=> ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
& ( ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(300,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ ( hAPP @ ( c_List_Ofilter @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ E ) @ B ) @ A ) ) )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( c_List_Ofilter @ C @ ( hAPP @ ( c_Fun_Ocomp @ E @ tc_HOL_Obool @ C @ D ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__filter__map) ).
thf(2553,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ ( hAPP @ ( c_List_Ofilter @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ E ) @ B ) @ A ) ) )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( c_List_Ofilter @ C @ ( hAPP @ ( c_Fun_Ocomp @ E @ tc_HOL_Obool @ C @ D ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_List_OtakeWhile @ E @ D @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ E ) @ B ) @ ( c_List_OtakeWhile @ C @ ( hAPP @ ( c_Fun_Ocomp @ E @ tc_HOL_Obool @ C @ D ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__map) ).
thf(1381,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_List_OtakeWhile @ E @ D @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ E ) @ B ) @ ( c_List_OtakeWhile @ C @ ( hAPP @ ( c_Fun_Ocomp @ E @ tc_HOL_Obool @ C @ D ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(357,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__mono2) ).
thf(2842,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(109,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) )
& ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__le) ).
thf(1688,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) )
& ( B != A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) )
& ( B != A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(786,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_List_Oset @ E ) @ C ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ B @ D ) )
=> ( ( c_List_OdropWhile @ E @ B @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ ( c_List_OdropWhile @ E @ B @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile__append1) ).
thf(4541,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_List_Oset @ E ) @ C ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ B @ D ) )
=> ( ( c_List_OdropWhile @ E @ B @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ ( c_List_OdropWhile @ E @ B @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(334,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Otrans @ B @ A )
=> ( c_Relation_Otrans @ ( tc_List_Olist @ B ) @ ( c_List_Olistrel @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__trans) ).
thf(2742,plain,
! [A: $i,B: $i] :
( ( c_Relation_Otrans @ B @ A )
=> ( c_Relation_Otrans @ ( tc_List_Olist @ B ) @ ( c_List_Olistrel @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(1136,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ B ) @ ( c_SetInterval_Oord_OatMost @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_OatMost__iff) ).
thf(5920,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ B ) @ ( c_SetInterval_Oord_OatMost @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ B ) @ ( c_SetInterval_Oord_OatMost @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__Cons__0) ).
thf(1339,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(412,axiom,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
thf(3027,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(1088,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Orefl__on @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ A ) @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__onD) ).
thf(5730,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Orefl__on @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ A ) @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).
thf(573,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) )
<=> ~ ( ( ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split__asm) ).
thf(3668,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ~ ( ( ( hBOOL @ ( hAPP @ ( 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 @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(862,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc_Osimps) ).
thf(4833,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(922,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__mono) ).
thf(5082,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(795,axiom,
! [A: $i,B: $i] :
( ( c_List_Olistrel1 @ B @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) )
= ( hAPP @ ( c_Relation_Oconverse @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olistrel1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1__converse) ).
thf(4569,plain,
! [A: $i,B: $i] :
( ( c_List_Olistrel1 @ B @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) )
= ( hAPP @ ( c_Relation_Oconverse @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olistrel1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(663,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__diffD) ).
thf(4064,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(857,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_Relation_ODomain @ D @ B ) @ A ) ) )
=> ~ ! [E: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ B ) @ C ) @ E ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainE) ).
thf(4818,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_Relation_ODomain @ D @ B ) @ A ) ) )
=> ~ ! [E: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ B ) @ C ) @ E ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(1016,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ C ) @ ( hAPP @ ( c_Relation_ODomain @ E @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainI) ).
thf(5439,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ C ) @ ( hAPP @ ( c_Relation_ODomain @ E @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(116,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__commute) ).
thf(1731,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)],[116]) ).
thf(608,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ tc_Nat_Onat @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__greaterThanAtMost) ).
thf(3800,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ tc_Nat_Onat @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(1233,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ D @ C @ B ) @ A ) )
<=> ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainP_Oequations) ).
thf(6353,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ D @ C @ B ) @ A ) )
=> ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ E ) ) )
& ( ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ D @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1233]) ).
thf(635,axiom,
! [A: $i,B: $i] :
~ ( c_List_Olist__ex1 @ B @ A @ ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex1__simps_I1_J) ).
thf(3932,plain,
! [A: $i,B: $i] :
~ ( c_List_Olist__ex1 @ B @ A @ ( c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(874,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__atLeastLessThan) ).
thf(4897,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(892,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Osym @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ A ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ A ) @ B ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_symD) ).
thf(4985,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Osym @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ A ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ A ) @ B ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(1056,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Osym @ B @ A )
<=> ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ D ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ D ) @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sym__def) ).
thf(5599,plain,
! [A: $i,B: $i] :
( ( ( c_Relation_Osym @ B @ A )
=> ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ D ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ D ) @ C ) ) @ A ) ) ) )
& ( ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ D ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ D ) @ C ) ) @ A ) ) )
=> ( c_Relation_Osym @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).
thf(973,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SucE) ).
thf(5286,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(414,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0__eq__0) ).
thf(3034,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(141,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zero) ).
thf(1838,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( 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)],[141]) ).
thf(984,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ B ) ) )
=> ( ( c_List_Oremove1 @ D @ C @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ ( c_List_Oremove1 @ D @ C @ B ) ) @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ B ) ) )
=> ( ( c_List_Oremove1 @ D @ C @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ B ) @ ( c_List_Oremove1 @ D @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remove1__append) ).
thf(5318,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ B ) ) )
=> ( ( c_List_Oremove1 @ D @ C @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ ( c_List_Oremove1 @ D @ C @ B ) ) @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ B ) ) )
=> ( ( c_List_Oremove1 @ D @ C @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ B ) @ ( c_List_Oremove1 @ D @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(815,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__atLeastAtMost) ).
thf(4652,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(1128,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__def) ).
thf(5885,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ A @ B ) ) )
& ( ( hBOOL @ ( hAPP @ A @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).
thf(643,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ C ) )
=> ! [E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ G ) @ B ) )
=> ( E
!= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ G ) @ F ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ E ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ E ) @ C ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_aset_I9_J) ).
thf(3971,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ C ) )
=> ! [E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ G ) @ B ) )
=> ( E
!= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ G ) @ F ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ E ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ E ) @ C ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(280,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel2) ).
thf(2461,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[280]) ).
thf(397,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
thf(2974,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(1010,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_List_Osublist @ C @ B @ ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sublist__upt__eq__take) ).
thf(5410,plain,
! [A: $i,B: $i,C: $i] :
( ( c_List_Osublist @ C @ B @ ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(325,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ A ) @ B )
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__all) ).
thf(2710,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ A ) @ B )
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(790,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_List_OremoveAll @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ ( hAPP @ ( c_List_OremoveAll @ D @ C ) @ B ) ) @ ( hAPP @ ( c_List_OremoveAll @ D @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_removeAll__append) ).
thf(4554,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_List_OremoveAll @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ ( hAPP @ ( c_List_OremoveAll @ D @ C ) @ B ) ) @ ( hAPP @ ( c_List_OremoveAll @ D @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(709,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
<=> ( ( ( B
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__1) ).
thf(4232,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( ( B
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) )
& ( ( ( ( B
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(925,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Owf @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ A ) ) @ C ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ A ) @ B ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__not__sym) ).
thf(5094,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Owf @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ A ) ) @ C ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ A ) @ B ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(97,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib) ).
thf(1643,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)],[97]) ).
thf(1222,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OgreaterThan @ D @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OgreaterThan__iff) ).
thf(6288,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OgreaterThan @ D @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ C ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OgreaterThan @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1222]) ).
thf(441,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
thf(3159,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(383,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofun__left__comm @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ D @ B ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__insert) ).
thf(2931,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofun__left__comm @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ D @ B ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(347,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_List_Olist__ex @ D @ C @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ B ) @ A ) )
<=> ( ( c_List_Olist__ex @ D @ C @ B )
| ( c_List_Olist__ex @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex__append) ).
thf(2797,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_List_Olist__ex @ D @ C @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ B ) @ A ) )
=> ( ( c_List_Olist__ex @ D @ C @ B )
| ( c_List_Olist__ex @ D @ C @ A ) ) )
& ( ( ( c_List_Olist__ex @ D @ C @ B )
| ( c_List_Olist__ex @ D @ C @ A ) )
=> ( c_List_Olist__ex @ D @ C @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_List_OdropWhile @ C @ B @ A )
= ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( c_List_OtakeWhile @ C @ B @ A ) ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile__eq__drop) ).
thf(1364,plain,
! [A: $i,B: $i,C: $i] :
( ( c_List_OdropWhile @ C @ B @ A )
= ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( c_List_OtakeWhile @ C @ B @ A ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(1223,axiom,
! [A: $i,B: $i,C: $i] :
( ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ D ) ) )
<=> ( c_List_Olist__ex @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bex__set__list__ex) ).
thf(6293,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ D ) ) )
=> ( c_List_Olist__ex @ C @ A @ B ) )
& ( ( c_List_Olist__ex @ C @ A @ B )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1223]) ).
thf(936,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_List_Olist__all @ D @ C @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ C @ B ) )
& ( c_List_Olist__all @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all__simps_I1_J) ).
thf(5139,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_List_Olist__all @ D @ C @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ C @ B ) )
& ( c_List_Olist__all @ D @ C @ A ) ) )
& ( ( ( hBOOL @ ( hAPP @ C @ B ) )
& ( c_List_Olist__all @ D @ C @ A ) )
=> ( c_List_Olist__all @ D @ C @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(1203,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ E @ D @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversepD) ).
thf(6212,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ E @ D @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1203]) ).
thf(340,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ B )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__if) ).
thf(2770,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ B )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(199,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Int_Oint ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__atLeastZeroLessThan__int) ).
thf(2075,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Int_Oint ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(267,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__le__cancel1) ).
thf(2418,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[267]) ).
thf(861,axiom,
class_Orderings_Owellorder @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Owellorder) ).
thf(4832,plain,
class_Orderings_Owellorder @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(831,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__atLeastAtMost) ).
thf(4720,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(142,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 @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ D ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ C ) @ F ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).
thf(1841,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 @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ D ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ C ) @ F ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(274,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ B ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) @ B )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__times__mod__eq) ).
thf(2439,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ B ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) @ B )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(1138,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Equiv__Relations_Oequiv @ H @ G @ F )
=> ( ( c_Equiv__Relations_Ocongruent2 @ H @ E @ D @ F @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ H ) @ A ) @ G ) )
=> ( c_Equiv__Relations_Ocongruent @ E @ D @ C @ ( hAPP @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_congruent2__implies__congruent) ).
thf(5931,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Equiv__Relations_Oequiv @ H @ G @ F )
=> ( ( c_Equiv__Relations_Ocongruent2 @ H @ E @ D @ F @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ H ) @ A ) @ G ) )
=> ( c_Equiv__Relations_Ocongruent @ E @ D @ C @ ( hAPP @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).
thf(1238,axiom,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ c_fNot @ A ) )
| ~ ( hBOOL @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__1) ).
thf(6377,plain,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ c_fNot @ A ) )
| ~ ( hBOOL @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1238]) ).
thf(593,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
thf(3759,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)],[593]) ).
thf(617,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).
thf(3838,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(1242,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Big__Operators_Osemilattice__big @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) )
=> ( ( hAPP @ B @ A )
= ( hAPP @ ( c_Finite__Set_Ofold1 @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semilattice__big_OF__eq) ).
thf(6394,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Big__Operators_Osemilattice__big @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) )
=> ( ( hAPP @ B @ A )
= ( hAPP @ ( c_Finite__Set_Ofold1 @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1242]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( 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 ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ D ) ) ) @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult2__lemma__aux2) ).
thf(1445,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( 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 ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ D ) ) ) @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(490,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ C ) @ B ) ) @ ( c_List_Olistrel1 @ D @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ C ) @ B ) ) @ ( c_List_Olistrel @ D @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__reflcl__if__listrel1) ).
thf(3363,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ C ) @ B ) ) @ ( c_List_Olistrel1 @ D @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ C ) @ B ) ) @ ( c_List_Olistrel @ D @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(1118,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ D @ C @ B )
=> ( ( hAPP @ ( hAPP @ C @ A ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Oidem) ).
thf(5849,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ D @ C @ B )
=> ( ( hAPP @ ( hAPP @ C @ A ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).
thf(1074,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ C ) ) @ B ) @ ( hAPP @ ( c_Relation_Oconverse @ C @ D ) @ A ) ) )
=> ~ ! [E: $i,F: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ F ) @ E ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ D ) @ E ) @ F ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converseE) ).
thf(5667,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ C ) ) @ B ) @ ( hAPP @ ( c_Relation_Oconverse @ C @ D ) @ A ) ) )
=> ~ ! [E: $i,F: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ F ) @ E ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ D ) @ E ) @ F ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(699,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) ) )
& ( ( D
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__Cons_H) ).
thf(4196,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) ) )
& ( ( D
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(254,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_OwfP @ B @ A )
=> ( c_Wellfounded_Oacyclic @ B @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ B @ tc_HOL_Obool ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfP__acyclicP) ).
thf(2303,plain,
! [A: $i,B: $i] :
( ( c_Wellfounded_OwfP @ B @ A )
=> ( c_Wellfounded_Oacyclic @ B @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ B @ tc_HOL_Obool ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(701,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__cancel2) ).
thf(4209,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(689,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__eq) ).
thf(4158,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(496,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ C @ B ) @ ( hAPP @ ( c_Relation_Oconverse @ B @ C ) @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__converse) ).
thf(3380,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ C @ B ) @ ( hAPP @ ( c_Relation_Oconverse @ B @ C ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__less__cancel1) ).
thf(1562,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[77]) ).
thf(628,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Equiv__Relations_Oequiv @ C @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ C @ C @ C ) @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ A ) ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__comp__eq) ).
thf(3881,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Equiv__Relations_Oequiv @ C @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ C @ C @ C ) @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ A ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(407,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le0) ).
thf(3009,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( 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)],[407]) ).
thf(1040,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( c_SetInterval_Oord__class_OgreaterThanLessThan @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__greaterThanLessThan) ).
thf(5548,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( c_SetInterval_Oord__class_OgreaterThanLessThan @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(836,axiom,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessThan__Suc) ).
thf(4741,plain,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(390,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( c_Fun_Oinj__on @ E @ B @ A @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ C ) )
<=> ( c_Fun_Oinj__on @ F @ B @ ( hAPP @ ( c_Fun_Ocomp @ E @ B @ F @ A ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comp__inj__on__iff) ).
thf(2952,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ D @ C )
=> ( ( ( c_Fun_Oinj__on @ E @ B @ A @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ C ) )
=> ( c_Fun_Oinj__on @ F @ B @ ( hAPP @ ( c_Fun_Ocomp @ E @ B @ F @ A ) @ D ) @ C ) )
& ( ( c_Fun_Oinj__on @ F @ B @ ( hAPP @ ( c_Fun_Ocomp @ E @ B @ F @ A ) @ D ) @ C )
=> ( c_Fun_Oinj__on @ E @ B @ A @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(765,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( c_Fun_Ofun__upd @ E @ D @ C @ B @ A )
= C )
<=> ( ( hAPP @ C @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__idem__iff) ).
thf(4456,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( c_Fun_Ofun__upd @ E @ D @ C @ B @ A )
= C )
=> ( ( hAPP @ C @ B )
= A ) )
& ( ( ( hAPP @ C @ B )
= A )
=> ( ( c_Fun_Ofun__upd @ E @ D @ C @ B @ A )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(781,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__1__Cons) ).
thf(4529,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(723,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).
thf(4292,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(381,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ C ) ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__append1) ).
thf(2927,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ C ) ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(678,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Osym @ B @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) )
<=> ( c_Relation_Osym @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sym__converse) ).
thf(4113,plain,
! [A: $i,B: $i] :
( ( ( c_Relation_Osym @ B @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) )
=> ( c_Relation_Osym @ B @ A ) )
& ( ( c_Relation_Osym @ B @ A )
=> ( c_Relation_Osym @ B @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(171,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ B )
= A )
<=> ( ( C
= ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) @ A ) )
& ( B
= ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__eq__conv__conj) ).
thf(1958,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ B )
= A )
=> ( ( C
= ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) @ A ) )
& ( B
= ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) @ A ) ) ) )
& ( ( ( C
= ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) @ A ) )
& ( B
= ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) @ A ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(738,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ ( c_List_OdropWhile @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__dropWhile) ).
thf(4355,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ ( c_List_OdropWhile @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(478,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Equiv__Relations_Oequiv @ C @ B @ A )
<=> ( ( c_Relation_Orefl__on @ C @ B @ A )
& ( c_Relation_Osym @ C @ A )
& ( c_Relation_Otrans @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__def) ).
thf(3292,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Equiv__Relations_Oequiv @ C @ B @ A )
=> ( ( c_Relation_Orefl__on @ C @ B @ A )
& ( c_Relation_Osym @ C @ A )
& ( c_Relation_Otrans @ C @ A ) ) )
& ( ( ( c_Relation_Orefl__on @ C @ B @ A )
& ( c_Relation_Osym @ C @ A )
& ( c_Relation_Otrans @ C @ A ) )
=> ( c_Equiv__Relations_Oequiv @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(832,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__trans) ).
thf(4722,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
<=> ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) )
& ( ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ A ) @ D )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__conv__nth) ).
