TSTP Solution File: SWW337+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW337+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n003.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 12:23:25 EDT 2023
% Result : Theorem 91.70s 31.10s
% Output : Refutation 95.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2940
% Syntax : Number of formulae : 5647 (1895 unt; 259 typ; 0 def)
% Number of atoms : 13591 (4730 equ; 0 cnn)
% Maximal formula atoms : 22 ( 2 avg)
% Number of connectives : 170743 (1024 ~; 218 |;1317 &;161524 @)
% ( 489 <=>;6171 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 559 ( 559 >; 0 *; 0 +; 0 <<)
% Number of symbols : 261 ( 259 usr; 28 con; 0-6 aty)
% Number of variables : 19853 ( 0 ^;19525 !; 328 ?;19853 :)
% 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_G_type,type,
v_G: $i ).
thf(c_Hoare__Mirabelle_Otriple__valid_type,type,
c_Hoare__Mirabelle_Otriple__valid: $i > $i > $i > $o ).
thf(v_ts_type,type,
v_ts: $i ).
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_Groups_Ozero__class_Ozero_type,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
thf(c_Orderings_Oord__class_Oless_type,type,
c_Orderings_Oord__class_Oless: $i > $i ).
thf(tc_Nat_Onat_type,type,
tc_Nat_Onat: $i ).
thf(c_Int_Onat_type,type,
c_Int_Onat: $i ).
thf(c_Groups_Ouminus__class_Ouminus_type,type,
c_Groups_Ouminus__class_Ouminus: $i > $i ).
thf(class_Groups_Ocomm__monoid__add_type,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
thf(c_Finite__Set_Ofinite_type,type,
c_Finite__Set_Ofinite: $i > $i ).
thf(c_Big__Operators_Ocomm__monoid__add__class_Osetsum_type,type,
c_Big__Operators_Ocomm__monoid__add__class_Osetsum: $i > $i > $i ).
thf(c_COMBS_type,type,
c_COMBS: $i > $i > $i > $i ).
thf(tc_fun_type,type,
tc_fun: $i > $i > $i ).
thf(tc_HOL_Obool_type,type,
tc_HOL_Obool: $i ).
thf(c_COMBB_type,type,
c_COMBB: $i > $i > $i > $i ).
thf(tc_prod_type,type,
tc_prod: $i > $i > $i ).
thf(c_Product__Type_Oprod_Oprod__case_type,type,
c_Product__Type_Oprod_Oprod__case: $i > $i > $i > $i ).
thf(c_Product__Type_OSigma_type,type,
c_Product__Type_OSigma: $i > $i > $i ).
thf(c_Enum_On__lists_type,type,
c_Enum_On__lists: $i > $i > $i > $i ).
thf(c_Nat_OSuc_type,type,
c_Nat_OSuc: $i ).
thf(c_List_Oconcat_type,type,
c_List_Oconcat: $i > $i > $i ).
thf(tc_List_Olist_type,type,
tc_List_Olist: $i > $i ).
thf(c_List_Omap_type,type,
c_List_Omap: $i > $i > $i ).
thf(c_COMBC_type,type,
c_COMBC: $i > $i > $i > $i ).
thf(c_List_Olist_OCons_type,type,
c_List_Olist_OCons: $i > $i ).
thf(c_Groups_Oone__class_Oone_type,type,
c_Groups_Oone__class_Oone: $i > $i ).
thf(c_Groups_Oplus__class_Oplus_type,type,
c_Groups_Oplus__class_Oplus: $i > $i ).
thf(c_Groups_Otimes__class_Otimes_type,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
thf(class_Lattices_Osemilattice__inf_type,type,
class_Lattices_Osemilattice__inf: $i > $o ).
thf(c_List_Otl_type,type,
c_List_Otl: $i > $i ).
thf(c_List_Otake_type,type,
c_List_Otake: $i > $i ).
thf(c_Groups_Ominus__class_Ominus_type,type,
c_Groups_Ominus__class_Ominus: $i > $i ).
thf(c_Product__Type_OPair_type,type,
c_Product__Type_OPair: $i > $i > $i ).
thf(c_List_Olexord_type,type,
c_List_Olexord: $i > $i > $i ).
thf(c_Nat_Osize__class_Osize_type,type,
c_Nat_Osize__class_Osize: $i > $i ).
thf(c_Orderings_Oord__class_Omin_type,type,
c_Orderings_Oord__class_Omin: $i > $i ).
thf(c_List_Onth_type,type,
c_List_Onth: $i > $i ).
thf(class_Rings_Osemiring__0_type,type,
class_Rings_Osemiring__0: $i > $o ).
thf(c_SetInterval_Oord__class_OatLeastLessThan_type,type,
c_SetInterval_Oord__class_OatLeastLessThan: $i > $i > $i ).
thf(c_Set_Oinsert_type,type,
c_Set_Oinsert: $i > $i ).
thf(c_Int_OAbs__Integ_type,type,
c_Int_OAbs__Integ: $i ).
thf(c_Relation_OImage_type,type,
c_Relation_OImage: $i > $i > $i > $i ).
thf(c_Int_Ointrel_type,type,
c_Int_Ointrel: $i ).