thf(1551,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) )
& ( ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ A ) @ D )
= B ) ) )
& ( ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) )
& ( ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ A ) @ D )
= B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(621,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( c_List_Oset @ tc_Nat_Onat ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( c_List_Ofoldl @ tc_Nat_Onat @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_elem__le__sum) ).
thf(3849,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( c_List_Oset @ tc_Nat_Onat ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( c_List_Ofoldl @ tc_Nat_Onat @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(413,axiom,
! [A: $i] :
( ( c_List_Oupt @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_List_Olist_ONil @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__0) ).
thf(3031,plain,
! [A: $i] :
( ( c_List_Oupt @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_List_Olist_ONil @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(825,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ B ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__refl) ).
thf(4690,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ B ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_List_Ofoldl @ F @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ B ) @ A ) )
= ( hAPP @ ( c_List_Ofoldl @ F @ E @ D @ ( hAPP @ ( c_List_Ofoldl @ F @ E @ D @ C ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldl__append) ).
thf(1304,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_List_Ofoldl @ F @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ B ) @ A ) )
= ( hAPP @ ( c_List_Ofoldl @ F @ E @ D @ ( hAPP @ ( c_List_Ofoldl @ F @ E @ D @ C ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1129,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ B ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__dropD) ).
thf(5890,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ B ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).
thf(451,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__infinite) ).
thf(3193,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(511,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__1) ).
thf(3427,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(876,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
| ( B
= ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__eq) ).
thf(4901,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
| ( B
= ( hAPP @ c_Nat_OSuc @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
| ( B
= ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(210,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ D ) ) ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult2__lemma__aux1) ).
thf(2107,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ D ) ) ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(713,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).
thf(4260,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(855,axiom,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__rtrancl__absorb) ).
thf(4813,plain,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(799,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( ( ( B
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__is__add) ).
thf(4580,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( ( B
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) )
& ( ( ( ( B
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
=> ( ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(282,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__0__less__mult__iff) ).
thf(2471,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[282]) ).
thf(1104,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ ( hAPP @ ( c_Relation_Oconverse @ D @ D ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_Oconverse @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__converseD) ).
thf(5785,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ ( hAPP @ ( c_Relation_Oconverse @ D @ D ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_Oconverse @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).
thf(442,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_le__imp__diff__is__add) ).
thf(3161,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( 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 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(158,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ D ) @ B ) ) ) @ ( c_List_Olexord @ E @ A ) ) )
=> ( ! [F: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ F ) @ F ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ C ) @ B ) ) @ ( c_List_Olexord @ E @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__append__leftD) ).
thf(1905,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ D ) @ B ) ) ) @ ( c_List_Olexord @ E @ A ) ) )
=> ( ! [F: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ F ) @ F ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ C ) @ B ) ) @ ( c_List_Olexord @ E @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ A ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__div__cancel) ).
thf(1420,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ A ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(645,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ A ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ D ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ A ) )
=> ( B
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ E ) @ D ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ C )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bset_I3_J) ).
thf(3981,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ A ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ D ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ A ) )
=> ( B
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ E ) @ D ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ C )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(1175,axiom,
! [A: $i,B: $i,C: $i] :
( ? [D: $i] : ( hBOOL @ ( hAPP @ C @ D ) )
=> ( ( B
= ( c_Hilbert__Choice_OEps @ A @ C ) )
=> ( hBOOL @ ( hAPP @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exE__some) ).
thf(6088,plain,
! [A: $i,B: $i,C: $i] :
( ? [D: $i] : ( hBOOL @ ( hAPP @ C @ D ) )
=> ( ( B
= ( c_Hilbert__Choice_OEps @ A @ C ) )
=> ( hBOOL @ ( hAPP @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1175]) ).
thf(215,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olist_ONil @ C ) ) @ B ) ) @ ( c_List_Olistrel @ C @ A ) ) )
=> ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__Nil1) ).
thf(2124,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olist_ONil @ C ) ) @ B ) ) @ ( c_List_Olistrel @ C @ A ) ) )
=> ( B
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(235,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ C ) @ A ) ) ) @ c_FunDef_Opair__less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__lessI1) ).
thf(2234,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ C ) @ A ) ) ) @ c_FunDef_Opair__less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(730,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A )
= ( c_SetInterval_Oord__class_OgreaterThanLessThan @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastSucLessThan__greaterThanLessThan) ).
thf(4319,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A )
= ( c_SetInterval_Oord__class_OgreaterThanLessThan @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(177,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ E ) @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) @ B ) @ A ) ) @ ( c_List_Olistrel @ F @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ E ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ D ) @ A ) ) ) @ ( c_List_Olistrel @ F @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel_OCons) ).
thf(1990,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ E ) @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) @ B ) @ A ) ) @ ( c_List_Olistrel @ F @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ E ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ D ) @ A ) ) ) @ ( c_List_Olistrel @ F @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(1078,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Orefl__on @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__onD1) ).
thf(5678,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Orefl__on @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).
thf(317,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel1) ).
thf(2684,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(1183,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ C @ B ) @ A ) )
=> ( ( c_Divides_Odivmod__nat @ C @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__eq) ).
thf(6132,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ C @ B ) @ A ) )
=> ( ( c_Divides_Odivmod__nat @ C @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183]) ).
thf(546,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl2) ).
thf(3571,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(431,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
thf(3112,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)],[431]) ).
thf(821,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Finite__Set_Ofold1 @ C @ B ) @ A )
= ( c_HOL_OThe @ C @ ( c_Finite__Set_Ofold1Set @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__def) ).
thf(4673,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Finite__Set_Ofold1 @ C @ B ) @ A )
= ( c_HOL_OThe @ C @ ( c_Finite__Set_Ofold1Set @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(435,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_Oacyclic @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__acyclic) ).
thf(3129,plain,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_Oacyclic @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(263,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__diff1__eq) ).
thf(2407,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( 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)],[263]) ).
thf(372,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
<=> ? [B: $i] :
( A
= ( hAPP @ c_Nat_OSuc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
thf(2888,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ? [B: $i] :
( A
= ( hAPP @ c_Nat_OSuc @ B ) ) )
& ( ? [B: $i] :
( A
= ( hAPP @ c_Nat_OSuc @ B ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[372]) ).
thf(1156,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ B ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ ( c_List_Osublist @ D @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_notin__set__sublistI) ).
thf(6012,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ B ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ ( c_List_Osublist @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).
thf(817,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).
thf(4658,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(387,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_le__add2) ).
thf(2942,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( 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)],[387]) ).
thf(646,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) )
<=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__nat__less__eq) ).
thf(3988,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) )
=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) )
& ( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) )
=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(711,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__diff) ).
thf(4255,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(1049,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite_OinsertI) ).
thf(5570,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_zadd__strict__right__mono) ).
thf(1547,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[73]) ).
thf(252,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__assoc) ).
thf(2298,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)],[252]) ).
thf(500,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Otake @ ( tc_prod @ E @ D ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ E ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__zip) ).
thf(3391,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Otake @ ( tc_prod @ E @ D ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ E ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(1062,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Big__Operators_Ocomm__monoid__big @ G @ F @ E @ D @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hAPP @ ( hAPP @ C @ A ) @ B )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ G @ F @ E ) @ A ) @ D ) @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hAPP @ ( hAPP @ C @ A ) @ B )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__monoid__big_OF__eq) ).
thf(5624,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Big__Operators_Ocomm__monoid__big @ G @ F @ E @ D @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hAPP @ ( hAPP @ C @ A ) @ B )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ G @ F @ E ) @ A ) @ D ) @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hAPP @ ( hAPP @ C @ A ) @ B )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).
thf(957,axiom,
! [A: $i,B: $i] :
( ( c_Predicate_Oreflp @ B @ A )
=> ( ( c_Predicate_Osymp @ B @ A )
=> ( ( c_Predicate_Otransp @ B @ A )
=> ( c_Equiv__Relations_Oequivp @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivpI) ).
thf(5229,plain,
! [A: $i,B: $i] :
( ( c_Predicate_Oreflp @ B @ A )
=> ( ( c_Predicate_Osymp @ B @ A )
=> ( ( c_Predicate_Otransp @ B @ A )
=> ( c_Equiv__Relations_Oequivp @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(364,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ G @ F @ E @ D ) @ C )
= B )
=> ( ( hAPP @ D @ ( hAPP @ C @ A ) )
= ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__eq__dest__lhs) ).
thf(2863,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ G @ F @ E @ D ) @ C )
= B )
=> ( ( hAPP @ D @ ( hAPP @ C @ A ) )
= ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(85,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_le__imp__0__less) ).
thf(1598,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[85]) ).
thf(883,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ B ) @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Oinject) ).
thf(4937,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ B ) @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(1002,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl_Or__into__trancl) ).
thf(5388,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(1123,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OatLeast @ D @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OatLeast__iff) ).
thf(5871,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OatLeast @ D @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ C ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OatLeast @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).
thf(718,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).
thf(4272,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono2) ).
thf(1400,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[36]) ).
thf(741,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ B ) @ A ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ A ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( D != B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ D ) @ C )
!= B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bset_I4_J) ).
thf(4366,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ B ) @ A ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ A ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( D != B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ D ) @ C )
!= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(87,axiom,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__self) ).
thf(1605,plain,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( hAPP @ ( hAPP @ ( 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)],[87]) ).
thf(466,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ B @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastAtMostSuc__conv) ).
thf(3260,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ B @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(310,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0__right) ).
thf(2588,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)],[310]) ).
thf(880,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( ( c_List_Oinsert @ C @ B @ A )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__in__set__insert) ).
thf(4922,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( ( c_List_Oinsert @ C @ B @ A )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(1094,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__imp__le) ).
thf(5748,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).
thf(783,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
thf(4534,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)],[783]) ).
thf(570,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Odrop @ ( tc_prod @ E @ D ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ E ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__zip) ).
thf(3659,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Odrop @ ( tc_prod @ E @ D ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ E ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(354,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_List_Olist__all @ D @ C @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ B ) @ A ) )
<=> ( ( c_List_Olist__all @ D @ C @ B )
& ( c_List_Olist__all @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all__append) ).
thf(2821,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_List_Olist__all @ D @ C @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ B ) @ A ) )
=> ( ( c_List_Olist__all @ D @ C @ B )
& ( c_List_Olist__all @ D @ C @ A ) ) )
& ( ( ( c_List_Olist__all @ D @ C @ B )
& ( c_List_Olist__all @ D @ C @ A ) )
=> ( c_List_Olist__all @ D @ C @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(454,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__is__0__eq_H) ).
thf(3209,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( 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)],[454]) ).
thf(554,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
thf(3608,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[554]) ).
thf(360,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( hAPP @ ( c_Wellfounded_Omeasure @ D ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ A @ C ) ) @ ( hAPP @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__measure) ).
thf(2850,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( hAPP @ ( c_Wellfounded_Omeasure @ D ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ A @ C ) ) @ ( hAPP @ A @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ A @ C ) ) @ ( hAPP @ A @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( hAPP @ ( c_Wellfounded_Omeasure @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(370,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ G @ F @ E @ D ) @ ( hAPP @ ( c_Fun_Ocomp @ C @ G @ E @ B ) @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ C @ F @ E @ ( hAPP @ ( c_Fun_Ocomp @ G @ F @ C @ D ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__assoc) ).
thf(2882,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ G @ F @ E @ D ) @ ( hAPP @ ( c_Fun_Ocomp @ C @ G @ E @ B ) @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ C @ F @ E @ ( hAPP @ ( c_Fun_Ocomp @ G @ F @ C @ D ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(900,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( hBOOL @ ( hAPP @ E @ D ) )
=> ( ( c_List_OtakeWhile @ C @ E @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ D ) @ A ) ) )
= ( c_List_OtakeWhile @ C @ E @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__tail) ).
thf(5018,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( hBOOL @ ( hAPP @ E @ D ) )
=> ( ( c_List_OtakeWhile @ C @ E @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ D ) @ A ) ) )
= ( c_List_OtakeWhile @ C @ E @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(1142,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fimplies__1) ).
thf(5955,plain,
! [A: $i,B: $i] :
( ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).
thf(729,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ C ) )
=> ! [E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ G ) @ B ) )
=> ( E
!= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ G ) @ F ) ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ E ) @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ E ) @ C ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_aset_I10_J) ).
thf(4314,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ C ) )
=> ! [E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ G ) @ B ) )
=> ( E
!= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ G ) @ F ) ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ E ) @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ E ) @ C ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(1219,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertI2) ).
thf(6280,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1219]) ).
thf(480,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F = E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= A ) )
& ( ( F != E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= ( hAPP @ B @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__apply) ).
thf(3305,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F = E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= A ) )
& ( ( F != E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= ( hAPP @ B @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(321,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_le__cube) ).
thf(2700,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( 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)],[321]) ).
thf(899,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Oantisym @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ A ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ A ) @ B ) ) @ C ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisymD) ).
thf(5015,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Oantisym @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ A ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ A ) @ B ) ) @ C ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(1250,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ C @ ( hAPP @ c_Nat_OSuc @ B ) @ A )
=> ( c_Hoare__Mirabelle_Otriple__valid @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_triple__valid__Suc) ).
thf(6421,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ C @ ( hAPP @ c_Nat_OSuc @ B ) @ A )
=> ( c_Hoare__Mirabelle_Otriple__valid @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1250]) ).
thf(130,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) )
<=> ( ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel__disj) ).
thf(1785,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) )
=> ( ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ) )
& ( ( ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(1268,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( ( c_List_Oinsert @ C @ B @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__insert) ).
thf(6513,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( ( c_List_Oinsert @ C @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1268]) ).
thf(613,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ C ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ C @ A ) ) ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel__mult2__eq) ).
thf(3823,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ C ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ C @ A ) ) ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(281,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ D ) ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ A ) @ A ) ) @ ( c_List_Olexord @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__irreflexive) ).
thf(2468,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ D ) ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ A ) @ A ) ) @ ( c_List_Olexord @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(581,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_List_OdropWhile @ C @ B @ A )
= ( c_List_Olist_ONil @ C ) )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile__eq__Nil__conv) ).
thf(3715,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( c_List_OdropWhile @ C @ B @ A )
= ( c_List_Olist_ONil @ C ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ B @ D ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ B @ D ) ) )
=> ( ( c_List_OdropWhile @ C @ B @ A )
= ( c_List_Olist_ONil @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(463,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__less) ).
thf(3246,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( 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)],[463]) ).
thf(760,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add2) ).
thf(4437,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[760]) ).
thf(748,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ C ) @ B ) ) @ ( c_List_Olistrel1 @ D @ ( hAPP @ ( c_Relation_Oconverse @ D @ D ) @ A ) ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_Oconverse @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( c_List_Olistrel1 @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__listrel1__converse) ).
thf(4398,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ C ) @ B ) ) @ ( c_List_Olistrel1 @ D @ ( hAPP @ ( c_Relation_Oconverse @ D @ D ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_Oconverse @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( c_List_Olistrel1 @ D @ A ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_Oconverse @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( c_List_Olistrel1 @ D @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ C ) @ B ) ) @ ( c_List_Olistrel1 @ D @ ( hAPP @ ( c_Relation_Oconverse @ D @ D ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(671,axiom,
! [A: $i,B: $i] :
~ ( c_List_Olist__ex @ B @ A @ ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex__simps_I2_J) ).
thf(4092,plain,
! [A: $i,B: $i] :
~ ( c_List_Olist__ex @ B @ A @ ( c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(1012,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ c_Nat_OSuc @ B )
= ( hAPP @ c_Nat_OSuc @ A ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__inject) ).
thf(5420,plain,
! [A: $i,B: $i] :
( ( ( hAPP @ c_Nat_OSuc @ B )
= ( hAPP @ c_Nat_OSuc @ A ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(1164,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( C = A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertCI) ).
thf(6036,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( C = A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164]) ).
thf(136,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
<=> ( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ A ) ) @ C )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ A ) ) @ B ) )
& ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ A @ A ) ) @ D ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ A @ A ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ A @ A ) @ C ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ A @ A @ tc_HOL_Obool ) @ c_fequal ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__eq__iff__zip__eq) ).
thf(1813,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C = B )
=> ( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ A ) ) @ C )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ A ) ) @ B ) )
& ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ A @ A ) ) @ D ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ A @ A ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ A @ A ) @ C ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ A @ A @ tc_HOL_Obool ) @ c_fequal ) @ D ) ) ) ) )
& ( ( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ A ) ) @ C )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ A ) ) @ B ) )
& ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ A @ A ) ) @ D ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ A @ A ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ A @ A ) @ C ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ A @ A @ tc_HOL_Obool ) @ c_fequal ) @ D ) ) ) )
=> ( C = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) )
<=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ C @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( 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 @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mod) ).
thf(1452,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ C @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( 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 @ E ) ) ) ) ) ) )
& ( ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ C @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( 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 @ E ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(542,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ B @ A ) @ ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp_ONil) ).
thf(3554,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ B @ A ) @ ( c_List_Olist_ONil @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(1177,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ H @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ F @ ( hAPP @ D @ A ) ) @ ( hAPP @ C @ B ) )
= ( hAPP @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oin__idem) ).
thf(6093,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ H @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ F @ ( hAPP @ D @ A ) ) @ ( hAPP @ C @ B ) )
= ( hAPP @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).
thf(1043,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Owf @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ A ) ) @ C ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ A ) @ B ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__asym) ).
thf(5555,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Owf @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ A ) ) @ C ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ A ) @ B ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).
thf(150,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ E ) @ D ) )
=> ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_List_Onth @ B ) @ A ) @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ ( c_List_OtakeWhile @ B @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__takeWhile__less__P__nth) ).
thf(1869,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ E ) @ D ) )
=> ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_List_Onth @ B ) @ A ) @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ ( c_List_OtakeWhile @ B @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(1182,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ C @ B ) @ A ) )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__listsp__conv__set) ).
thf(6125,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ C @ B ) @ A ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ B @ D ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ B @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182]) ).
thf(217,axiom,
! [A: $i,B: $i] :
( ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ? [C: $i] :
( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__eq__0__iff) ).
thf(2128,plain,
! [A: $i,B: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ? [C: $i] :
( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ C ) ) )
& ( ? [C: $i] :
( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ C ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(1153,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eqelem__imp__iff) ).
thf(5995,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ B ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__append) ).
thf(1317,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ B ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(125,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ A )
= ( c_SetInterval_Oord__class_OgreaterThanLessThan @ tc_Int_Oint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastPlusOneLessThan__greaterThanLessThan__int) ).
thf(1763,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ A )
= ( c_SetInterval_Oord__class_OgreaterThanLessThan @ tc_Int_Oint @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(1255,axiom,
! [A: $i,B: $i] :
( ( class_Enum_Oenum @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__ex @ B ) @ A ) )
<=> ? [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_enum__ex) ).
thf(6436,plain,
! [A: $i,B: $i] :
( ( class_Enum_Oenum @ B )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__ex @ B ) @ A ) )
=> ? [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) ) )
& ( ? [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__ex @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1255]) ).
thf(620,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ ( hAPP @ ( c_Fun_Ocomp @ D @ E @ F @ C ) @ B ) @ A )
=> ( c_Fun_Oinj__on @ F @ D @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__imageI2) ).
thf(3847,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ ( hAPP @ ( c_Fun_Ocomp @ D @ E @ F @ C ) @ B ) @ A )
=> ( c_Fun_Oinj__on @ F @ D @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(851,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__absorb2) ).
thf(4800,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(891,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ B ) )
=> ( ( c_List_Oremove1 @ C @ A @ B )
= ( hAPP @ ( c_List_OremoveAll @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__remove1__removeAll) ).
thf(4982,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ B ) )
=> ( ( c_List_Oremove1 @ C @ A @ B )
= ( hAPP @ ( c_List_OremoveAll @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(560,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__assoc) ).
thf(3623,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ B ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__append) ).
thf(1285,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ B ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(623,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_List_Oupt @ D @ C )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ C ) )
& ( D = B )
& ( ( c_List_Oupt @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ C )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__eq__Cons__conv) ).
thf(3853,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( c_List_Oupt @ D @ C )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ C ) )
& ( D = B )
& ( ( c_List_Oupt @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ C )
= A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ C ) )
& ( D = B )
& ( ( c_List_Oupt @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ C )
= A ) )
=> ( ( c_List_Oupt @ D @ C )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_List_OtakeWhile @ C @ B @ A )
= ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( c_List_OtakeWhile @ C @ B @ A ) ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__eq__take) ).
thf(1336,plain,
! [A: $i,B: $i,C: $i] :
( ( c_List_OtakeWhile @ C @ B @ A )
= ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( c_List_OtakeWhile @ C @ B @ A ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(871,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ B @ B ) ) @ A ) )
=> ( ( c_Wellfounded_Owf @ B @ A )
<=> ( c_Wellfounded_Oacyclic @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__iff__acyclic__if__finite) ).
thf(4875,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ B @ B ) ) @ A ) )
=> ( ( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_Oacyclic @ B @ A ) )
& ( ( c_Wellfounded_Oacyclic @ B @ A )
=> ( c_Wellfounded_Owf @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(1141,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_SetInterval_Oord_OatLeastAtMost @ E @ C @ B @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OatLeastAtMost__iff) ).
thf(5949,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_SetInterval_Oord_OatLeastAtMost @ E @ C @ B @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_SetInterval_Oord_OatLeastAtMost @ E @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
<=> ( ( B = A )
| ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel1) ).
thf(1766,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)],[126]) ).
thf(145,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__imp__zdiv__neg__iff) ).
thf(1849,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( 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)],[145]) ).
thf(1077,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__drop) ).
thf(5675,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).
thf(507,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__imp__le) ).
thf(3415,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(1227,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ E @ D @ C ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep_Oequations) ).
thf(6333,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ E @ D @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ E @ D @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1227]) ).
thf(803,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_List_Oremdups @ C @ ( hAPP @ ( c_List_Ofilter @ C @ B ) @ A ) )
= ( hAPP @ ( c_List_Ofilter @ C @ B ) @ ( c_List_Oremdups @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remdups__filter) ).
thf(4611,plain,
! [A: $i,B: $i,C: $i] :
( ( c_List_Oremdups @ C @ ( hAPP @ ( c_List_Ofilter @ C @ B ) @ A ) )
= ( hAPP @ ( c_List_Ofilter @ C @ B ) @ ( c_List_Oremdups @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(1271,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F
= ( hAPP @ E @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ F ) @ ( hAPP @ ( c_Set_Oimage @ C @ A @ E ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__eqI) ).
thf(6526,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F
= ( hAPP @ E @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ F ) @ ( hAPP @ ( c_Set_Oimage @ C @ A @ E ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1271]) ).
thf(758,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Nitpick_Opair__box_Opair__box__size @ F @ E @ D @ C @ ( c_Nitpick_Opair__box_OPairBox @ F @ E @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ D @ B ) ) @ ( hAPP @ C @ A ) ) ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__box_Osize_I1_J) ).
thf(4431,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Nitpick_Opair__box_Opair__box__size @ F @ E @ D @ C @ ( c_Nitpick_Opair__box_OPairBox @ F @ E @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ D @ B ) ) @ ( hAPP @ C @ A ) ) ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(637,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_List_OremoveAll @ B @ A ) @ ( c_List_Olist_ONil @ B ) )
= ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_removeAll_Osimps_I1_J) ).
thf(3943,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_List_OremoveAll @ B @ A ) @ ( c_List_Olist_ONil @ B ) )
= ( c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(1085,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ( ( C = B )
| ( ( C != B )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtranclD) ).
thf(5717,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ( ( C = B )
| ( ( C != B )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).
thf(1234,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_New__DSequence_Opos__empty @ B ) @ A )
= ( c_Lazy__Sequence_Oempty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Opos__empty__def) ).
thf(6358,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_New__DSequence_Opos__empty @ B ) @ A )
= ( c_Lazy__Sequence_Oempty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1234]) ).
thf(1116,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ ( hAPP @ ( c_List_Oset @ D ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ B @ E ) ) )
=> ( ( c_List_OtakeWhile @ D @ B @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ ( c_List_OtakeWhile @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__append2) ).
thf(5841,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ ( hAPP @ ( c_List_Oset @ D ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ B @ E ) ) )
=> ( ( c_List_OtakeWhile @ D @ B @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ ( c_List_OtakeWhile @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).
thf(574,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add2) ).
thf(3684,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[574]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono) ).
thf(1404,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[38]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib2) ).
thf(1358,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)],[23]) ).
thf(683,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Nitpick_Onat__gcd__rel ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ C ) @ B ) ) )
=> ( ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Nitpick_Onat__gcd__rel ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ D ) @ E ) ) )
=> ( ( ( E
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ D @ E ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ D ) @ E ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__gcd_Opinduct) ).
thf(4133,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Nitpick_Onat__gcd__rel ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ C ) @ B ) ) )
=> ( ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Nitpick_Onat__gcd__rel ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ D ) @ E ) ) )
=> ( ( ( E
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ D @ E ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ D ) @ E ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__less__cancel1) ).
thf(1536,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(298,axiom,
! [A: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ tc_Nat_Onat ) @ A ) ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osize_I4_J) ).
thf(2543,plain,
! [A: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ tc_Nat_Onat ) @ A ) ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(960,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__greaterThanAtMost) ).
thf(5240,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_List_Ofoldl @ tc_Nat_Onat @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_start__le__sum) ).
thf(1353,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_List_Ofoldl @ tc_Nat_Onat @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(839,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__asym) ).
thf(4748,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(170,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) @ C ) ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zmult2__eq) ).
thf(1955,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) @ C ) ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(56,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Suc__right) ).
thf(1485,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(173,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ ( c_List_Obutlast @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__butlast) ).
thf(1972,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ ( c_List_Obutlast @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(1021,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ E @ D @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ B ) ) @ A ) )
=> ~ ! [F: $i,G: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ F ) @ G ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ E @ E @ D @ F @ G ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__fold1SetE) ).
thf(5453,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ E @ D @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ B ) ) @ A ) )
=> ~ ! [F: $i,G: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ F ) @ G ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ E @ E @ D @ F @ G ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(121,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__mod__sign) ).
thf(1749,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(1110,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_List_Olistrelp @ F @ E @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ E @ D ) @ B ) )
& ( c_List_Olistrelp @ F @ E @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrelp_Oequations_I2_J) ).
thf(5809,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_List_Olistrelp @ F @ E @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ E @ D ) @ B ) )
& ( c_List_Olistrelp @ F @ E @ C @ A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ E @ D ) @ B ) )
& ( c_List_Olistrelp @ F @ E @ C @ A ) )
=> ( c_List_Olistrelp @ F @ E @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).
thf(686,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( B = A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
thf(4143,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( B = A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(457,axiom,
! [A: $i,B: $i] : ( c_Relation_Oantisym @ B @ ( c_Relation_OId__on @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisym__Id__on) ).
thf(3224,plain,
! [A: $i,B: $i] : ( c_Relation_Oantisym @ B @ ( c_Relation_OId__on @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(81,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ ( c_List_Oremdups @ B @ A ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ ( hAPP @ ( c_List_Oset @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__remdups__card__conv) ).
thf(1585,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ ( c_List_Oremdups @ B @ A ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ ( hAPP @ ( c_List_Oset @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(288,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__mod__conj) ).
thf(2511,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(810,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ A ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__commute) ).
thf(4634,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(956,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
thf(5226,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(132,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ C @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B ) )
<=> ? [D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mod__eq__iff) ).
thf(1797,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ C @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B ) )
=> ? [D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ E ) ) ) )
& ( ? [D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ E ) ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ C @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(411,axiom,
! [A: $i,B: $i,C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olist_ONil @ C ) ) @ B ) ) @ ( c_List_Olistrel1 @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__Nil__listrel1) ).
thf(3024,plain,
! [A: $i,B: $i,C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olist_ONil @ C ) ) @ B ) ) @ ( c_List_Olistrel1 @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(363,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Finite__Set_Ofolding__image__simple @ G @ F @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ A ) )
=> ( ( hAPP @ B @ A )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ G @ F @ E ) @ C ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Oeq__fold__g) ).
thf(2860,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Finite__Set_Ofolding__image__simple @ G @ F @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ A ) )
=> ( ( hAPP @ B @ A )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ G @ F @ E ) @ C ) @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(995,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessD) ).
thf(5364,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(640,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ tc_Nat_Onat ) @ ( c_List_Oupt @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__upt) ).
thf(3961,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ tc_Nat_Onat ) @ ( c_List_Oupt @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(1027,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Osingle__valued @ C @ B @ A )
<=> ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ B ) @ D ) @ E ) ) @ A ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ B ) @ D ) @ F ) ) @ A ) )
=> ( E = F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__def) ).
thf(5472,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Relation_Osingle__valued @ C @ B @ A )
=> ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ B ) @ D ) @ E ) ) @ A ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ B ) @ D ) @ F ) ) @ A ) )
=> ( E = F ) ) ) )
& ( ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ B ) @ D ) @ E ) ) @ A ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ B ) @ D ) @ F ) ) @ A ) )
=> ( E = F ) ) )
=> ( c_Relation_Osingle__valued @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).
thf(419,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ B ) @ A ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ A ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ D ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bset_I7_J) ).
thf(3071,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ B ) @ A ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ A ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ D ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(349,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__le__divisor) ).
thf(2807,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(850,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).
thf(4795,plain,
! [A: $i,B: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(532,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( B != A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
thf(3520,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( B != A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(1055,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_New__Random__Sequence_Opos__empty @ D @ C @ B @ A )
= ( c_New__DSequence_Opos__empty @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__empty__def) ).
thf(5596,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_New__Random__Sequence_Opos__empty @ D @ C @ B @ A )
= ( c_New__DSequence_Opos__empty @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).
thf(638,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ? [C: $i] :
( ( B
= ( hAPP @ c_Nat_OSuc @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).
thf(3946,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ? [C: $i] :
( ( B
= ( hAPP @ c_Nat_OSuc @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ? [C: $i] :
( ( B
= ( hAPP @ c_Nat_OSuc @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(559,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__inverse) ).
thf(3620,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(279,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ A ) ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__append__length) ).
thf(2458,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ A ) ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(1252,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ G @ F @ E @ D @ C ) @ B ) @ A ) )
<=> ? [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ H ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ H ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__comp_Oequations) ).
thf(6425,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ G @ F @ E @ D @ C ) @ B ) @ A ) )
=> ? [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ H ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ H ) @ A ) ) ) )
& ( ? [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ H ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ H ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ G @ F @ E @ D @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1252]) ).
thf(732,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse) ).
thf(4325,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(843,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ H @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ B ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ D @ A ) ) @ ( hAPP @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oinsert__idem) ).
thf(4770,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ H @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ B ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ D @ A ) ) @ ( hAPP @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(371,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl) ).
thf(2885,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(1165,axiom,
! [A: $i,B: $i] :
( ? [C: $i] : ( hBOOL @ ( hAPP @ B @ C ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Hilbert__Choice_OEps @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_someI__ex) ).
thf(6041,plain,
! [A: $i,B: $i] :
( ? [C: $i] : ( hBOOL @ ( hAPP @ B @ C ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Hilbert__Choice_OEps @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).
thf(753,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc2) ).
thf(4419,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(515,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) @ E ) @ D ) ) @ ( c_List_Olistrel1 @ F @ C ) ) )
& ( B = A ) )
| ( ( E = D )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) @ B ) @ A ) ) @ ( c_List_Olistrel1 @ F @ C ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ F ) @ E ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ F ) @ D ) @ A ) ) ) @ ( c_List_Olistrel1 @ F @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__listrel1I) ).
thf(3447,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) @ E ) @ D ) ) @ ( c_List_Olistrel1 @ F @ C ) ) )
& ( B = A ) )
| ( ( E = D )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) @ B ) @ A ) ) @ ( c_List_Olistrel1 @ F @ C ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ F ) @ E ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ F ) @ D ) @ A ) ) ) @ ( c_List_Olistrel1 @ F @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(102,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__mult__div__cancel) ).
thf(1654,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(284,axiom,
! [A: $i,B: $i] :
( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__if) ).
thf(2490,plain,
! [A: $i,B: $i] :
( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(1121,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_List_Olist__ex @ C @ B @ A )
<=> ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
& ( hBOOL @ ( hAPP @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex__iff) ).
thf(5860,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_List_Olist__ex @ C @ B @ A )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
& ( hBOOL @ ( hAPP @ B @ D ) ) ) )
& ( ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
& ( hBOOL @ ( hAPP @ B @ D ) ) )
=> ( c_List_Olist__ex @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).
thf(341,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Orefl__on @ C @ B @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ A ) )
<=> ( c_Relation_Orefl__on @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__converse) ).
thf(2775,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Relation_Orefl__on @ C @ B @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ A ) )
=> ( c_Relation_Orefl__on @ C @ B @ A ) )
& ( ( c_Relation_Orefl__on @ C @ B @ A )
=> ( c_Relation_Orefl__on @ C @ B @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(572,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ F @ E @ D @ C ) @ B ) @ A )
= ( hAPP @ C @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__def) ).
thf(3665,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ F @ E @ D @ C ) @ B ) @ A )
= ( hAPP @ C @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(607,axiom,
! [A: $i,B: $i] :
( ( c_List_Oremove1 @ B @ A @ ( c_List_Olist_ONil @ B ) )
= ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remove1_Osimps_I1_J) ).
thf(3797,plain,
! [A: $i,B: $i] :
( ( c_List_Oremove1 @ B @ A @ ( c_List_Olist_ONil @ B ) )
= ( c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(368,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__le__dividend) ).
thf(2875,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(1100,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ C @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Relation_ORange @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Range) ).
thf(5771,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ C @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Relation_ORange @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).
thf(443,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).
thf(3168,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(812,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq2) ).
thf(4639,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(338,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ B @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__idemp__self__comp) ).
thf(2760,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ B @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(183,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ E @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ A @ tc_HOL_Obool ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ A ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_prod__caseI) ).
thf(2013,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ E @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ A @ tc_HOL_Obool ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ A ) @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(380,axiom,
! [A: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatMost @ tc_Nat_Onat ) @ A ) )
= ( hAPP @ c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__atMost) ).
thf(2924,plain,
! [A: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatMost @ tc_Nat_Onat ) @ A ) )
= ( hAPP @ c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(684,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofun__left__comm @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ E @ D @ C @ A @ B ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ E @ D @ C ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__graph__fold) ).
thf(4138,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofun__left__comm @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ E @ D @ C @ A @ B ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ E @ D @ C ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(517,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( ( hAPP @ K @ ( hAPP @ J @ I ) )
= ( hAPP @ H @ ( hAPP @ G @ F ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ E @ D @ C @ K ) @ J ) @ I )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ B @ D @ A @ H ) @ G ) @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comp__cong) ).