thf(c_Orderings_Obot__class_Obot_type,type,
c_Orderings_Obot__class_Obot: $i > $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_Typedef_Otype__definition_type,type,
c_Typedef_Otype__definition: $i > $i > $i > $i > $i > $o ).
thf(c_Int_ORep__Integ_type,type,
c_Int_ORep__Integ: $i ).
thf(c_Int_OInteg_type,type,
c_Int_OInteg: $i ).
thf(c_Finite__Set_Ocard_type,type,
c_Finite__Set_Ocard: $i > $i ).
thf(c_Lattices_Osemilattice__sup__class_Osup_type,type,
c_Lattices_Osemilattice__sup__class_Osup: $i > $i ).
thf(c_Lattices_Osemilattice__inf__class_Oinf_type,type,
c_Lattices_Osemilattice__inf__class_Oinf: $i > $i ).
thf(c_Fun_Ocomp_type,type,
c_Fun_Ocomp: $i > $i > $i > $i > $i ).
thf(c_List_Olist_ONil_type,type,
c_List_Olist_ONil: $i > $i ).
thf(c_List_Ohd_type,type,
c_List_Ohd: $i > $i ).
thf(c_If_type,type,
c_If: $i > $i ).
thf(c_Set_OCollect_type,type,
c_Set_OCollect: $i > $i ).
thf(c_fequal_type,type,
c_fequal: $i ).
thf(c_List_Oappend_type,type,
c_List_Oappend: $i > $i ).
thf(c_List_Olist_Olist__case_type,type,
c_List_Olist_Olist__case: $i > $i > $i > $i > $i ).
thf(c_COMBK_type,type,
c_COMBK: $i > $i > $i ).
thf(c_Nat_Onat_Onat__case_type,type,
c_Nat_Onat_Onat__case: $i > $i > $i > $i > $i ).
thf(c_Complete__Lattice_OSup__class_OSup_type,type,
c_Complete__Lattice_OSup__class_OSup: $i > $i > $i ).
thf(c_Fun_Oid_type,type,
c_Fun_Oid: $i > $i ).
thf(class_Orderings_Oord_type,type,
class_Orderings_Oord: $i > $o ).
thf(c_List_Odrop_type,type,
c_List_Odrop: $i > $i ).
thf(c_List_Odistinct_type,type,
c_List_Odistinct: $i > $i ).
thf(c_List_Oset_type,type,
c_List_Oset: $i > $i ).
thf(c_List_OtakeWhile_type,type,
c_List_OtakeWhile: $i > $i > $i > $i ).
thf(c_fNot_type,type,
c_fNot: $i ).
thf(c_List_Orev_type,type,
c_List_Orev: $i > $i ).
thf(c_List_OdropWhile_type,type,
c_List_OdropWhile: $i > $i > $i > $i ).
thf(c_Orderings_Otop__class_Otop_type,type,
c_Orderings_Otop__class_Otop: $i > $i ).
thf(c_fconj_type,type,
c_fconj: $i ).
thf(class_Groups_Ocomm__monoid__mult_type,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
thf(c_List_Otranspose_type,type,
c_List_Otranspose: $i > $i > $i ).
thf(c_List_Olast_type,type,
c_List_Olast: $i > $i > $i ).
thf(c_Finite__Set_Ofold__image_type,type,
c_Finite__Set_Ofold__image: $i > $i > $i > $i ).
thf(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR_type,type,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR: $i > $i > $i ).
thf(c_List_Oupt_type,type,
c_List_Oupt: $i > $i > $i ).
thf(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(c_List_Ofilter_type,type,
c_List_Ofilter: $i > $i > $i ).
thf(c_List_Ozip_type,type,
c_List_Ozip: $i > $i > $i ).
thf(c_List_Olistrel_type,type,
c_List_Olistrel: $i > $i > $i ).
thf(c_Product__Type_Ofst_type,type,
c_Product__Type_Ofst: $i > $i > $i ).
thf(class_Complete__Lattice_Ocomplete__lattice_type,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
thf(c_Nitpick_Ofold__graph_H_type,type,
c_Nitpick_Ofold__graph_H: $i > $i > $i > $i > $i > $i > $o ).
thf(c_Inductive_Ocomplete__lattice__class_Ogfp_type,type,
c_Inductive_Ocomplete__lattice__class_Ogfp: $i > $i > $i ).
thf(c_Orderings_Oorder__class_Omono_type,type,
c_Orderings_Oorder__class_Omono: $i > $i > $i > $o ).
thf(c_Complete__Lattice_Ocomplete__lattice__class_OINFI_type,type,
c_Complete__Lattice_Ocomplete__lattice__class_OINFI: $i > $i > $i ).
thf(c_SetInterval_Oord__class_OgreaterThan_type,type,
c_SetInterval_Oord__class_OgreaterThan: $i > $i ).
thf(c_Finite__Set_Ofolding_type,type,
c_Finite__Set_Ofolding: $i > $i > $i > $i > $o ).
thf(c_Finite__Set_Ofold_type,type,
c_Finite__Set_Ofold: $i > $i > $i > $i ).
thf(c_Product__Type_Osnd_type,type,
c_Product__Type_Osnd: $i > $i > $i ).
thf(c_Relation_Osym_type,type,
c_Relation_Osym: $i > $i > $o ).
thf(c_List_Olist__update_type,type,
c_List_Olist__update: $i > $i > $i ).