thf(3457,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( ( hAPP @ K @ ( hAPP @ J @ I ) )
= ( hAPP @ H @ ( hAPP @ G @ F ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ E @ D @ C @ K ) @ J ) @ I )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ B @ D @ A @ H ) @ G ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__zdiffD) ).
thf(1649,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(366,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Relation_ORange @ C @ B ) @ A )
= ( hAPP @ ( c_Relation_ODomain @ B @ C ) @ ( hAPP @ ( c_Relation_Oconverse @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__def) ).
thf(2870,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Relation_ORange @ C @ B ) @ A )
= ( hAPP @ ( c_Relation_ODomain @ B @ C ) @ ( hAPP @ ( c_Relation_Oconverse @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(691,axiom,
! [A: $i,B: $i] : ( c_Relation_Osingle__valued @ B @ B @ ( c_Relation_OId__on @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__Id__on) ).
thf(4165,plain,
! [A: $i,B: $i] : ( c_Relation_Osingle__valued @ B @ B @ ( c_Relation_OId__on @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(257,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1__right) ).
thf(2310,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)],[257]) ).
thf(143,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
thf(1844,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[143]) ).
thf(626,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ B ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ D ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_aset_I7_J) ).
thf(3874,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ B ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ D ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(231,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__pos__pos__trivial) ).
thf(2215,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( 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)],[231]) ).
thf(835,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Relation_Osingle__valued @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ C ) @ B ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ C ) @ A ) ) @ D ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valuedD) ).
thf(4738,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Relation_Osingle__valued @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ C ) @ B ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ C ) @ A ) ) @ D ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(931,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__into__trancl2) ).
thf(5115,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(582,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( ? [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) )
=> ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card_Oneutral) ).
thf(3725,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( ? [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) )
=> ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(1133,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( c_SetInterval_Oord_OatLeastLessThan @ F @ D @ C @ B @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OatLeastLessThan__iff) ).
thf(5907,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( c_SetInterval_Oord_OatLeastLessThan @ F @ D @ C @ B @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( c_SetInterval_Oord_OatLeastLessThan @ F @ D @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).
thf(255,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).
thf(2305,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)],[255]) ).
thf(378,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ ( c_List_Osublist @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__sublistI) ).
thf(2919,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ ( c_List_Osublist @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(693,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono1) ).
thf(4170,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[693]) ).
thf(1275,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Typedef_Otype__definition @ F @ E @ D @ C @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ ( hAPP @ D @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_ORep) ).
thf(6543,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Typedef_Otype__definition @ F @ E @ D @ C @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ ( hAPP @ D @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1275]) ).
thf(766,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Relation_OImage @ B @ B @ ( c_Relation_OId @ B ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__Id) ).
thf(4463,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Relation_OImage @ B @ B @ ( c_Relation_OId @ B ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(117,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__number__of__int__code) ).
thf(1734,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(134,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__imp__zdiv__neg__iff) ).
thf(1807,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( 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)],[134]) ).
thf(662,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_Divides_Odivmod__nat @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__base) ).
thf(4061,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_Divides_Odivmod__nat @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(948,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D = C )
=> ( ( c_List_Oremove1 @ B @ D @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ C ) @ A ) )
= A ) )
& ( ( D != C )
=> ( ( c_List_Oremove1 @ B @ D @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ C ) @ ( c_List_Oremove1 @ B @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remove1_Osimps_I2_J) ).
thf(5184,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D = C )
=> ( ( c_List_Oremove1 @ B @ D @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ C ) @ A ) )
= A ) )
& ( ( D != C )
=> ( ( c_List_Oremove1 @ B @ D @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ C ) @ ( c_List_Oremove1 @ B @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(376,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
& ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__le) ).
thf(2907,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
& ( B != A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
& ( B != A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(680,axiom,
! [A: $i,B: $i] :
( ( c_SetInterval_Oord__class_OgreaterThanLessThan @ tc_Nat_Onat @ B @ A )
= ( hAPP @ ( c_List_Oset @ tc_Nat_Onat ) @ ( c_List_Oupt @ ( hAPP @ c_Nat_OSuc @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_greaterThanLessThan__upt) ).
thf(4121,plain,
! [A: $i,B: $i] :
( ( c_SetInterval_Oord__class_OgreaterThanLessThan @ tc_Nat_Onat @ B @ A )
= ( hAPP @ ( c_List_Oset @ tc_Nat_Onat ) @ ( c_List_Oupt @ ( hAPP @ c_Nat_OSuc @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(249,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ E ) ) @ C ) ) @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__add__iff1) ).
thf(2283,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( 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)],[249]) ).
thf(1229,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ B ) @ A ) )
| ( hBOOL @ B )
| ( hBOOL @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fdisj__3) ).
thf(6341,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ B ) @ A ) )
| ( hBOOL @ B )
| ( hBOOL @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1229]) ).
thf(361,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ F @ E @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__conv) ).
thf(2855,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ F @ E @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(497,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__dvd__not__less) ).
thf(3383,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(492,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ A ) @ ( c_List_Olist_ONil @ B ) )
= ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__Nil) ).
thf(3369,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ A ) @ ( c_List_Olist_ONil @ B ) )
= ( c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(351,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__antisym) ).
thf(2811,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(997,axiom,
! [A: $i,B: $i] :
( ( c_Equiv__Relations_Oequivp @ B @ A )
=> ( c_Equiv__Relations_Opart__equivp @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__implies__part__equivp) ).
thf(5368,plain,
! [A: $i,B: $i] :
( ( c_Equiv__Relations_Oequivp @ B @ A )
=> ( c_Equiv__Relations_Opart__equivp @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(590,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ ( hAPP @ ( c_Set_Oimage @ D @ B @ A ) @ C ) ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__image__le) ).
thf(3748,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ ( hAPP @ ( c_Set_Oimage @ D @ B @ A ) @ C ) ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(271,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ C @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ C ) )
=> ? [D: $i] :
( C
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mod__eq__lemma) ).
thf(2431,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ C @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ C ) )
=> ? [D: $i] :
( C
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(923,axiom,
! [A: $i,B: $i] :
( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oneq__le__trans) ).
thf(5087,plain,
! [A: $i,B: $i] :
( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(873,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ D ) @ C )
= ( hAPP @ ( c_List_Ofilter @ E @ B ) @ A ) )
<=> ? [F: $i,G: $i] :
( ( A
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ F ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ D ) @ G ) ) )
& ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ H ) @ ( hAPP @ ( c_List_Oset @ E ) @ F ) ) )
=> ~ ( hBOOL @ ( hAPP @ B @ H ) ) )
& ( hBOOL @ ( hAPP @ B @ D ) )
& ( C
= ( hAPP @ ( c_List_Ofilter @ E @ B ) @ G ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__eq__filter__iff) ).
thf(4881,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ D ) @ C )
= ( hAPP @ ( c_List_Ofilter @ E @ B ) @ A ) )
=> ? [F: $i,G: $i] :
( ( A
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ F ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ D ) @ G ) ) )
& ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ H ) @ ( hAPP @ ( c_List_Oset @ E ) @ F ) ) )
=> ~ ( hBOOL @ ( hAPP @ B @ H ) ) )
& ( hBOOL @ ( hAPP @ B @ D ) )
& ( C
= ( hAPP @ ( c_List_Ofilter @ E @ B ) @ G ) ) ) )
& ( ? [F: $i,G: $i] :
( ( A
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ F ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ D ) @ G ) ) )
& ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ H ) @ ( hAPP @ ( c_List_Oset @ E ) @ F ) ) )
=> ~ ( hBOOL @ ( hAPP @ B @ H ) ) )
& ( hBOOL @ ( hAPP @ B @ D ) )
& ( C
= ( hAPP @ ( c_List_Ofilter @ E @ B ) @ G ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ D ) @ C )
= ( hAPP @ ( c_List_Ofilter @ E @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(384,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_List_Oupt @ B @ A )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ tc_Nat_Onat ) @ B ) @ ( c_List_Oupt @ ( hAPP @ c_Nat_OSuc @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__conv__Cons) ).
thf(2934,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_List_Oupt @ B @ A )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ tc_Nat_Onat ) @ B ) @ ( c_List_Oupt @ ( hAPP @ c_Nat_OSuc @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(422,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Relation_ODomain @ B @ B ) @ ( c_Relation_OId__on @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__Id__on) ).
thf(3085,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Relation_ODomain @ B @ B ) @ ( c_Relation_OId__on @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(311,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ E ) @ F ) ) @ C ) )
| ( E = F )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ F ) @ E ) ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ B ) @ A ) ) @ ( c_List_Olexord @ D @ C ) ) )
| ( B = A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ A ) @ B ) ) @ ( c_List_Olexord @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__linear) ).
thf(2591,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ E ) @ F ) ) @ C ) )
| ( E = F )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ F ) @ E ) ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ B ) @ A ) ) @ ( c_List_Olexord @ D @ C ) ) )
| ( B = A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ A ) @ B ) ) @ ( c_List_Olexord @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__mono) ).
thf(1590,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(98,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__zmod__imp__zdvd) ).
thf(1646,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(1064,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ C @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( c_Relation_ODomain @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Domain) ).
thf(5632,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ C @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( c_Relation_ODomain @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(556,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ B @ A ) @ ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp_Oequations_I1_J) ).
thf(3613,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ B @ A ) @ ( c_List_Olist_ONil @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(324,axiom,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zdiv__equality_H) ).
thf(2707,plain,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(829,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( hAPP @ ( c_List_Ofilter @ B @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ C ) @ ( hAPP @ ( c_List_Ofilter @ B @ D ) @ A ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( hAPP @ ( c_List_Ofilter @ B @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ C ) @ A ) )
= ( hAPP @ ( c_List_Ofilter @ B @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter_Osimps_I2_J) ).
thf(4710,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( hAPP @ ( c_List_Ofilter @ B @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ C ) @ ( hAPP @ ( c_List_Ofilter @ B @ D ) @ A ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( hAPP @ ( c_List_Ofilter @ B @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ C ) @ A ) )
= ( hAPP @ ( c_List_Ofilter @ B @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(403,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
thf(2988,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)],[403]) ).
thf(624,axiom,
! [A: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__lessThan) ).
thf(3864,plain,
! [A: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(242,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__commute) ).
thf(2251,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)],[242]) ).
thf(614,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_le__add1) ).
thf(3825,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( 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)],[614]) ).
thf(819,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ B @ D ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ D ) @ C ) ) ) ) )
=> ( ( hBOOL @ ( hAPP @ B @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__induct__0) ).
thf(4666,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ B @ D ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ D ) @ C ) ) ) ) )
=> ( ( hBOOL @ ( hAPP @ B @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(218,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ C ) @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__Cons__Suc) ).
thf(2135,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ C ) @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(897,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__insert) ).
thf(5008,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(670,axiom,
! [A: $i,B: $i] :
( ( c_List_Oremdups @ B @ ( c_List_Oremdups @ B @ A ) )
= ( c_List_Oremdups @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remdups__remdups) ).
thf(4089,plain,
! [A: $i,B: $i] :
( ( c_List_Oremdups @ B @ ( c_List_Oremdups @ B @ A ) )
= ( c_List_Oremdups @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(768,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__pos__if__in__set) ).
thf(4468,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(1281,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ B ) @ A ) )
| ( hBOOL @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__3) ).
thf(6567,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ B ) @ A ) )
| ( hBOOL @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1281]) ).
thf(823,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Relation_OImage @ C @ E @ B ) @ A ) ) )
<=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ E ) @ F ) @ D ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__iff) ).
thf(4681,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Relation_OImage @ C @ E @ B ) @ A ) ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ E ) @ F ) @ D ) ) @ B ) ) ) )
& ( ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ E ) @ F ) @ D ) ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Relation_OImage @ C @ E @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(1109,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq) ).
thf(5800,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( B = A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( B = A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).
thf(571,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Otake @ tc_Nat_Onat ) @ B ) @ ( c_List_Oupt @ C @ A ) )
= ( c_List_Oupt @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__upt) ).
thf(3662,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Otake @ tc_Nat_Onat ) @ B ) @ ( c_List_Oupt @ C @ A ) )
= ( c_List_Oupt @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(266,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Int_Oint ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Int_Oint @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__atLeastLessThan__int) ).
thf(2416,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Int_Oint ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Int_Oint @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(1269,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ ( hAPP @ A @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ B @ A ) @ C ) )
= ( hAPP @ ( c_Set_Oimage @ E @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__image) ).
thf(6516,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ ( hAPP @ A @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ B @ A ) @ C ) )
= ( hAPP @ ( c_Set_Oimage @ E @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1269]) ).
thf(201,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_List_OdropWhile @ E @ D @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ E ) @ B ) @ ( c_List_OdropWhile @ C @ ( hAPP @ ( c_Fun_Ocomp @ E @ tc_HOL_Obool @ C @ D ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile__map) ).
thf(2081,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_List_OdropWhile @ E @ D @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ E ) @ B ) @ ( c_List_OdropWhile @ C @ ( hAPP @ ( c_Fun_Ocomp @ E @ tc_HOL_Obool @ C @ D ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(814,axiom,
! [A: $i] :
( ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
= ( hAPP @ ( c_SetInterval_Oord__class_OatMost @ tc_Nat_Onat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeast0AtMost) ).
thf(4649,plain,
! [A: $i] :
( ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
= ( hAPP @ ( c_SetInterval_Oord__class_OatMost @ tc_Nat_Onat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(1243,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Equiv__Relations_Oequivp @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__symp) ).
thf(6397,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Equiv__Relations_Oequivp @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1243]) ).
thf(627,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__less__divisor) ).
thf(3879,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(229,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( A
= ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__0__conv) ).
thf(2198,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( A
= ( c_List_Olist_ONil @ B ) ) )
& ( ( A
= ( c_List_Olist_ONil @ B ) )
=> ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(1248,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ E @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ B @ A @ E ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainP_Ointros) ).
thf(6412,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ E @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ B @ A @ E ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1248]) ).
thf(1218,axiom,
! [A: $i,B: $i] :
( ( class_Enum_Oenum @ B )
=> ( ? [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) )
<=> ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__ex @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exists__code) ).
thf(6277,plain,
! [A: $i,B: $i] :
( ( class_Enum_Oenum @ B )
=> ( ( ? [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__ex @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__ex @ B ) @ A ) )
=> ? [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1218]) ).
thf(605,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) )
=> ( c_Wellfounded_Owf @ B @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__converse__trancl) ).
thf(3793,plain,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) )
=> ( c_Wellfounded_Owf @ B @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(954,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Nitpick_Opair__box_OPairBox @ F @ E @ D @ C )
= ( c_Nitpick_Opair__box_OPairBox @ F @ E @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__box_Oinject) ).
thf(5211,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( c_Nitpick_Opair__box_OPairBox @ F @ E @ D @ C )
= ( c_Nitpick_Opair__box_OPairBox @ F @ E @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( c_Nitpick_Opair__box_OPairBox @ F @ E @ D @ C )
= ( c_Nitpick_Opair__box_OPairBox @ F @ E @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(870,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_Relation_ODomain @ D @ D ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ B ) ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Not__Domain__rtrancl) ).
thf(4869,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_Relation_ODomain @ D @ D ) @ B ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ B ) ) )
=> ( C = A ) )
& ( ( C = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(1264,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ G @ F @ E @ D @ C @ B )
=> ( ( hAPP @ ( hAPP @ E @ A ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oidem) ).
thf(6499,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ G @ F @ E @ D @ C @ B )
=> ( ( hAPP @ ( hAPP @ E @ A ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1264]) ).
thf(806,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Osym @ B @ A )
=> ( c_Relation_Osym @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sym__rtrancl) ).
thf(4619,plain,
! [A: $i,B: $i] :
( ( c_Relation_Osym @ B @ A )
=> ( c_Relation_Osym @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(1200,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ F ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ D @ C @ B @ E ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ D @ C @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ F ) @ E ) ) @ ( hAPP @ ( hAPP @ C @ F ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_OinsertI) ).
thf(6198,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ F ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ D @ C @ B @ E ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ D @ C @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ F ) @ E ) ) @ ( hAPP @ ( hAPP @ C @ F ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1200]) ).
thf(268,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ D ) @ C ) ) @ ( c_List_Olexord @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ A ) @ C ) ) ) @ ( c_List_Olexord @ E @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__append__leftI) ).
thf(2421,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ D ) @ C ) ) @ ( c_List_Olexord @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ A ) @ C ) ) ) @ ( c_List_Olexord @ E @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(277,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) )
<=> ( A
!= ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__greater__0__conv) ).
thf(2447,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ( A
!= ( c_List_Olist_ONil @ B ) ) )
& ( ( A
!= ( c_List_Olist_ONil @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(388,axiom,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Otrancl @ B @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) )
= ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__converse) ).
thf(2944,plain,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Otrancl @ B @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) )
= ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(866,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Relation_ORange @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( hAPP @ ( c_Relation_ORange @ E @ D ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__insert) ).
thf(4855,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Relation_ORange @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( hAPP @ ( c_Relation_ORange @ E @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(344,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Ototal__on @ C @ B @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ A ) )
<=> ( c_Relation_Ototal__on @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_total__on__converse) ).
thf(2786,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Relation_Ototal__on @ C @ B @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ A ) )
=> ( c_Relation_Ototal__on @ C @ B @ A ) )
& ( ( c_Relation_Ototal__on @ C @ B @ A )
=> ( c_Relation_Ototal__on @ C @ B @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(191,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ C ) @ A ) )
<=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__eq__iff__index__eq) ).