thf(c_Partial__Function_Ofun__lub_type,type,
c_Partial__Function_Ofun__lub: $i > $i > $i > $i > $i > $i > $i ).
thf(c_HOL_OEx_type,type,
c_HOL_OEx: $i > $i ).
thf(c_COMBI_type,type,
c_COMBI: $i > $i ).
thf(c_List_Olists_type,type,
c_List_Olists: $i > $i > $i ).
thf(c_Wellfounded_Oacc_type,type,
c_Wellfounded_Oacc: $i > $i > $i ).
thf(c_List_Olistrel1_type,type,
c_List_Olistrel1: $i > $i > $i ).
thf(c_Rings_Odvd__class_Odvd_type,type,
c_Rings_Odvd__class_Odvd: $i > $i ).
thf(c_SetInterval_Oord_OatLeastAtMost_type,type,
c_SetInterval_Oord_OatLeastAtMost: $i > $i > $i > $i > $i ).
thf(c_Finite__Set_Ofun__left__comm__idem_type,type,
c_Finite__Set_Ofun__left__comm__idem: $i > $i > $i > $o ).
thf(c_Orderings_Oord__class_OLeast_type,type,
c_Orderings_Oord__class_OLeast: $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_Oremdups_type,type,
c_List_Oremdups: $i > $i > $i ).
thf(c_Hilbert__Choice_OEps_type,type,
c_Hilbert__Choice_OEps: $i > $i > $i ).
thf(c_Complete__Lattice_OInf__class_OInf_type,type,
c_Complete__Lattice_OInf__class_OInf: $i > $i > $i ).
thf(c_SetInterval_Oord__class_OatLeast_type,type,
c_SetInterval_Oord__class_OatLeast: $i > $i ).
thf(c_List_Olexn_type,type,
c_List_Olexn: $i > $i > $i ).
thf(c_Finite__Set_Ofolding__idem_type,type,
c_Finite__Set_Ofolding__idem: $i > $i > $i > $i > $o ).
thf(c_Set_Ovimage_type,type,
c_Set_Ovimage: $i > $i > $i > $i ).
thf(c_Relation_OId_type,type,
c_Relation_OId: $i > $i ).
thf(c_List_Obutlast_type,type,
c_List_Obutlast: $i > $i > $i ).
thf(c_Set_Othe__elem_type,type,
c_Set_Othe__elem: $i > $i > $i ).
thf(c_Equiv__Relations_Opart__equivp_type,type,
c_Equiv__Relations_Opart__equivp: $i > $i > $o ).
thf(c_fTrue_type,type,
c_fTrue: $i ).
thf(c_List_Oset__Cons_type,type,
c_List_Oset__Cons: $i > $i > $i > $i ).
thf(c_List_Osublist_type,type,
c_List_Osublist: $i > $i > $i > $i ).
thf(c_Relation_Otrans_type,type,
c_Relation_Otrans: $i > $i > $o ).
thf(c_Equiv__Relations_Oequiv_type,type,
c_Equiv__Relations_Oequiv: $i > $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_List_Opartition_type,type,
c_List_Opartition: $i > $i > $i > $i ).
thf(c_Relation_ODomain_type,type,
c_Relation_ODomain: $i > $i > $i ).
thf(c_Divides_Odivmod__nat_type,type,
c_Divides_Odivmod__nat: $i > $i > $i ).
thf(c_Transitive__Closure_Ortrancl_type,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
thf(c_Nat_Ocompow_type,type,
c_Nat_Ocompow: $i > $i > $i ).
thf(c_FunDef_Oreduction__pair_type,type,
c_FunDef_Oreduction__pair: $i > $i > $o ).
thf(c_FunDef_Omin__strict_type,type,
c_FunDef_Omin__strict: $i ).
thf(c_FunDef_Omin__weak_type,type,
c_FunDef_Omin__weak: $i ).
thf(c_Fun_Obij__betw_type,type,
c_Fun_Obij__betw: $i > $i > $i > $i > $i > $o ).
thf(c_Relation_Orefl__on_type,type,
c_Relation_Orefl__on: $i > $i > $i > $o ).
thf(c_HOL_OAll_type,type,
c_HOL_OAll: $i > $i ).
thf(c_fimplies_type,type,
c_fimplies: $i ).
thf(c_List_Olist__ex_type,type,
c_List_Olist__ex: $i > $i > $i > $o ).
thf(c_fFalse_type,type,
c_fFalse: $i ).
thf(c_List_Olistset_type,type,
c_List_Olistset: $i > $i > $i ).
thf(c_Relation_ORange_type,type,
c_Relation_ORange: $i > $i > $i ).
thf(c_Relation_Orel__comp_type,type,
c_Relation_Orel__comp: $i > $i > $i > $i ).
thf(c_Enum_Oproduct_type,type,
c_Enum_Oproduct: $i > $i > $i > $i > $i ).
thf(c_FunDef_Opair__less_type,type,
c_FunDef_Opair__less: $i ).
thf(c_FunDef_Omax__strict_type,type,
c_FunDef_Omax__strict: $i ).
thf(c_List_Olist__all_type,type,
c_List_Olist__all: $i > $i > $i > $o ).
thf(c_Hilbert__Choice_Oinv__into_type,type,
c_Hilbert__Choice_Oinv__into: $i > $i > $i > $i > $i ).
thf(c_Wellfounded_Omax__ext_type,type,
c_Wellfounded_Omax__ext: $i > $i > $i ).
thf(c_List_Oremove1_type,type,
c_List_Oremove1: $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_Wellfounded_Omin__ext_type,type,
c_Wellfounded_Omin__ext: $i > $i > $i ).
thf(c_Enum_Osublists_type,type,
c_Enum_Osublists: $i > $i > $i ).
thf(c_Nitpick_Ocard_H_type,type,
c_Nitpick_Ocard_H: $i > $i > $i ).
thf(c_Divides_Odivmod__nat__rel_type,type,
c_Divides_Odivmod__nat__rel: $i > $i > $i ).
thf(c_Wellfounded_Omlex__prod_type,type,
c_Wellfounded_Omlex__prod: $i > $i > $i > $i ).
thf(c_FunDef_Omax__weak_type,type,
c_FunDef_Omax__weak: $i ).
thf(c_Wellfounded_Olex__prod_type,type,
c_Wellfounded_Olex__prod: $i > $i > $i > $i > $i ).
thf(c_Transitive__Closure_Otrancl_type,type,
c_Transitive__Closure_Otrancl: $i > $i > $i ).
thf(c_List_OremoveAll_type,type,
c_List_OremoveAll: $i > $i > $i ).
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_Wellfounded_OwfP_type,type,
c_Wellfounded_OwfP: $i > $i > $o ).
thf(c_Set_OPow_type,type,
c_Set_OPow: $i > $i ).
thf(c_Relation_Oinv__image_type,type,
c_Relation_Oinv__image: $i > $i > $i ).
thf(c_Relation_OField_type,type,
c_Relation_OField: $i > $i ).
thf(c_Finite__Set_Ofold1Set_type,type,
c_Finite__Set_Ofold1Set: $i > $i > $i > $i ).
thf(c_Relation_Osingle__valued_type,type,
c_Relation_Osingle__valued: $i > $i > $i > $o ).
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_Wellfounded_Oacyclic_type,type,
c_Wellfounded_Oacyclic: $i > $i > $o ).
thf(c_Predicate_Oconversep_type,type,
c_Predicate_Oconversep: $i > $i > $i > $i ).
thf(c_Relation_Oantisym_type,type,
c_Relation_Oantisym: $i > $i > $o ).
thf(c_List_Olistsp_type,type,
c_List_Olistsp: $i > $i > $i ).
thf(c_Finite__Set_Ofun__left__comm_type,type,
c_Finite__Set_Ofun__left__comm: $i > $i > $i > $o ).
thf(c_List_Omeasures_type,type,
c_List_Omeasures: $i > $i > $i ).
thf(c_Wellfounded_Ofinite__psubset_type,type,
c_Wellfounded_Ofinite__psubset: $i > $i ).
thf(c_Finite__Set_Ofolding__one_type,type,
c_Finite__Set_Ofolding__one: $i > $i > $i > $o ).
thf(c_Partial__Function_Oflat__lub_type,type,
c_Partial__Function_Oflat__lub: $i > $i > $i > $i ).
thf(c_Hoare__Mirabelle_Ohoare__derivs_type,type,
c_Hoare__Mirabelle_Ohoare__derivs: $i > $i > $i > $o ).
thf(c_Wellfounded_Opred__nat_type,type,
c_Wellfounded_Opred__nat: $i ).
thf(c_Finite__Set_Ofolding__one__idem_type,type,
c_Finite__Set_Ofolding__one__idem: $i > $i > $i > $o ).
thf(c_List_Oinsert_type,type,
c_List_Oinsert: $i > $i > $i > $i ).
thf(c_Relation_Oirrefl_type,type,
c_Relation_Oirrefl: $i > $i > $o ).
thf(c_Fun_Ofun__upd_type,type,
c_Fun_Ofun__upd: $i > $i > $i > $i > $i > $i ).
thf(c_Equiv__Relations_Oquotient_type,type,
c_Equiv__Relations_Oquotient: $i > $i ).
thf(class_Orderings_Owellorder_type,type,
class_Orderings_Owellorder: $i > $o ).
thf(c_Predicate_OPowp_type,type,
c_Predicate_OPowp: $i > $i > $i ).
thf(c_Equiv__Relations_Ocongruent_type,type,
c_Equiv__Relations_Ocongruent: $i > $i > $i > $i > $o ).
thf(class_Nat_Osize_type,type,
class_Nat_Osize: $i > $o ).
thf(c_SetInterval_Oord_OatLeastLessThan_type,type,
c_SetInterval_Oord_OatLeastLessThan: $i > $i > $i > $i > $i > $i ).
thf(c_Finite__Set_Ofold__graph_type,type,
c_Finite__Set_Ofold__graph: $i > $i > $i > $i > $i > $i ).
thf(c_Predicate_ODomainP_type,type,
c_Predicate_ODomainP: $i > $i > $i > $i ).
thf(c_Predicate_ORangeP_type,type,
c_Predicate_ORangeP: $i > $i > $i > $i ).
thf(c_Predicate_Osymp_type,type,
c_Predicate_Osymp: $i > $i > $o ).