thf(2041,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ C ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(1196,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__ident) ).
thf(6181,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1196]) ).
thf(619,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThanSuc__atLeastAtMost) ).
thf(3844,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(512,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= ( c_List_Olist_ONil @ C ) ) )
& ( ( D
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__Cons_H) ).
thf(3430,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= ( c_List_Olist_ONil @ C ) ) )
& ( ( D
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ D ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(1102,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ~ ! [D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ ( hAPP @ A @ ( hAPP @ c_Nat_OSuc @ D ) ) ) @ ( hAPP @ A @ D ) ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__no__infinite__down__chainE) ).
thf(5781,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ~ ! [D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ ( hAPP @ A @ ( hAPP @ c_Nat_OSuc @ D ) ) ) @ ( hAPP @ A @ D ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).
thf(844,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__1__Cons) ).
thf(4774,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
<=> ( ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).
thf(1294,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)],[6]) ).
thf(908,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ole__neq__trans) ).
thf(5040,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(488,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ B ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ E @ E @ D ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one_Oeq__fold_H) ).
thf(3351,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ B ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ E @ E @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__add1__eq__le) ).
thf(1513,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[65]) ).
thf(1033,axiom,
! [A: $i,B: $i] :
( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oeq__refl) ).
thf(5517,plain,
! [A: $i,B: $i] :
( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).
thf(233,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ E @ D @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splitD) ).
thf(2230,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ E @ D @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(189,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono2) ).
thf(2036,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[189]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__trans) ).
thf(1309,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1257,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ A ) )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp_Oequations) ).
thf(6444,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ A ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ D ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1257]) ).
thf(951,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_List_Oset @ E ) @ C ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ B @ D ) )
=> ( ( c_List_OtakeWhile @ E @ B @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ C ) @ A ) )
= ( c_List_OtakeWhile @ E @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__append1) ).
thf(5196,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_List_Oset @ E ) @ C ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ B @ D ) )
=> ( ( c_List_OtakeWhile @ E @ B @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ C ) @ A ) )
= ( c_List_OtakeWhile @ E @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(994,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( ( c_List_Oinsert @ C @ B @ A )
= A ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( ( c_List_Oinsert @ C @ B @ A )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_List_Oinsert__def) ).
thf(5357,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( ( c_List_Oinsert @ C @ B @ A )
= A ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( ( c_List_Oinsert @ C @ B @ A )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(290,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ tc_Nat_Onat ) @ ( c_List_Oupt @ C @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__upt) ).
thf(2517,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ tc_Nat_Onat ) @ ( c_List_Oupt @ C @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(1087,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ D @ B ) @ A ) ) )
=> ( ( c_Fun_Oinj__on @ C @ D @ B @ A )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__imageD) ).
thf(5728,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ D @ B ) @ A ) ) )
=> ( ( c_Fun_Oinj__on @ C @ D @ B @ A )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).
thf(460,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ C ) )
=> ! [E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ G ) @ B ) )
=> ( E
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ G ) @ F ) ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ E ) @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ E ) @ C ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bset_I10_J) ).
thf(3232,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ C ) )
=> ! [E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ G ) @ B ) )
=> ( E
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ G ) @ F ) ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ E ) @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ E ) @ C ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(1256,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D != C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ ( hAPP @ ( c_List_Oset @ B ) @ ( c_List_Oremove1 @ B @ C @ A ) ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ ( hAPP @ ( c_List_Oset @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__remove1) ).
thf(6439,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D != C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ ( hAPP @ ( c_List_Oset @ B ) @ ( c_List_Oremove1 @ B @ C @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ ( hAPP @ ( c_List_Oset @ B ) @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ ( hAPP @ ( c_List_Oset @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ ( hAPP @ ( c_List_Oset @ B ) @ ( c_List_Oremove1 @ B @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1256]) ).
thf(401,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leI) ).
thf(2983,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(584,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_List_Oupt @ B @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ tc_Nat_Onat ) @ ( c_List_Oupt @ B @ A ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ tc_Nat_Onat ) @ A ) @ ( c_List_Olist_ONil @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__Suc__append) ).
thf(3733,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_List_Oupt @ B @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ tc_Nat_Onat ) @ ( c_List_Oupt @ B @ A ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ tc_Nat_Onat ) @ A ) @ ( c_List_Olist_ONil @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(800,axiom,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).
thf(4596,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(864,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ A ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__irrefl) ).
thf(4843,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ A ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(739,axiom,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neq0__conv) ).
thf(4357,plain,
! [A: $i] :
( ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( 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)],[739]) ).
thf(963,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq) ).
thf(5247,plain,
! [A: $i,B: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ B ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(159,axiom,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Omod__div__equality_H) ).
thf(1908,plain,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(221,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_n__less__m__mult__n) ).
thf(2142,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[221]) ).
thf(382,axiom,
c_Wellfounded_Owf @ tc_Nat_Onat @ c_Wellfounded_Opred__nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__pred__nat) ).
thf(2930,plain,
c_Wellfounded_Owf @ tc_Nat_Onat @ c_Wellfounded_Opred__nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(232,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( c_List_Ofoldl @ tc_Nat_Onat @ tc_Nat_Onat @ ( 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 ) )
& ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_List_Oset @ tc_Nat_Onat ) @ A ) ) )
=> ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__eq__0__conv) ).
thf(2218,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( c_List_Ofoldl @ tc_Nat_Onat @ tc_Nat_Onat @ ( 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 ) )
& ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_List_Oset @ tc_Nat_Onat ) @ A ) ) )
=> ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_List_Oset @ tc_Nat_Onat ) @ A ) ) )
=> ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
=> ( ( hAPP @ ( c_List_Ofoldl @ tc_Nat_Onat @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(245,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ E ) @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ B ) @ E )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ A ) @ E ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ D ) @ B )
= ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__take__lemma) ).
thf(2258,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ E ) @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ B ) @ E )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ A ) @ E ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ D ) @ B )
= ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(911,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__not__sym) ).
thf(5051,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(208,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( c_List_OdropWhile @ C @ B @ A ) ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__dropWhile__le) ).
thf(2102,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( c_List_OdropWhile @ C @ B @ A ) ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(856,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ ( hAPP @ D @ ( hAPP @ c_Nat_OSuc @ F ) ) ) @ ( hAPP @ D @ F ) ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ ( hAPP @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) @ ( hAPP @ D @ B ) ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sequence__trans) ).
thf(4816,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ ( hAPP @ D @ ( hAPP @ c_Nat_OSuc @ F ) ) ) @ ( hAPP @ D @ F ) ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ ( hAPP @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) @ ( hAPP @ D @ B ) ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(1169,axiom,
! [A: $i] : ( class_Nat_Osize @ ( tc_Hoare__Mirabelle_Otriple @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Hoare____Mirabelle__Otriple__Nat_Osize) ).
thf(6055,plain,
! [A: $i] : ( class_Nat_Osize @ ( tc_Hoare__Mirabelle_Otriple @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).
thf(770,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ B ) @ A )
= B )
<=> ( A
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__self__conv) ).
thf(4472,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ B ) @ A )
= B )
=> ( A
= ( c_List_Olist_ONil @ C ) ) )
& ( ( A
= ( c_List_Olist_ONil @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ B ) @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(824,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( c_Equiv__Relations_Ocongruent2 @ J @ I @ H @ G @ F @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ J @ J ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ J @ J ) @ D ) @ C ) ) @ G ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ I @ I ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ I @ I ) @ B ) @ A ) ) @ F ) )
=> ( ( hAPP @ ( hAPP @ E @ D ) @ B )
= ( hAPP @ ( hAPP @ E @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_congruent2D) ).
thf(4687,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( c_Equiv__Relations_Ocongruent2 @ J @ I @ H @ G @ F @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ J @ J ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ J @ J ) @ D ) @ C ) ) @ G ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ I @ I ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ I @ I ) @ B ) @ A ) ) @ F ) )
=> ( ( hAPP @ ( hAPP @ E @ D ) @ B )
= ( hAPP @ ( hAPP @ E @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(820,axiom,
! [A: $i,B: $i] :
( ( c_Predicate_Opred__comp @ B @ B @ B @ c_fequal @ ( c_Predicate_Opred__comp @ B @ B @ B @ A @ c_fequal ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__comp__r) ).
thf(4670,plain,
! [A: $i,B: $i] :
( ( c_Predicate_Opred__comp @ B @ B @ B @ c_fequal @ ( c_Predicate_Opred__comp @ B @ B @ B @ A @ c_fequal ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(529,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Relation_ORange @ B @ B ) @ ( c_Relation_OId__on @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__Id__on) ).
thf(3511,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Relation_ORange @ B @ B ) @ ( c_Relation_OId__on @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(1057,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C ) ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ F @ E ) @ B ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ C ) @ ( hAPP @ ( c_List_Oset @ E ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__zip__rightD) ).
thf(5606,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C ) ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ F @ E ) @ B ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ C ) @ ( hAPP @ ( c_List_Oset @ E ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).
thf(1279,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ ( c_Transitive__Closure_Otrancl @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_r__into__trancl_H) ).
thf(6563,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ ( c_Transitive__Closure_Otrancl @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1279]) ).
thf(234,axiom,
class_Enum_Oenum @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Enum_Oenum) ).
thf(2233,plain,
class_Enum_Oenum @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(1235,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_List_Olist__all @ C @ B @ A )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all__iff__raw) ).
thf(6361,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_List_Olist__all @ C @ B @ A )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ B @ D ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ B @ D ) ) )
=> ( c_List_Olist__all @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1235]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__not__zless) ).
thf(1395,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(93,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ D ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma) ).
thf(1625,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ D ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(1168,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_List_Omember @ C ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( hAPP @ ( c_List_Oset @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_List_Omember__def) ).
thf(6050,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_List_Omember @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( hAPP @ ( c_List_Oset @ C ) @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( hAPP @ ( c_List_Oset @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_List_Omember @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).
thf(292,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ C ) @ B ) @ A ) ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult2__eq) ).
thf(2522,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ C ) @ B ) @ A ) ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(427,axiom,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) )
= ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__converse) ).
thf(3100,plain,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) )
= ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(604,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( c_Product__Type_Omap__pair @ J @ I @ H @ G @ ( hAPP @ ( c_Fun_Ocomp @ F @ I @ J @ E ) @ D ) @ ( hAPP @ ( c_Fun_Ocomp @ C @ G @ H @ B ) @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ ( tc_prod @ F @ C ) @ ( tc_prod @ I @ G ) @ ( tc_prod @ J @ H ) @ ( c_Product__Type_Omap__pair @ F @ I @ C @ G @ E @ B ) ) @ ( c_Product__Type_Omap__pair @ J @ F @ H @ C @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair__compose) ).
thf(3790,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( c_Product__Type_Omap__pair @ J @ I @ H @ G @ ( hAPP @ ( c_Fun_Ocomp @ F @ I @ J @ E ) @ D ) @ ( hAPP @ ( c_Fun_Ocomp @ C @ G @ H @ B ) @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ ( tc_prod @ F @ C ) @ ( tc_prod @ I @ G ) @ ( tc_prod @ J @ H ) @ ( c_Product__Type_Omap__pair @ F @ I @ C @ G @ E @ B ) ) @ ( c_Product__Type_Omap__pair @ J @ F @ H @ C @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
<=> ( ( B
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__1__iff) ).
thf(1527,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( B
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
& ( ( ( B
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(1261,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( ( hAPP @ ( c_List_OremoveAll @ C @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_removeAll__id) ).
thf(6490,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( ( hAPP @ ( c_List_OremoveAll @ C @ B ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1261]) ).
thf(1036,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__trans__Suc) ).
thf(5527,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).
thf(1045,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ E ) @ D ) ) @ ( c_Transitive__Closure_Ortrancl @ F @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) @ B ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_List_Olist @ F ) @ ( c_List_Olistrel1 @ F @ C ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ E ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ D ) @ A ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_List_Olist @ F ) @ ( c_List_Olistrel1 @ F @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__listrel1__ConsI2) ).
thf(5559,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ E ) @ D ) ) @ ( c_Transitive__Closure_Ortrancl @ F @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) @ B ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_List_Olist @ F ) @ ( c_List_Olistrel1 @ F @ C ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ E ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ D ) @ A ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_List_Olist @ F ) @ ( c_List_Olistrel1 @ F @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(409,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ G @ F ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ E ) @ D ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ C @ F ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ F ) )
=> ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ G ) @ C ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ E ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ A ) ) @ F ) ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ A ) @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel__add1__eq) ).
thf(3015,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ G @ F ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ E ) @ D ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ C @ F ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ F ) )
=> ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ G ) @ C ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ E ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ A ) ) @ F ) ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ A ) @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__imp__le) ).
thf(1436,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(1152,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_List_Omember @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__member) ).
thf(5990,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_List_Omember @ C ) @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_List_Omember @ C ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152]) ).
thf(651,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ G @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ G ) @ F ) @ E ) ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ G ) @ ( tc_List_Olist @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ G ) @ ( tc_List_Olist @ G ) ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ G ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ G ) @ F ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ G ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ G ) @ E ) @ A ) ) ) ) @ ( c_List_Olexord @ G @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__append__left__rightI) ).
thf(4007,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ G @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ G ) @ F ) @ E ) ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ G ) @ ( tc_List_Olist @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ G ) @ ( tc_List_Olist @ G ) ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ G ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ G ) @ F ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ G ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ G ) @ E ) @ A ) ) ) ) @ ( c_List_Olexord @ G @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(305,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Onth @ B ) @ A ) @ C ) ) @ ( hAPP @ ( c_List_Oset @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__mem) ).
thf(2572,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Onth @ B ) @ A ) @ C ) ) @ ( hAPP @ ( c_List_Oset @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(1047,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ ( hAPP @ ( c_Relation_Oconverse @ D @ D ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__converseD) ).
thf(5564,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ ( hAPP @ ( c_Relation_Oconverse @ D @ D ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).
thf(1017,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SigmaD1) ).
thf(5441,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(483,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ G @ F @ E @ D ) @ ( c_Fun_Ofun__upd @ E @ G @ C @ B @ A ) )
= ( c_Fun_Ofun__upd @ E @ F @ ( hAPP @ ( c_Fun_Ocomp @ G @ F @ E @ D ) @ C ) @ B @ ( hAPP @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__comp) ).
thf(3323,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ G @ F @ E @ D ) @ ( c_Fun_Ofun__upd @ E @ G @ C @ B @ A ) )
= ( c_Fun_Ofun__upd @ E @ F @ ( hAPP @ ( c_Fun_Ocomp @ G @ F @ E @ D ) @ C ) @ B @ ( hAPP @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(452,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ C @ B @ B ) @ A ) @ ( c_Relation_OId @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_R__O__Id) ).
thf(3196,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ C @ B @ B ) @ A ) @ ( c_Relation_OId @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(929,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ G @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ E ) @ D ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ ( hAPP @ ( hAPP @ A @ E ) @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ G @ F ) @ B @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ G @ F @ B ) @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__imageI) ).
thf(5110,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ G @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ E ) @ D ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ ( hAPP @ ( hAPP @ A @ E ) @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ G @ F ) @ B @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ G @ F @ B ) @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(343,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Odrop @ tc_Nat_Onat ) @ C ) @ ( c_List_Oupt @ B @ A ) )
= ( c_List_Oupt @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__upt) ).
thf(2783,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Odrop @ tc_Nat_Onat ) @ C ) @ ( c_List_Oupt @ B @ A ) )
= ( c_List_Oupt @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(632,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ H @ H ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ H ) @ G ) @ F ) ) @ E ) )
=> ( ( D
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ H ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ H ) @ G ) @ B ) ) )
=> ( ( A
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ H ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ H ) @ F ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ H ) @ ( tc_List_Olist @ H ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ H ) @ ( tc_List_Olist @ H ) ) @ D ) @ A ) ) @ ( c_List_Olistrel1 @ H @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1I) ).
thf(3897,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ H @ H ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ H ) @ G ) @ F ) ) @ E ) )
=> ( ( D
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ H ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ H ) @ G ) @ B ) ) )
=> ( ( A
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ H ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ H ) @ F ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ H ) @ ( tc_List_Olist @ H ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ H ) @ ( tc_List_Olist @ H ) ) @ D ) @ A ) ) @ ( c_List_Olistrel1 @ H @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(794,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ H @ G @ F @ E ) @ D )
= ( hAPP @ ( c_Fun_Ocomp @ C @ G @ F @ B ) @ A ) )
=> ! [I: $i] :
( ( hAPP @ E @ ( hAPP @ D @ I ) )
= ( hAPP @ B @ ( hAPP @ A @ I ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__eq__elim) ).
thf(4565,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ H @ G @ F @ E ) @ D )
= ( hAPP @ ( c_Fun_Ocomp @ C @ G @ F @ B ) @ A ) )
=> ! [I: $i] :
( ( hAPP @ E @ ( hAPP @ D @ I ) )
= ( hAPP @ B @ ( hAPP @ A @ I ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(845,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oorder__refl) ).
thf(4777,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(978,axiom,
! [A: $i,B: $i] :
( ( c_Divides_Odivmod__nat @ B @ A )
= ( c_HOL_OThe @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Divides_Odivmod__nat__rel @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__def) ).