thf(c_SetInterval_Oord_OgreaterThanAtMost_type,type,
c_SetInterval_Oord_OgreaterThanAtMost: $i > $i > $i > $i > $i > $i ).
thf(c_Finite__Set_Ofolding__image_type,type,
c_Finite__Set_Ofolding__image: $i > $i > $i > $i > $i > $o ).
thf(c_fdisj_type,type,
c_fdisj: $i ).
thf(c_Fun_Othe__inv__into_type,type,
c_Fun_Othe__inv__into: $i > $i > $i > $i > $i ).
thf(c_Nitpick_Oprod_type,type,
c_Nitpick_Oprod: $i > $i > $i > $i > $i ).
thf(c_FunDef_Orp__inv__image_type,type,
c_FunDef_Orp__inv__image: $i > $i > $i ).
thf(c_List_Olistrelp_type,type,
c_List_Olistrelp: $i > $i > $i > $i > $o ).
thf(c_Product__Type_Ocurry_type,type,
c_Product__Type_Ocurry: $i > $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OgreaterThanLessThan_type,type,
c_SetInterval_Oord_OgreaterThanLessThan: $i > $i > $i > $i > $i ).
thf(c_Predicate_Oreflp_type,type,
c_Predicate_Oreflp: $i > $i > $o ).
thf(c_Predicate_Opred__comp_type,type,
c_Predicate_Opred__comp: $i > $i > $i > $i > $i > $i ).
thf(c_Equiv__Relations_Ocongruent2_type,type,
c_Equiv__Relations_Ocongruent2: $i > $i > $i > $i > $i > $i > $o ).
thf(c_Predicate_Otransp_type,type,
c_Predicate_Otransp: $i > $i > $o ).
thf(c_List_Olist__ex1_type,type,
c_List_Olist__ex1: $i > $i > $i > $o ).
thf(class_Enum_Oenum_type,type,
class_Enum_Oenum: $i > $o ).
thf(c_Enum_Oenum__class_Oenum__all_type,type,
c_Enum_Oenum__class_Oenum__all: $i > $i ).
thf(c_Wellfounded_Omax__extp_type,type,
c_Wellfounded_Omax__extp: $i > $i > $i > $i > $o ).
thf(c_Equiv__Relations_Oequivp_type,type,
c_Equiv__Relations_Oequivp: $i > $i > $o ).
thf(c_Enum_Oenum__class_Oenum__ex_type,type,
c_Enum_Oenum__class_Oenum__ex: $i > $i ).
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_Quotient_OBabs_type,type,
c_Quotient_OBabs: $i > $i > $i > $i > $i ).
thf(c_Quotient_ORespects_type,type,
c_Quotient_ORespects: $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_Wellfounded_Oaccp_type,type,
c_Wellfounded_Oaccp: $i > $i > $i ).
thf(c_FunDef_Oin__rel_type,type,
c_FunDef_Oin__rel: $i > $i > $i > $i ).
thf(c_Nitpick_Opair__box_OPairBox_type,type,
c_Nitpick_Opair__box_OPairBox: $i > $i > $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_SetInterval_Oord_OatLeast_type,type,
c_SetInterval_Oord_OatLeast: $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OlessThan_type,type,
c_SetInterval_Oord_OlessThan: $i > $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_SetInterval_Oord_OatMost_type,type,
c_SetInterval_Oord_OatMost: $i > $i > $i > $i ).
thf(c_New__DSequence_Opos__map_type,type,
c_New__DSequence_Opos__map: $i > $i > $i > $i > $i > $i ).
thf(c_Lazy__Sequence_Omap_type,type,
c_Lazy__Sequence_Omap: $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_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_New__Random__Sequence_Opos__single_type,type,
c_New__Random__Sequence_Opos__single: $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_SetInterval_Oord_OgreaterThan_type,type,
c_SetInterval_Oord_OgreaterThan: $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_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(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(1575,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/sandbox/benchmark/theBenchmark.p',fact_not__add__less1) ).
thf(8607,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)],[1575]) ).
thf(97,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ ( hAPP @ ( c_List_Otl @ 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/sandbox/benchmark/theBenchmark.p',fact_length__tl) ).
thf(3021,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ ( hAPP @ ( c_List_Otl @ 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)],[97]) ).
thf(417,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
thf(4201,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(352,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/sandbox/benchmark/theBenchmark.p',fact_finite__atLeastLessThan) ).
thf(3944,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)],[352]) ).
thf(986,axiom,
! [A: $i,B: $i] :
( ( ( c_List_Oremdups @ B @ A )
= ( c_List_Olist_ONil @ B ) )
<=> ( A
= ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remdups__eq__nil__iff) ).
thf(6405,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)],[986]) ).
thf(1136,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/sandbox/benchmark/theBenchmark.p',fact_length__filter__less) ).
thf(6979,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)],[1136]) ).
thf(1704,axiom,
! [A: $i] : ( c_Relation_Orefl__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Relation_OId @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__Id) ).
thf(9077,plain,
! [A: $i] : ( c_Relation_Orefl__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Relation_OId @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1704]) ).
thf(546,axiom,
! [A: $i,B: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( c_Complete__Lattice_OSup__class_OSup @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ B @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ B ) ) @ ( c_Orderings_Obot__class_Obot @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fold__sup) ).