thf(5300,plain,
! [A: $i,B: $i] :
( ( c_Divides_Odivmod__nat @ B @ A )
= ( c_HOL_OThe @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Divides_Odivmod__nat__rel @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux1) ).
thf(1314,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[11]) ).
thf(940,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ D ) @ C ) ) @ ( c_Relation_OId__on @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__on__eqI) ).
thf(5159,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ D ) @ C ) ) @ ( c_Relation_OId__on @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__neg__neg__trivial) ).
thf(1495,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( 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)],[60]) ).
thf(1008,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ C ) ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) )
=> ( c_Wellfounded_Oacyclic @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclicI) ).
thf(5404,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ C ) ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) )
=> ( c_Wellfounded_Oacyclic @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zmult2__eq) ).
thf(1657,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(924,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ F @ E @ D @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph__imp__finite) ).
thf(5092,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ F @ E @ D @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(809,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leE) ).
thf(4631,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(445,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ A ) @ ( c_List_Olist_ONil @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct_Osimps_I1_J) ).
thf(3177,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ A ) @ ( c_List_Olist_ONil @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(1011,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_List_Olist__ex @ D @ C @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ C @ B ) )
| ( c_List_Olist__ex @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex__simps_I1_J) ).
thf(5413,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_List_Olist__ex @ D @ C @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ C @ B ) )
| ( c_List_Olist__ex @ D @ C @ A ) ) )
& ( ( ( hBOOL @ ( hAPP @ C @ B ) )
| ( c_List_Olist__ex @ D @ C @ A ) )
=> ( c_List_Olist__ex @ D @ C @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(1024,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__commute) ).
thf(5462,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(323,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self1__is__m) ).
thf(2704,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( 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)],[323]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ C ) @ B ) ) @ ( c_List_Olistrel @ D @ A ) ) )
=> ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__eq__len) ).
thf(1288,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ C ) @ B ) ) @ ( c_List_Olistrel @ D @ A ) ) )
=> ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(114,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) ) )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__eq__0__iff) ).
thf(1710,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) ) )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ B ) ) ) ) )
& ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) ) )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ B ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( 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)],[114]) ).
thf(869,axiom,
! [A: $i,B: $i] :
( ( c_Equiv__Relations_Oequivp @ B @ A )
=> ~ ( ( c_Predicate_Oreflp @ B @ A )
=> ( ( c_Predicate_Osymp @ B @ A )
=> ~ ( c_Predicate_Otransp @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivpE) ).
thf(4865,plain,
! [A: $i,B: $i] :
( ( c_Equiv__Relations_Oequivp @ B @ A )
=> ~ ( ( c_Predicate_Oreflp @ B @ A )
=> ( ( c_Predicate_Osymp @ B @ A )
=> ~ ( c_Predicate_Otransp @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(762,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ ( c_List_Oinsert @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__insert) ).
thf(4442,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ ( c_List_Oinsert @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(1068,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ E @ D @ C ) @ B ) @ A )
= ( c_HOL_OThe @ D @ ( c_Finite__Set_Ofold__graph @ E @ D @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__def) ).
thf(5642,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ E @ D @ C ) @ B ) @ A )
= ( c_HOL_OThe @ D @ ( c_Finite__Set_Ofold__graph @ E @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).
thf(510,axiom,
! [A: $i,B: $i] :
( ( c_List_Osublist @ B @ ( c_List_Olist_ONil @ B ) @ A )
= ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sublist__nil) ).
thf(3424,plain,
! [A: $i,B: $i] :
( ( c_List_Osublist @ B @ ( c_List_Olist_ONil @ B ) @ A )
= ( c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(878,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ B ) @ A ) ) @ ( c_Relation_OId @ C ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__in__Id__conv) ).
thf(4912,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ B ) @ A ) ) @ ( c_Relation_OId @ C ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ B ) @ A ) ) @ ( c_Relation_OId @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(196,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ B ) ) )
=> ( C
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_impossible__Cons) ).
thf(2063,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ B ) ) )
=> ( C
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(89,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__linear) ).
thf(1610,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(1215,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertI1) ).
thf(6269,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1215]) ).
thf(1265,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fdisj__1) ).
thf(6503,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1265]) ).
thf(462,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono1) ).
thf(3244,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[462]) ).
thf(227,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( 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 @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_split__div) ).
thf(2159,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( 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 @ ( 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 @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(137,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_n__less__n__mult__m) ).
thf(1827,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[137]) ).
thf(394,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ ( tc_prod @ J @ I ) @ ( tc_prod @ H @ G ) @ ( tc_prod @ F @ E ) @ ( c_Product__Type_Omap__pair @ J @ H @ I @ G @ D @ C ) ) @ ( c_Product__Type_Omap__pair @ F @ J @ E @ I @ B @ A ) )
= ( c_Product__Type_Omap__pair @ F @ H @ E @ G @ ( hAPP @ ( c_Fun_Ocomp @ J @ H @ F @ D ) @ B ) @ ( hAPP @ ( c_Fun_Ocomp @ I @ G @ E @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair_Ocomp) ).
thf(2966,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ ( tc_prod @ J @ I ) @ ( tc_prod @ H @ G ) @ ( tc_prod @ F @ E ) @ ( c_Product__Type_Omap__pair @ J @ H @ I @ G @ D @ C ) ) @ ( c_Product__Type_Omap__pair @ F @ J @ E @ I @ B @ A ) )
= ( c_Product__Type_Omap__pair @ F @ H @ E @ G @ ( hAPP @ ( c_Fun_Ocomp @ J @ H @ F @ D ) @ B ) @ ( hAPP @ ( c_Fun_Ocomp @ I @ G @ E @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(939,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ D @ D ) @ A ) @ A ) ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ A ) ) )
& ( C = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__same) ).
thf(5151,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ D @ D ) @ A ) @ A ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ A ) ) )
& ( C = B ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ A ) ) )
& ( C = B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ D @ D ) @ A ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(30,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_le__square) ).
thf(1384,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( 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)],[30]) ).
thf(679,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ C ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__diff__iff) ).
thf(4118,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(1052,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( c_List_OtakeWhile @ B @ D @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ C ) @ ( c_List_OtakeWhile @ B @ D @ A ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( c_List_OtakeWhile @ B @ D @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ C ) @ A ) )
= ( c_List_Olist_ONil @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile_Osimps_I2_J) ).
thf(5581,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( c_List_OtakeWhile @ B @ D @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ C ) @ ( c_List_OtakeWhile @ B @ D @ A ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( c_List_OtakeWhile @ B @ D @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ C ) @ A ) )
= ( c_List_Olist_ONil @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).
thf(522,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Owf @ D @ C )
=> ( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_Owf @ ( tc_prod @ D @ B ) @ ( c_Wellfounded_Olex__prod @ D @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__lex__prod) ).
thf(3489,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Owf @ D @ C )
=> ( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_Owf @ ( tc_prod @ D @ B ) @ ( c_Wellfounded_Olex__prod @ D @ B @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(751,axiom,
! [A: $i,B: $i] : ( c_List_Olistrelp @ B @ A @ ( c_List_Olist_ONil @ B ) @ ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrelp_ONil) ).
thf(4410,plain,
! [A: $i,B: $i] : ( c_List_Olistrelp @ B @ A @ ( c_List_Olist_ONil @ B ) @ ( c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(959,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image__simple @ H @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ A ) @ B ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ D @ A ) ) @ ( hAPP @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Oinsert) ).
thf(5236,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image__simple @ H @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ A ) @ B ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ D @ A ) ) @ ( hAPP @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(747,axiom,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
thf(4395,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(653,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Ozip @ C @ B ) @ A ) @ ( c_List_Olist_ONil @ B ) )
= ( c_List_Olist_ONil @ ( tc_prod @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip_Osimps_I1_J) ).
thf(4019,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Ozip @ C @ B ) @ A ) @ ( c_List_Olist_ONil @ B ) )
= ( c_List_Olist_ONil @ ( tc_prod @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(154,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__1__eq__mult__iff) ).
thf(1885,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)],[154]) ).
thf(1069,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__eq) ).
thf(5645,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ C @ B )
= A )
=> ? [D: $i] :
( C
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__eqD) ).
thf(1621,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ C @ B )
= A )
=> ? [D: $i] :
( C
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(163,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib2) ).
thf(1930,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)],[163]) ).
thf(1232,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Owellorder @ C )
=> ( ( hBOOL @ ( hAPP @ B @ A ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Orderings_Oord__class_OLeast @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_LeastI) ).
thf(6351,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Owellorder @ C )
=> ( ( hBOOL @ ( hAPP @ B @ A ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Orderings_Oord__class_OLeast @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1232]) ).
thf(287,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ C ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ C ) ) )
<=> ! [D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ E ) @ C ) )
& ( A
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__pos__lemma) ).
thf(2502,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ C ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ C ) ) )
=> ! [D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ E ) @ C ) )
& ( A
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ E ) ) ) )
& ( ! [D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ E ) @ C ) )
& ( A
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ C ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(238,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__neg__pos__less0) ).
thf(2241,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( 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)],[238]) ).
thf(1198,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
<=> ! [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ ( c_Wellfounded_Oacc @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__acc__iff) ).
thf(6190,plain,
! [A: $i,B: $i] :
( ( ( c_Wellfounded_Owf @ B @ A )
=> ! [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ ( c_Wellfounded_Oacc @ B @ A ) ) ) )
& ( ! [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ ( c_Wellfounded_Oacc @ B @ A ) ) )
=> ( c_Wellfounded_Owf @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198]) ).
thf(216,axiom,
hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
thf(2127,plain,
hBOOL @ ( hAPP @ ( 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)],[216]) ).
thf(953,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ c_Nat_OSuc @ B )
= ( hAPP @ c_Nat_OSuc @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Oinject) ).
thf(5204,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ B )
= ( hAPP @ c_Nat_OSuc @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ c_Nat_OSuc @ B )
= ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(138,axiom,
! [A: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__self) ).
thf(1829,plain,
! [A: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(1191,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fimplies__2) ).
thf(6155,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191]) ).
thf(359,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ D @ D ) @ ( hAPP @ ( hAPP @ ( c_Relation_Oinv__image @ C @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Relation_Oinv__image @ C @ D ) @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__inv__image) ).
thf(2847,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ D @ D ) @ ( hAPP @ ( hAPP @ ( c_Relation_Oinv__image @ C @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Relation_Oinv__image @ C @ D ) @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(915,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__imp__not__less) ).
thf(5061,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(1148,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_r__into__rtrancl) ).
thf(5975,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).
thf(1202,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Typedef_Otype__definition @ G @ F @ E @ D @ C )
=> ( ( ( hAPP @ E @ B )
= ( hAPP @ E @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_ORep__inject) ).
thf(6205,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Typedef_Otype__definition @ G @ F @ E @ D @ C )
=> ( ( ( ( hAPP @ E @ B )
= ( hAPP @ E @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ E @ B )
= ( hAPP @ E @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1202]) ).
thf(893,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Transitive__Closure_Otrancl__into__trancl) ).
thf(4987,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(308,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Int_Oint ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ tc_Int_Oint @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__greaterThanAtMost__int) ).
thf(2583,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Int_Oint ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(664,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_le__diff__conv) ).
thf(4066,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( 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 @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(1099,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__Suc__Cons) ).
thf(5768,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).
thf(708,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).
thf(4229,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( 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)],[708]) ).
thf(318,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ C ) @ B ) ) @ B ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ C @ B ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zmod__equality2) ).
thf(2687,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ C ) @ B ) ) @ B ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ C @ B ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(587,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ C ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) @ D ) ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel__mult1__eq) ).
thf(3740,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ C ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) @ D ) ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(420,axiom,
! [A: $i] : ( class_Nat_Osize @ ( tc_List_Olist @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_List__Olist__Nat_Osize) ).
thf(3076,plain,
! [A: $i] : ( class_Nat_Osize @ ( tc_List_Olist @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(665,axiom,
( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_One__nat__def) ).
thf(4071,plain,
( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(157,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 @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ C ) @ F ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ E ) @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__lemma) ).
thf(1902,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 @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ C ) @ F ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ E ) @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(1000,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_List_Omember @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ C ) @ B ) ) @ A ) )
<=> ( ( C = A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_List_Omember @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_member__rec_I1_J) ).
thf(5376,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_List_Omember @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ C ) @ B ) ) @ A ) )
=> ( ( C = A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_List_Omember @ D ) @ B ) @ A ) ) ) )
& ( ( ( C = A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_List_Omember @ D ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_List_Omember @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ C ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(501,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Oacyclic @ B @ A )
=> ( c_Relation_Oantisym @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclic__impl__antisym__rtrancl) ).
thf(3394,plain,
! [A: $i,B: $i] :
( ( c_Wellfounded_Oacyclic @ B @ A )
=> ( c_Relation_Oantisym @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(990,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_Oconverse @ D @ E ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ E ) @ B ) @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__iff) ).
thf(5344,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_Oconverse @ D @ E ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ E ) @ B ) @ C ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ E ) @ B ) @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_Oconverse @ D @ E ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(219,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ E ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ E ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma__neg) ).
thf(2138,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ E ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ E ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(633,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ F ) @ E ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ D ) @ ( c_List_Olist_ONil @ F ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ F ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ B ) @ ( c_List_Olist_ONil @ F ) ) ) ) ) @ ( c_List_Olistrel1 @ F @ A ) ) )
<=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) @ E ) @ C ) ) @ ( c_List_Olistrel1 @ F @ A ) ) )
& ( D = B ) )
| ( ( E = C )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ D ) @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_snoc__listrel1__snoc__iff) ).
thf(3901,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ F ) @ E ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ D ) @ ( c_List_Olist_ONil @ F ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ F ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ B ) @ ( c_List_Olist_ONil @ F ) ) ) ) ) @ ( c_List_Olistrel1 @ F @ A ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) @ E ) @ C ) ) @ ( c_List_Olistrel1 @ F @ A ) ) )
& ( D = B ) )
| ( ( E = C )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ D ) @ B ) ) @ A ) ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) @ E ) @ C ) ) @ ( c_List_Olistrel1 @ F @ A ) ) )
& ( D = B ) )
| ( ( E = C )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ D ) @ B ) ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ F ) @ E ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ D ) @ ( c_List_Olist_ONil @ F ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ F ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ B ) @ ( c_List_Olist_ONil @ F ) ) ) ) ) @ ( c_List_Olistrel1 @ F @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(816,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_List_Olist @ D ) @ ( c_List_Olistrel1 @ D @ A ) ) ) )
=> ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__listrel1__eq__len) ).
thf(4655,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_List_Olist @ D ) @ ( c_List_Olistrel1 @ D @ A ) ) ) )
=> ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(846,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__antisym) ).
thf(4779,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(920,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ H @ G ) ) @ F ) @ ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ E @ D ) @ ( tc_prod @ H @ G ) @ ( c_Product__Type_Omap__pair @ E @ H @ D @ G @ C @ B ) ) @ A ) ) )
=> ~ ! [I: $i,J: $i] :
( ( F
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ ( hAPP @ C @ I ) ) @ ( hAPP @ B @ J ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ I ) @ J ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_prod__fun__imageE) ).
thf(5073,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ H @ G ) ) @ F ) @ ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ E @ D ) @ ( tc_prod @ H @ G ) @ ( c_Product__Type_Omap__pair @ E @ H @ D @ G @ C @ B ) ) @ A ) ) )
=> ~ ! [I: $i,J: $i] :
( ( F
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ ( hAPP @ C @ I ) ) @ ( hAPP @ B @ J ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ I ) @ J ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(885,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Wellfounded_Oacc @ D @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ A ) @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( c_Wellfounded_Oacc @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__downward) ).
thf(4949,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Wellfounded_Oacc @ D @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ A ) @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( c_Wellfounded_Oacc @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(185,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__is__0) ).
thf(2018,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)],[185]) ).
thf(195,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A ) ) @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__nonzero) ).
thf(2059,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)],[195]) ).
thf(1172,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Owellorder @ B )
=> ( ? [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) )
=> ( hBOOL @ ( hAPP @ A @ ( c_Orderings_Oord__class_OLeast @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_LeastI__ex) ).
thf(6072,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Owellorder @ B )
=> ( ? [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) )
=> ( hBOOL @ ( hAPP @ A @ ( c_Orderings_Oord__class_OLeast @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).
thf(755,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ ( hAPP @ ( c_Fun_Ocomp @ D @ E @ F @ C ) @ B ) @ A )
=> ( c_Fun_Oinj__on @ D @ E @ C @ ( hAPP @ ( c_Set_Oimage @ F @ D @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__imageI) ).
thf(4423,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Oinj__on @ F @ E @ ( hAPP @ ( c_Fun_Ocomp @ D @ E @ F @ C ) @ B ) @ A )
=> ( c_Fun_Oinj__on @ D @ E @ C @ ( hAPP @ ( c_Set_Oimage @ F @ D @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult2__eq) ).
thf(1449,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(203,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_List_Olist__all @ C @ B @ A )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all__length) ).
thf(2087,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_List_Olist__all @ C @ B @ A )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ A ) @ D ) ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ A ) @ D ) ) ) )
=> ( c_List_Olist__all @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(867,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__imp__neq) ).
thf(4858,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Omap @ G @ F ) @ E ) @ D )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ F ) @ B ) @ A ) )
=> ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ G ) ) @ D )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__eq__imp__length__eq) ).
thf(1417,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Omap @ G @ F ) @ E ) @ D )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ F ) @ B ) @ A ) )
=> ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ G ) ) @ D )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(534,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add1) ).
thf(3528,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( 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)],[534]) ).
thf(859,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_OCollect @ B ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__def) ).
thf(4826,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_OCollect @ B ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ C ) @ B ) ) ) @ ( c_List_Olexord @ F @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ E ) @ C ) ) @ A ) )
| ( ( E = C )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) @ D ) @ B ) ) @ ( c_List_Olexord @ F @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__cons__cons) ).
thf(1320,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ C ) @ B ) ) ) @ ( c_List_Olexord @ F @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ E ) @ C ) ) @ A ) )
| ( ( E = C )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) @ D ) @ B ) ) @ ( c_List_Olexord @ F @ A ) ) ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ E ) @ C ) ) @ A ) )
| ( ( E = C )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) @ D ) @ B ) ) @ ( c_List_Olexord @ F @ A ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ F ) @ ( tc_List_Olist @ F ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ C ) @ B ) ) ) @ ( c_List_Olexord @ F @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1134,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( c_Wellfounded_Oacc @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__wfD) ).
thf(5913,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( c_Wellfounded_Oacc @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).
thf(168,axiom,
! [A: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zero) ).
thf(1944,plain,
! [A: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__neg) ).
thf(1367,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(1039,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) ) )
<=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
& ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct_Osimps_I2_J) ).
thf(5542,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
& ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ A ) ) ) )
& ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
& ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).
thf(261,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ C ) @ B ) ) @ ( c_List_Olistrel @ D @ A ) ) )
<=> ( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ B ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ E ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ C ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ B ) @ E ) ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__iff__nth) ).
thf(2321,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ C ) @ B ) ) @ ( c_List_Olistrel @ D @ A ) ) )
=> ( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ B ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ E ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ C ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ B ) @ E ) ) ) @ A ) ) ) ) )
& ( ( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ B ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ E ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ C ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ B ) @ E ) ) ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ C ) @ B ) ) @ ( c_List_Olistrel @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(813,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ? [C: $i] :
( A
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
thf(4642,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ? [C: $i] :
( A
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) ) ) )
& ( ? [C: $i] :
( A
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(303,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_List_Ofoldl @ F @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ B ) @ A ) )
= ( hAPP @ ( c_List_Ofoldl @ F @ E @ D @ ( hAPP @ ( hAPP @ D @ C ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldl__Cons) ).
thf(2563,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_List_Ofoldl @ F @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ B ) @ A ) )
= ( hAPP @ ( c_List_Ofoldl @ F @ E @ D @ ( hAPP @ ( hAPP @ D @ C ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(981,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Equiv__Relations_Ocongruent @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ B ) @ A ) ) @ D ) )
=> ( ( hAPP @ C @ B )
= ( hAPP @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_congruentD) ).
thf(5307,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Equiv__Relations_Ocongruent @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ B ) @ A ) ) @ D ) )
=> ( ( hAPP @ C @ B )
= ( hAPP @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(561,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ C ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ C ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ B ) @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__add) ).
thf(3626,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ C ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ C ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ B ) @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(455,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ ( c_Relation_OId__on @ B @ A ) )
= ( c_Relation_OId__on @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__Id__on) ).
thf(3212,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ ( c_Relation_OId__on @ B @ A ) )
= ( c_Relation_OId__on @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(479,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ B ) ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).
thf(3299,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ B ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(1022,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ ( c_Wellfounded_Oacc @ D @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Wellfounded_Oacc @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__downwards__aux) ).
thf(5458,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ ( c_Wellfounded_Oacc @ D @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Wellfounded_Oacc @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(1106,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_Relation_ORange @ B @ D ) @ A ) ) )
=> ~ ! [E: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ D ) @ E ) @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeE) ).
thf(5789,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_Relation_ORange @ B @ D ) @ A ) ) )
=> ~ ! [E: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ D ) @ E ) @ C ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).
thf(848,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__trancl__trancl) ).
thf(4784,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(319,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__cancel1) ).
thf(2690,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(1188,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ E @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ B @ A @ E ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep_Ointros) ).
thf(6145,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ E @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ B @ A @ E ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188]) ).
thf(405,axiom,
! [A: $i,B: $i] :
( ( ( c_List_Olist_ONil @ B )
= ( c_List_Oremdups @ B @ A ) )
<=> ( A
= ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remdups__eq__nil__right__iff) ).
thf(2998,plain,
! [A: $i,B: $i] :
( ( ( ( c_List_Olist_ONil @ B )
= ( c_List_Oremdups @ B @ A ) )
=> ( A
= ( c_List_Olist_ONil @ B ) ) )
& ( ( A
= ( c_List_Olist_ONil @ B ) )
=> ( ( c_List_Olist_ONil @ B )
= ( c_List_Oremdups @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult1__eq) ).
thf(1565,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(1015,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ A @ E ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ B ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__SigmaI) ).
thf(5436,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ A @ E ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ B ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).
thf(788,axiom,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
thf(4547,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(273,axiom,
! [A: $i] :
( ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__is__id) ).
thf(2436,plain,
! [A: $i] :
( ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(237,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ E ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ E ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ ( tc_prod @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ D @ B ) @ C ) @ A ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ C ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_List_Onth @ B ) @ A ) @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__zip) ).
thf(2238,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ E ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ E ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ ( tc_prod @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ D @ B ) @ C ) @ A ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ C ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_List_Onth @ B ) @ A ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__commute) ).
thf(1490,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)],[58]) ).
thf(965,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C ) ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ F @ E ) @ B ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ D ) @ ( hAPP @ ( c_List_Oset @ F ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__zip__leftD) ).
thf(5255,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C ) ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ F @ E ) @ B ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ D ) @ ( hAPP @ ( c_List_Oset @ F ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(1019,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ B ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ D ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ C ) @ ( hAPP @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__Sigma__iff) ).
thf(5445,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ D ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ C ) @ ( hAPP @ A @ D ) ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ D ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ C ) @ ( hAPP @ A @ D ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).
thf(660,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ C ) @ ( hAPP @ ( c_List_Omap @ E @ D ) @ B ) ) @ ( hAPP @ ( c_List_Omap @ C @ E ) @ A ) )
= ( hAPP @ ( c_List_Omap @ C @ D ) @ ( hAPP @ ( c_Fun_Ocomp @ E @ D @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_List_Omap_Ocomp) ).
thf(4056,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ C ) @ ( hAPP @ ( c_List_Omap @ E @ D ) @ B ) ) @ ( hAPP @ ( c_List_Omap @ C @ E ) @ A ) )
= ( hAPP @ ( c_List_Omap @ C @ D ) @ ( hAPP @ ( c_Fun_Ocomp @ E @ D @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(417,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) )
<=> ( ( ( hBOOL @ ( hAPP @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split) ).
thf(3052,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( 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 @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(1245,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Equiv__Relations_Oequivp @ C @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__reflp) ).
thf(6404,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Equiv__Relations_Oequivp @ C @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1245]) ).
thf(482,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ A ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ D ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ A ) )
=> ( B
!= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ E ) @ D ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ C )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_aset_I3_J) ).
thf(3316,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ A ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ D ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ A ) )
=> ( B
!= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ E ) @ D ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ C )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(1186,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ~ ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__1) ).
thf(6141,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ~ ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186]) ).
thf(1089,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__reduce) ).
thf(5732,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).
thf(400,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ E @ D @ C @ B @ A ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__same) ).
thf(2980,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ E @ D @ C @ B @ A ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(547,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ B ) @ A ) )
<=> ? [F: $i] :
( ( ( D
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ B ) @ F ) )
& ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ F ) @ C )
= A ) )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ D ) @ F )
= B )
& ( C
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ F ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__eq__append__conv2) ).
thf(3575,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ B ) @ A ) )
=> ? [F: $i] :
( ( ( D
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ B ) @ F ) )
& ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ F ) @ C )
= A ) )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ D ) @ F )
= B )
& ( C
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ F ) @ A ) ) ) ) )
& ( ? [F: $i] :
( ( ( D
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ B ) @ F ) )
& ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ F ) @ C )
= A ) )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ D ) @ F )
= B )
& ( C
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ F ) @ A ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(8114,plain,
$false,
inference(e,[status(thm)],[5385,4188,1501,4560,2094,5561,2295,6530,2072,2412,6431,6074,6014,2744,1369,2109,5593,2031,3399,1995,2263,4899,1559,4729,4022,1729,2921,4290,3698,5390,6285,3566,5028,5131,1549,6057,6022,6162,3813,3549,5878,2099,2837,4614,6017,5614,6480,4479,1855,2077,4043,3534,2976,4376,2940,1406,2104,5168,4226,4500,4075,1882,4311,3762,1443,3417,5242,3285,3460,2947,1939,4807,1544,2676,6338,5982,5265,4215,5529,4973,4408,6031,4532,4105,6505,3745,4575,5755,4097,4026,2316,5316,5701,3781,3693,5163,4980,5192,3276,1705,3017,5967,5550,1426,3530,6391,1608,4403,3365,2740,4110,4220,5257,2434,1872,1342,4294,2901,3313,5636,2844,3629,5740,3502,3088,6009,5903,2067,1482,4386,3335,6138,1746,3103,6236,1835,2972,5252,5977,1914,5393,2763,5486,1782,2985,5123,3249,1441,6381,2010,4803,4124,3730,5723,5056,1386,3281,4322,2819,5750,1518,1703,5024,5352,4637,4539,4151,3495,6423,3821,2501,1330,3148,3485,3776,2682,3410,1832,3803,4428,5765,3263,4439,3976,2916,4524,2814,4563,1985,1660,5883,1760,3131,6274,4692,3689,3542,6315,4349,5182,5640,5712,6519,1992,5289,5231,6253,3638,2049,6149,1741,5746,4265,6025,5077,5617,4967,5792,2713,3517,5355,3385,4353,5866,4862,4617,5521,5199,4179,5193,6379,4492,4928,5925,4270,4551,1568,5829,2520,4383,2301,2007,5787,6002,5013,4258,1632,4001,5333,2236,6410,4724,1978,3290,6157,3152,5259,3851,5834,6259,5957,1415,5433,5892,2794,3887,3966,3199,6227,1911,4600,6135,1682,5680,1858,6300,4050,3438,6187,5650,2254,1677,2034,6559,6451,3068,4033,3505,5846,1345,5489,2750,3226,3184,3378,5045,5572,3537,5773,5096,3421,1447,5370,4364,6347,4040,2809,2804,5665,5629,4519,1600,4707,4379,1697,3559,3606,2154,6103,1521,5328,4628,2718,5970,2205,1975,4082,3229,3011,6020,5070,5291,2737,4910,4059,5298,1863,6282,1651,5174,3097,5783,3591,2574,1438,3635,5443,6250,4557,2047,5117,1311,3767,4172,2000,4925,6092,3795,3037,6200,2673,1900,6343,2541,2147,3610,3154,1619,3514,4466,5611,6079,3827,6122,2428,2249,3603,3867,5002,1355,2277,5794,4434,4878,5579,4989,5349,1751,5815,3742,6565,2969,5366,3752,4521,5470,2937,4204,3884,6496,5507,4821,5396,4661,2528,3778,2015,3810,2477,3403,5690,3600,3894,6143,1291,5330,2958,1423,3271,3958,2445,4280,2873,5492,3269,3618,5655,4140,5465,4608,2332,6043,4757,3750,5177,3556,5021,5460,5038,4746,5566,6060,6168,5658,3050,2313,5858,1634,1392,3784,5714,5270,4544,1498,4845,3963,5687,3440,1402,6215,1350,1936,2498,3615,1541,2157,5609,3482,5053,5145,2100,3413,1794,5673,5006,5423,1804,2895,4248,6195,6028,2724,2858,3632,4095,3119,4840,3078,3916,3237,1397,4263,4676,1493,5031,1361,1942,3179,5915,5743,5337,5588,2038,6539,4444,6271,3935,3141,4951,2877,3326,5166,2561,6116,3094,4167,1739,4425,2868,3596,4421,2455,4750,4744,1700,6164,6256,1810,1612,2978,4621,6097,5374,3787,2598,3354,5134,2581,4829,1947,1852,1429,2272,4223,5063,5947,1776,5273,3656,3654,1588,2536,3126,5900,3770,6433,2243,6475,5973,4482,2566,5058,4717,1874,5823,5305,2052,2697,3109,5026,3005,2140,4086,6224,1627,3215,1333,3834,5310,4782,3173,1846,5964,3508,2423,4572,5170,4163,3454,4148,5112,5557,4184,2702,2546,1779,5402,3279,4212,3999,2963,5737,1663,3190,2189,6400,3841,5295,4004,4308,1510,2556,2585,5278,3491,4412,1927,5048,6243,3686,3343,2121,2144,6368,1648,5483,4919,4131,5524,4470,1754,2904,1680,2149,5762,3257,5451,3738,2028,4340,3375,1595,3523,4503,4577,6546,3274,3696,4489,3396,4453,5400,4786,3372,6493,5067,3736,5984,4328,2716,6407,4946,1488,2827,3387,3187,4268,5933,2727,4283,1389,6510,2791,2525,5065,3266,2514,5099,5876,2991,4485,2308,6532,4218,6302,3487,3700,3641,6248,6549,3091,6372,2319,5634,4537,1503,4978,3773,3651,4099,3340,3594,5148,4764,3123,2442,2753,3532,6048,5407,3500,3182,4388,2721,2119,4337,2679,4704,3996,2538,1408,5671,1282,2084,5244,3764,1894,2415,5103,5325,3551,4305,6147,6217,3287,1524,5303,5827,2097,5853,2257,1933,2955,2246,3106,5880,4805,5222,4073,5531,1571,1376,4107,1969,5267,1307,5552,5035,4009,2111,2780,4277,4181,6414,4296,2289,2553,1381,2842,1688,4541,2742,5920,1339,3027,5730,3668,4833,5082,4569,4064,4818,5439,1731,3800,6353,3932,4897,4985,5599,5286,3034,1838,5318,4652,5885,3971,2461,2974,5410,2710,4554,4232,5094,1643,6288,3159,2931,2797,1364,6293,5139,6212,2770,2075,2418,4832,4720,1841,2439,5931,6377,3759,3838,6394,1445,3363,5849,5667,4196,2303,4209,4158,3380,1562,3881,3009,5548,4741,2952,4456,4529,4292,2927,4113,1958,4355,3292,4722,1551,3849,3031,4690,1304,5890,3193,3427,4901,2107,4260,4813,4580,2471,5785,3161,1905,1420,3981,6088,2124,2234,4319,1990,5678,2684,6132,3571,3112,4673,3129,2407,2888,6012,4658,2942,3988,4255,5570,1547,2298,3391,5624,5229,2863,1598,4937,5388,5871,4272,1400,4366,1605,3260,2588,4922,5748,4534,3659,2821,3209,3608,2850,2882,5018,5955,4314,6280,3305,2700,5015,6421,1785,6513,3823,2468,3715,3246,4437,4398,4092,5420,6036,1813,1452,3554,6093,5555,1869,6125,2128,5995,1317,1763,6436,3847,4800,4982,3623,1285,3853,1336,4875,5949,1766,1849,5675,3415,6333,4611,6526,4431,3943,5717,6358,5841,3684,1404,1358,4133,1536,2543,5240,1353,4748,1955,1485,1972,5453,1749,5809,4143,3224,1585,2511,4634,5226,1797,3024,2860,5364,3961,5472,3071,2807,4795,3520,5596,3946,3620,2458,6425,4325,4770,2885,6041,4419,3447,1654,2490,5860,2775,3665,3797,2875,5771,3168,4639,2760,2013,2924,4138,3457,1649,2870,4165,2310,1844,3874,2215,4738,5115,3725,5907,2305,2919,4170,6543,4463,1734,1807,4061,5184,2907,4121,2283,6341,2855,3383,3369,2811,5368,3748,2431,5087,4881,2934,3085,2591,1590,1646,5632,3613,2707,4710,2988,3864,2251,3825,4666,2135,5008,4089,4468,6567,4681,5800,3662,2416,6516,2081,4649,6397,3879,2198,6412,6277,3793,5211,4869,6499,4619,6198,2421,2447,2944,4855,2786,2041,6181,3844,3430,5781,4774,1294,5040,3351,1513,5517,2230,2036,1309,6444,5196,5357,2517,5728,3232,6439,2983,3733,4596,4843,4357,5247,1908,2142,2930,2218,2258,5051,2102,4816,6055,4472,4687,4670,3511,5606,6563,2233,6361,1395,1625,6050,2522,3100,3790,1527,6490,5527,5559,3015,1436,5990,4007,2572,5564,5441,3323,3196,5110,2783,3897,4565,4777,5300,1314,5159,1495,5404,1657,5092,4631,3177,5413,5462,2704,1288,1710,4865,4442,5642,3424,4912,2063,1610,6269,6503,3244,2159,1827,2966,5151,1384,4118,5581,3489,4410,5236,4395,4019,1885,5645,1621,1930,6351,2502,2241,6190,2127,5204,1829,6155,2847,5061,5975,6205,4987,2583,4066,5768,4229,2687,3740,3076,4071,1902,5376,3394,5344,2138,3901,4655,4779,5073,4949,2018,2059,6072,4423,1449,2087,4858,1417,3528,4826,1320,5913,1944,1367,5542,2321,4642,2563,5307,3626,3212,3299,5458,5789,4784,2690,6145,2998,1565,5436,4547,2436,2238,1490,5255,5445,4056,3052,6404,3316,6141,5732,2980,3575]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW298+1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n025.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 22:30:19 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.91/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.85/1.34 % [INFO] Parsing done (511ms).