thf(4729,plain,
! [A: $i,B: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( c_Complete__Lattice_OSup__class_OSup @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ B @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ B ) ) @ ( c_Orderings_Obot__class_Obot @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(579,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/sandbox/benchmark/theBenchmark.p',fact_neq0__conv) ).
thf(4852,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)],[579]) ).
thf(1016,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Set_OPow @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Powp__Pow__eq) ).
thf(6512,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Set_OPow @ C ) @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Set_OPow @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(1907,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 ) )
=> ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ D @ ( hAPP @ C @ A ) ) @ ( hAPP @ C @ B ) )
= ( hAPP @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Osubset__idem) ).
thf(9864,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 ) )
=> ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ D @ ( hAPP @ C @ A ) ) @ ( hAPP @ C @ B ) )
= ( hAPP @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1907]) ).
thf(743,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ D @ A ) ) @ ( hAPP @ C @ B ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ B ) ) @ ( hAPP @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__comp_H) ).
thf(5509,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ D @ A ) ) @ ( hAPP @ C @ B ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ B ) ) @ ( hAPP @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ocomm__monoid__add @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ B @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__empty) ).
thf(2822,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ocomm__monoid__add @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ B @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(1724,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/sandbox/benchmark/theBenchmark.p',fact_le__diff__iff) ).
thf(9131,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)],[1724]) ).
thf(412,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/sandbox/benchmark/theBenchmark.p',fact_length__takeWhile__le) ).
thf(4188,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)],[412]) ).
thf(478,axiom,
! [A: $i,B: $i] :
( ( ( c_List_Olist_ONil @ B )
= ( c_List_Oconcat @ B @ A ) )
<=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ B ) ) @ C ) @ ( hAPP @ ( c_List_Oset @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ( C
= ( c_List_Olist_ONil @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nil__eq__concat__conv) ).
thf(4447,plain,
! [A: $i,B: $i] :
( ( ( ( c_List_Olist_ONil @ B )
= ( c_List_Oconcat @ B @ A ) )
=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ B ) ) @ C ) @ ( hAPP @ ( c_List_Oset @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ( C
= ( c_List_Olist_ONil @ B ) ) ) )
& ( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ B ) ) @ C ) @ ( hAPP @ ( c_List_Oset @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ( C
= ( c_List_Olist_ONil @ B ) ) )
=> ( ( c_List_Olist_ONil @ B )
= ( c_List_Oconcat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(2344,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ C ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ C @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ C @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ C @ C ) ) ) ) @ ( c_Product__Type_OPair @ C @ C ) ) ) ) @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( c_Wellfounded_Oacc @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp__acc__eq) ).
thf(11472,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ C ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ C @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ C @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ C @ C ) ) ) ) @ ( c_Product__Type_OPair @ C @ C ) ) ) ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( c_Wellfounded_Oacc @ C @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( c_Wellfounded_Oacc @ C @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ C ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ C @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ C @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ C @ C ) ) ) ) @ ( c_Product__Type_OPair @ C @ C ) ) ) ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2344]) ).
thf(2513,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/sandbox/benchmark/theBenchmark.p',fact_list__ex__iff) ).
thf(12055,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)],[2513]) ).
thf(1986,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ D ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) @ C ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__equiv__class__iff2) ).
thf(10166,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ D ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) @ 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 @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1986]) ).
thf(975,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) )
<=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__insert__iff) ).
thf(6355,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(2006,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ B @ E @ A ) @ D ) ) @ ( hAPP @ ( c_Set_Ovimage @ B @ E @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__mono) ).
thf(10259,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ B @ E @ A ) @ D ) ) @ ( hAPP @ ( c_Set_Ovimage @ B @ E @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2006]) ).
thf(2037,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) @ ( c_List_Olistsp @ C @ B ) ) @ ( c_List_Olistsp @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsp__mono) ).
thf(10373,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) @ ( c_List_Olistsp @ C @ B ) ) @ ( c_List_Olistsp @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2037]) ).
thf(1059,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= B ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I2_J) ).
thf(6669,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= B ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).
thf(2639,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/sandbox/benchmark/theBenchmark.p',fact_map__eq__conv) ).
thf(12607,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)],[2639]) ).
thf(2334,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Set_Ovimage @ C @ B @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__empty) ).
thf(11445,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Set_Ovimage @ C @ B @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2334]) ).
thf(506,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__1__eq__mult__iff) ).
thf(4571,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)],[506]) ).
thf(1849,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ C ) @ c_Int_OInteg ) )
=> ( hBOOL @ ( hAPP @ B @ ( hAPP @ c_Int_OAbs__Integ @ C ) ) ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Abs__Integ__induct) ).
thf(9653,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ C ) @ c_Int_OInteg ) )
=> ( hBOOL @ ( hAPP @ B @ ( hAPP @ c_Int_OAbs__Integ @ C ) ) ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1849]) ).
thf(831,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/sandbox/benchmark/theBenchmark.p',fact_append__same__eq) ).
thf(5857,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)],[831]) ).
thf(1915,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
<=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__is__empty) ).
thf(9886,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) )
& ( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1915]) ).
thf(843,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/sandbox/benchmark/theBenchmark.p',fact_refl__on__converse) ).
thf(5896,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)],[843]) ).