% 2.85/1.35 % [INFO] Running in sequential loop mode.
% 3.29/1.55 % [INFO] eprover registered as external prover.
% 3.29/1.55 % [INFO] cvc4 registered as external prover.
% 3.29/1.55 % [INFO] Scanning for conjecture ...
% 4.76/1.93 % [INFO] Found a conjecture and 5224 axioms. Running axiom selection ...
% 7.32/2.98 % [INFO] Axiom selection finished. Selected 1279 axioms (removed 3945 axioms).
% 8.99/3.53 % [INFO] Problem is first-order (TPTP FOF).
% 8.99/3.57 % [INFO] Type checking passed.
% 8.99/3.58 % [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 ...
% 40.13/11.35 % External prover 'e' found a proof!
% 40.13/11.35 % [INFO] Killing All external provers ...
% 40.13/11.35 % Time passed: 10840ms (effective reasoning time: 9994ms)
% 40.13/11.35 % 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)>
% 40.13/11.36 % Axioms used in derivation (1279): fact_wf__not__refl, fact_atLeastLessThan__upt, fact_divmod__nat__zero, fact_insertCI, fact_card__image__le, fact_le__imp__diff__is__add, fact_divmod__nat__rel__mult1__eq, fact_wf, fact_wf__not__sym, fact_refl__onD2, fact_wf__inv__image, fact_drop__butlast, fact_diff__0__eq__0, fact_zle__refl, fact_Nat_Oadd__0__right, fact_remdups_Osimps_I1_J, fact_converseI, fact_dvd_Oord__less__eq__trans, fact_le__SucI, fact_notin__set__remove1, fact_drop__Cons__number__of, fact_finite__greaterThanLessThan__int, fact_single__valued__Id__on, fact_nat__gcd_Opinduct, fact_divmod__nat__rel__divmod__nat, fact_append__Nil2, fact_divmod__nat__base, fact_nth__Cons__0, fact_nat_Osimps_I3_J, fact_ImageE, fact_dvd_Oless__trans, fact_length__filter__less, fact_lessThan__Suc__atMost, fact_sequence__trans, fact_converse__converse, fact_card__atLeastAtMost, fact_dropWhile_Osimps_I2_J, fact_zdvd__zmod, fact_pos__union__def, fact_sym__conv__converse__eq, fact_fold1Set_Ointros, fact_incr__mult__lemma, fact_in__set__conv__decomp, fact_q__pos__lemma, fact_length__0__conv, fact_finite__greaterThanAtMost, fact_pair__lessI2, fact_listrel1E, fact_image__insert, fact_diff__add__inverse, fact_part__equivp__transp, fact_take__drop, fact_zdvd__antisym__nonneg, fact_le__eq__less__or__eq, fact_nat__less__cases, fact_termination__basic__simps_I5_J, fact_odd__nonzero, fact_map_Osimps_I1_J, fact_trans__less__add1, fact_folding__image__simple__idem_Oin__idem, fact_comp__inj__on__iff, fact_accp_Oequations, fact_notin__set__sublistI, fact_lexord__append__leftI, fact_list__eq__iff__nth__eq, fact_nat__add__left__commute, fact_dvd_Oeq__iff, fact_nth__upt, fact_zdiv__eq__0__iff, fact_zdvd__not__zless, fact_insert__iff, fact_zip__append1, fact_atLeast__upt, fact_mod__mult2__eq, fact_drop__upt, fact_one__is__add, fact_diff__le__mono2, arity_prod__Enum_Oenum, fact_listrel__Cons1, fact_zip__Nil, fact_dvd_Oorder__trans, fact_zdiff__zmod__right, fact_equivI, fact_conversep_Oequations, fact_rtranclD, fact_less__imp__le__nat, fact_drop__eq__Nil, fact_pred__nat__trancl__eq__le, fact_le__imp__0__less, fact_add__leD1, fact_equivp__reflp__symp__transp, fact_dvd_Oless__asym_H, fact_divmod__nat__eq, fact_add__less__mono, fact_zadd__commute, fact_mult__0, fact_in__listrel1__converse, fact_zip__Cons__Cons, fact_pair__box_Oinject, fact_n__less__m__mult__n, fact_Transitive__Closure_Otrancl__into__trancl, fact_fun__left__comm_Ofold__equality, fact_Suc__times__mod__eq, fact_prod_Orecs, fact_mod__eq, fact_Suc__mono, fact_distinct__remdups, fact_self__append__conv, fact_O__assoc, fact_less__nat__zero__code, fact_trancl__id, fact_List_Omap_Ocompositionality, fact_nat_Osize_I4_J, fact_equivp__transp, fact_IdI, fact_List_Omap_Ocomp, fact_diff__Suc__less, fact_insertI1, fact_comm__monoid__big_Oinfinite, fact_folding__image__simple_Oeq__fold__g, fact_rtrancl_Ortrancl__refl, fact_diff__diff__cancel, fact_nat__add__right__cancel, fact_aset_I3_J, fact_gr0__conv__Suc, fact_o__eq__elim, fact_listrelp_Oequations_I2_J, fact_zdvd__mult__cancel, fact_take__upt, fact_CollectI, fact_Suc__le__mono, fact_dvd_Oless__imp__not__less, fact_div__mod__equality_H, fact_List_Omember__def, fact_div__nonpos__pos__le0, fact_dropWhile__eq__drop, fact_map__butlast, fact_equiv__def, fact_zero__less__diff, fact_remove1_Osimps_I1_J, fact_acc_Osimps, fact_zmult2__lemma__aux4, fact_inj__on__the__inv__into, fact_div__le__dividend, fact_takeWhile__eq__all__conv, fact_mod__pos__pos__trivial, fact_dvd_Oord__eq__less__trans, fact_SigmaE2, fact_trans__Id__on, fact_mult__le__mono2, help_c__fconj__3, fact_zmod__zdiv__equality, fact_Suc__diff__diff, fact_rel__compI, fact_filter__empty__conv, fact_distinct__zipI2, fact_length__takeWhile__less__P__nth, fact_zle__linear, fact_zmult__div__cancel, fact_comp__inj__on, fact_aset_I10_J, fact_List_Oset__insert, fact_Cons__acc__listrel1I, fact_nat__add__left__cancel__less, fact_int__0__less__1, fact_nth__Cons__Suc, fact_rtrancl__listrel1__if__listrel, fact_o__apply, fact_dropWhile__eq__Cons__conv, fact_mod__mult__distrib2, fact_r__into__trancl_H, fact_Bex__set__list__ex, fact_mod__less, fact_atLeastPlusOneLessThan__greaterThanLessThan__int, help_c__fequal__2, fact_mult__eq__self__implies__10, fact_acyclic__impl__antisym__rtrancl, fact_le__neq__implies__less, fact_tranclD2, fact_wf__less, fact_divmod__nat__rel__unique, fact_expand__Suc, fact_dvd__diffD, fact_list__all__iff, fact_append__eq__conv__conj, fact_neg__single__def, help_c__fFalse__1, fact_remdups__filter, fact_listsp_Oequations_I2_J, fact_aset_I6_J, fact_nat__mod__eq__lemma, fact_take__Suc__conv__app__nth, fact_rtrancl__converse, fact_finite__SigmaI, fact_div__if, fact_Divides_Omod__div__equality_H, fact_zadd__left__mono, fact_fun__left__comm_Ofun__left__comm, fact_distinct_Osimps_I2_J, fact_acyclic__converse, fact_nth__map, fact_finite__atLeastZeroLessThan__int, fact_inj__on__imageI2, fact_zdiv__zero, fact_acc_OaccI, 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fact_list__all__simps_I1_J, fact_diff__add__0, fact_in__set__insert, fact_Zero__neq__Suc, fact_drop__Nil, fact_congruentD, fact_diff__cancel2, fact_takeWhile__append2, fact_CollectD, fact_nat__less__add__iff2, fact_Pair__eq, fact_Suc__eq__plus1, fact_diff__self__eq__0, fact_in__set__conv__decomp__last, fact_image__iff, fact_rtrancl_Ortrancl__into__rtrancl, fact_map__map, fact_sublist__upt__eq__take, fact_Divides_Otransfer__nat__int__function__closures_I1_J, fact_self__quotient__aux2, fact_refl__on__converse, fact_distinct__filter, fact_split__conv, fact_listrelp_OCons, fact_congruent2D, fact_nat__mult__div__cancel1, fact_the__inv__into__onto, fact_splitD, fact_Suc__diff__le, fact_IdE, fact_atLeastAtMost__upt, fact_split__weak__cong, fact_listrel1I1, fact_zmult2__lemma__aux1, fact_distinct__conv__nth, fact_le0, fact_zmult__zless__mono2, fact_Suc__pred, fact_plus__numeral__code_I9_J, fact_finite_OinsertI, fact_nat__mult__eq__1__iff, fact_not__less__eq__eq, fact_n__less__n__mult__m, fact_less__not__refl, fact_append__in__listsp__conv, fact_ord_OgreaterThanAtMost__iff, fact_zmod__zmult2__eq, fact_drop__append, fact_fun__upd__def, fact_remdups__eq__nil__iff, fact_le__diff__conv2, fact_finite__lessThan, fact_ex__least__nat__less, fact_Domain__converse, fact_the__inv__into__f__eq, fact_card_Oeq__fold__g, fact_dvd_Oantisym, fact_f__the__inv__into__f, fact_le__trans, fact_all__code, fact_diff__Suc__diff__eq1, fact_wf__mlex, fact_equalityCE, fact_r__into__rtrancl, fact_nat__dvd__1__iff__1, fact_card__lessThan, fact_gr__implies__not0, fact_dvd_Ole__neq__trans, fact_fun__upd__twist, fact_conversep__conversep, fact_fun__left__comm_Ofold__graph__determ, help_c__COMBK__1, fact_le__mod__geq, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J, fact_listrel__sym, fact_rtrancl__into__trancl1, fact_dvd__antisym, fact_less__Suc__eq, fact_add__leE, fact_bset_I9_J, fact_fun__left__comm_Ofold__insert, fact_diff__Suc__1, fact_bset_I8_J, fact_Not__Domain__rtrancl, fact_greaterThanLessThan__upt, fact_rtrancl__idemp, fact_set__zip__rightD, fact_type__definition_OAbs__inverse, fact_image__eqI, fact_int__one__le__iff__zero__less, fact_not__Nil__listrel1, fact_zdiv__mono2, fact_append__take__drop__id, fact_sym__converse, fact_nat__add__commute, fact_Cons__eq__append__conv, fact_wf__same__fst, fact_part__equivp__def, fact_Suc__less__eq, fact_eq__card__imp__inj__on, fact_bset_I3_J, fact_total__on__converse, fact_trancl__rtrancl__trancl, fact_length__pos__if__in__set, fact_zdiv__mono2__lemma, help_c__fimplies__3, fact_upt__Suc__append, fact_mod__Suc__eq__Suc__mod, fact_exists__code, fact_Cons__eq__appendI, fact_not__listrel1__Nil, fact_set__upt, fact_dvd_Oless__le, fact_inj__Suc, fact_New__DSequence_Opos__single__def, fact_zdiv__self, fact_zip__append, fact_the__inv__into__f__f, fact_dvd_Oless__le__trans, fact_pos__imp__zdiv__nonneg__iff, fact_acc__downward, fact_butlast__append, fact_nat__mult__commute, fact_sympE, fact_zero__less__Suc, fact_divmod__int__rel__mod__eq, fact_card_Oneutral, fact_add1__zle__eq, fact_takeWhile_Osimps_I2_J, fact_eq__imp__le, fact_lexord__linear, help_c__fTrue__1, fact_card__atLeastLessThan, fact_trancl__unfold__left, fact_impossible__Cons, fact_Range__insert, fact_diff__add__inverse2, fact_in__inv__image, fact_plus__nat_Oadd__0, fact_Nil__is__append__conv, fact_append__eq__append__conv2, fact_listrel__rtrancl__trans, fact_nat_Osize_I3_J, fact_insertE, fact_removeAll_Osimps_I1_J, fact_take__add, fact_divmod__nat__rel, fact_dropWhile__nth, fact_some__sym__eq__trivial, fact_conversepD, fact_finite__greaterThanLessThan, fact_type__definition_ORep__inject, fact_exE__some, fact_le__SucE, fact_acyclicI, fact_aset_I7_J, fact_le__less__Suc__eq, fact_inj__onD, fact_equivE, fact_neq0__conv, fact_take__1__Cons, fact_mult__0__right, fact_f__inv__into__f, fact_zdvd__period, fact_map__eq__imp__length__eq, fact_le__antisym, fact_zless__linear, fact_trans__le__add1, fact_upt__conv__Nil, fact_map__comp__map, fact_zdvd__imp__le, fact_div__le__mono, fact_antisym__Id__on, fact_wf__acyclic, fact_Suc__n__not__n, fact_pos__not__random__dseq__def, fact_remove1__remdups, fact_split__neg__lemma, fact_eqelem__imp__iff, fact_zadd__0__right, fact_ord_OatLeastAtMost__iff, fact_card__infinite, fact_DomainP_Oequations, fact_Image__iff, fact_length__remdups__leq, fact_takeWhile__eq__take__P__nth, fact_New__DSequence_Opos__union__def, fact_length__map, fact_diff__le__mono, fact_rtrancl__listrel1__ConsI2, fact_part__equivp__refl__symp__transp, fact_pair__lessI1, fact_listsp_Oequations_I1_J, fact_zmult__1__right, fact_pair__box_Osimps_I2_J, fact_le__0__eq, fact_mult__Suc__right, fact_zdvd__zdiffD, fact_zle__add1__eq__le, fact_rtrancl__idemp__self__comp, fact_trans__trancl, fact_diff__is__0__eq, fact_antisym__Id, fact_bset_I5_J, fact_le__add__diff__inverse, fact_add__le__mono, fact_card__greaterThanLessThan, fact_dvd_Ole__less__trans, fact_wfP__acyclicP, fact_nat__mult__eq__cancel__disj, fact_le__diff__iff, fact_termination__basic__simps_I1_J, fact_nth__take__lemma, fact_less__iff__Suc__add, fact_Range__converse, fact_list__eq__iff__zip__eq, fact_symp__def, fact_mult__less__cancel2, fact_dvd__1__iff__1, fact_DIVISION__BY__ZERO, fact_wf__asym, fact_mod__lemma, fact_nth__eq__iff__index__eq, fact_SigmaD1, fact_wf__iff__acyclic__if__finite, fact_remdups__map__remdups, conj_0, fact_butlast__conv__take, fact_less__Suc0, fact_div__mult1__eq, fact_add__diff__inverse, fact_finite__atLeastLessThan__int, fact_mem__def, fact_diff__Suc__Suc, fact_length__dropWhile__le, fact_dropWhile__append2, fact_rtrancl__converseD, fact_distinct__drop, fact_vimageD, fact_atLeastLessThanSuc__atLeastAtMost, fact_map__removeAll__inj__on, fact_Cons__listrel1__Cons, fact_rtrancl__trancl__trancl, fact_filter_Osimps_I1_J, fact_dropWhile__eq__Nil__conv, fact_refl__on__Id__on, fact_bset_I10_J, fact_equiv__comp__eq, fact_dvd_Ole__imp__less__or__eq, fact_nat__less__le, fact_type__definition_ORep__inverse, fact_le__square, fact_Id__O__R, fact_wf__pair__less, fact_mult__eq__if, fact_take__map, fact_length__greater__0__conv, fact_card__insert__le, fact_zadd__zmult__distrib, fact_rel__compE, fact_less__SucE, fact_le__cube, fact_remdups__remdups, fact_zless__add1__eq, fact_map__pair__compose, fact_drop__Suc__Cons, fact_add__less__mono1, fact_finite__converse, fact_identity__equivp, fact_take__zip, fact_member__set, arity_Nat__Onat__Nat_Osize, fact_part__equivpI, fact_o__assoc, fact_sublist__singleton, fact_less__diff__iff, fact_odd__less__0, fact_dvd_Oless__imp__not__eq2, fact_list__ex__length, fact_not__acc__down, fact_map__eq__conv, fact_zdvd__iff__zmod__eq__0__number__of, fact_folding__image__simple__idem_Oidem, fact_atLeast0AtMost, fact_converse__Id, fact_not__less__Least, fact_map_Osimps_I2_J, fact_equivp__implies__part__equivp, fact_transpE, fact_zdiv__mono2__neg__lemma, fact_vimage__compose, fact_list__ex1__simps_I1_J, fact_lexord__append__rightI, fact_distinct__sublistI, fact_single__valuedD, fact_ord_OatLeast__iff, fact_imageI, fact_distinct__upt, fact_self__append__conv2, fact_converse__rel__comp, fact_add__Suc__shift, fact_less__SucI, fact_Suc__not__Zero, fact_butlast_Osimps_I1_J, fact_same__append__eq, fact_Suc__lessI, fact_add__Suc__right, fact_less__bin__lemma, help_c__fdisj__3, fact_Image__Id, fact_lexord__trans, fact_mod__mult__distrib, fact_trancl__domain, fact_lexord__irreflexive, fact_listrelp_ONil
% 40.13/11.36 % No. of inferences in proof: 2562
% 40.13/11.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 10840 ms resp. 9994 ms w/o parsing
% 41.98/11.94 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 41.98/11.96 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------