thf(936,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/sandbox/benchmark/theBenchmark.p',fact_map__append) ).
thf(6231,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)],[936]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__Un__Int) ).
thf(2778,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(1491,axiom,
! [A: $i,B: $i,C: $i] : ( c_Fun_Oinj__on @ ( tc_prod @ C @ B ) @ ( tc_prod @ B @ C ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ C @ B @ ( tc_prod @ B @ C ) ) @ ( hAPP @ ( c_COMBC @ B @ C @ ( tc_prod @ B @ C ) ) @ ( c_Product__Type_OPair @ B @ C ) ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_swap__inj__on) ).
thf(8288,plain,
! [A: $i,B: $i,C: $i] : ( c_Fun_Oinj__on @ ( tc_prod @ C @ B ) @ ( tc_prod @ B @ C ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ C @ B @ ( tc_prod @ B @ C ) ) @ ( hAPP @ ( c_COMBC @ B @ C @ ( tc_prod @ B @ C ) ) @ ( c_Product__Type_OPair @ B @ C ) ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1491]) ).
thf(1020,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/sandbox/benchmark/theBenchmark.p',fact_not__Nil__listrel1) ).
thf(6530,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)],[1020]) ).
thf(2271,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/sandbox/benchmark/theBenchmark.p',fact_finite__SigmaI) ).
thf(11211,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)],[2271]) ).
thf(1588,axiom,
! [A: $i,B: $i] : ( c_Relation_Osingle__valued @ B @ B @ ( c_Relation_OId__on @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__Id__on) ).
thf(8663,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)],[1588]) ).
thf(1135,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_Oconverse @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_Oconverse @ D @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__Int) ).
thf(6976,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_Oconverse @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_Oconverse @ D @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).
thf(379,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_List_Olist_ONil @ B ) )
=> ( ( c_List_Olast @ B @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ A ) @ C ) )
= ( c_List_Olast @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__appendR) ).
thf(4062,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_List_Olist_ONil @ B ) )
=> ( ( c_List_Olast @ B @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ A ) @ C ) )
= ( c_List_Olast @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(206,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ B ) @ ( hAPP @ ( c_List_Otl @ C ) @ A ) )
= ( hAPP @ ( c_List_Otl @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__tl) ).
thf(3399,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ B ) @ ( hAPP @ ( c_List_Otl @ C ) @ A ) )
= ( hAPP @ ( c_List_Otl @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(2061,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iso__tuple__UNIV__I) ).
thf(10452,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2061]) ).
thf(2527,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/sandbox/benchmark/theBenchmark.p',fact_acc__wfD) ).
thf(12116,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)],[2527]) ).
thf(589,axiom,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ A ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__singleton) ).
thf(4899,plain,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ A ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(313,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/sandbox/benchmark/theBenchmark.p',fact_mult__Suc__right) ).
thf(3798,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)],[313]) ).
thf(2629,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/sandbox/benchmark/theBenchmark.p',fact_LeastI) ).
thf(12570,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)],[2629]) ).
thf(2352,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ C @ C @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ C ) @ c_fNot ) ) @ c_fequal ) ) @ B ) @ A ) )
<=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_conversep__noteq) ).
thf(11517,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ C @ C @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ C ) @ c_fNot ) ) @ c_fequal ) ) @ B ) @ A ) )
=> ( B != A ) )
& ( ( B != A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ C @ C @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ C ) @ c_fNot ) ) @ c_fequal ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2352]) ).
thf(1395,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Diff) ).
thf(7922,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1395]) ).
thf(1552,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( c_Equiv__Relations_Oequiv @ K @ J @ I )
=> ( ( c_Equiv__Relations_Oequiv @ H @ G @ F )
=> ( ( c_Equiv__Relations_Ocongruent2 @ K @ H @ ( tc_fun @ E @ tc_HOL_Obool ) @ I @ F @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ K @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ K ) @ J ) @ I ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ H @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ H ) @ G ) @ F ) ) )
=> ( ! [L: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ K ) @ L ) @ J ) )
=> ! [M: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ H ) @ M ) @ G ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ D @ L ) @ M ) ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ K @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ H @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ K ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ H @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) ) @ D ) ) ) @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__equiv__class__type2) ).
thf(8514,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( c_Equiv__Relations_Oequiv @ K @ J @ I )
=> ( ( c_Equiv__Relations_Oequiv @ H @ G @ F )
=> ( ( c_Equiv__Relations_Ocongruent2 @ K @ H @ ( tc_fun @ E @ tc_HOL_Obool ) @ I @ F @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ K @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ K ) @ J ) @ I ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ H @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ H ) @ G ) @ F ) ) )
=> ( ! [L: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ K ) @ L ) @ J ) )
=> ! [M: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ H ) @ M ) @ G ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ D @ L ) @ M ) ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ K @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ H @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ K ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ H @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) ) @ D ) ) ) @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1552]) ).
thf(1876,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B )
= ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__Un__image__eq__iff) ).
thf(9754,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B )
= ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B )
= ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1876]) ).
thf(1323,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I5_J) ).
thf(7673,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1323]) ).
thf(955,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__Un__subset) ).
thf(6283,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(439,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/sandbox/benchmark/theBenchmark.p',fact_gr__implies__not0) ).
thf(4290,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)],[439]) ).
thf(2259,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__empty__eq) ).
thf(11164,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2259]) ).
thf(1549,axiom,
! [A: $i,B: $i] : ( c_Fun_Oinj__on @ ( tc_fun @ B @ A ) @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_HOL_Obool ) @ ( tc_fun @ B @ A ) ) @ ( c_Set_OCollect @ ( tc_prod @ B @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_HOL_Obool ) @ ( tc_fun @ B @ A ) ) @ ( c_Product__Type_Oprod_Oprod__case @ B @ A @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ tc_HOL_Obool ) @ B ) @ ( hAPP @ ( c_COMBC @ A @ A @ tc_HOL_Obool ) @ c_fequal ) ) ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_fun @ B @ A ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__graph) ).
thf(8507,plain,
! [A: $i,B: $i] : ( c_Fun_Oinj__on @ ( tc_fun @ B @ A ) @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_HOL_Obool ) @ ( tc_fun @ B @ A ) ) @ ( c_Set_OCollect @ ( tc_prod @ B @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_HOL_Obool ) @ ( tc_fun @ B @ A ) ) @ ( c_Product__Type_Oprod_Oprod__case @ B @ A @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ tc_HOL_Obool ) @ B ) @ ( hAPP @ ( c_COMBC @ A @ A @ tc_HOL_Obool ) @ c_fequal ) ) ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_fun @ B @ A ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1549]) ).
thf(956,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 ) )
=> ( ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ A ) )
=> ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ D @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Ounion__idem) ).
thf(6285,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 ) )
=> ( ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ A ) )
=> ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ D @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(2073,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_Oimage @ C @ D @ B ) @ A ) )
<=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__is__image) ).
thf(10495,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_Oimage @ C @ D @ B ) @ A ) )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_Oimage @ C @ D @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2073]) ).
thf(2156,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
thf(10812,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)],[2156]) ).
thf(31,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/sandbox/benchmark/theBenchmark.p',fact_q__pos__lemma) ).
thf(2787,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)],[31]) ).
thf(781,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/sandbox/benchmark/theBenchmark.p',fact_diffs0__imp__equal) ).
thf(5654,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)],[781]) ).
thf(899,axiom,
! [A: $i] : ( c_Relation_Oantisym @ A @ ( c_Relation_OId @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisym__Id) ).
thf(6121,plain,
! [A: $i] : ( c_Relation_Oantisym @ A @ ( c_Relation_OId @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(919,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( c_Fun_Oinj__on @ D @ ( tc_fun @ A @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ A @ C ) @ D ) @ ( c_COMBK @ C @ A ) ) @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__fun) ).
thf(6172,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( c_Fun_Oinj__on @ D @ ( tc_fun @ A @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ A @ C ) @ D ) @ ( c_COMBK @ C @ A ) ) @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(2498,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/sandbox/benchmark/theBenchmark.p',fact_remdups_Osimps_I2_J) ).
thf(11998,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)],[2498]) ).
thf(1027,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( c_Relation_Orefl__on @ C @ ( hAPP @ B @ F ) @ ( hAPP @ A @ F ) ) )
=> ( c_Relation_Orefl__on @ C @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ D ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__INTER) ).
thf(6555,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( c_Relation_Orefl__on @ C @ ( hAPP @ B @ F ) @ ( hAPP @ A @ F ) ) )
=> ( c_Relation_Orefl__on @ C @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).
thf(2469,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Obij__betw @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__is__inj) ).
thf(11898,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Obij__betw @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2469]) ).
thf(1522,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ B @ B ) @ ( hAPP @ ( c_Relation_OField @ B ) @ A ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ B ) @ ( hAPP @ ( c_Relation_OField @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__subset__Field2) ).
thf(8415,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ B @ B ) @ ( hAPP @ ( c_Relation_OField @ B ) @ A ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ B ) @ ( hAPP @ ( c_Relation_OField @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1522]) ).
thf(532,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/sandbox/benchmark/theBenchmark.p',fact_zip__append) ).
thf(4682,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)],[532]) ).
thf(1581,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ C @ B ) @ A )
= ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ B @ C ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ C @ B ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ C @ B ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ C @ B ) ) ) ) @ ( hAPP @ ( c_COMBC @ C @ B @ ( tc_prod @ C @ B ) ) @ ( c_Product__Type_OPair @ C @ B ) ) ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__def) ).
thf(8639,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ C @ B ) @ A )
= ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ B @ C ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ C @ B ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ C @ B ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ C @ B ) ) ) ) @ ( hAPP @ ( c_COMBC @ C @ B @ ( tc_prod @ C @ B ) ) @ ( c_Product__Type_OPair @ C @ B ) ) ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1581]) ).
thf(799,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ B ) @ ( hAPP @ ( c_Set_OCollect @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ A ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ E @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ E @ ( tc_fun @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ E @ ( tc_fun @ E @ E ) ) @ D ) @ ( c_If @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ A ) ) ) @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ E ) ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__restrict__set_H) ).
thf(5733,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ B ) @ ( hAPP @ ( c_Set_OCollect @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ A ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ E @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ E @ ( tc_fun @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ E @ ( tc_fun @ E @ E ) ) @ D ) @ ( c_If @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ A ) ) ) @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ E ) ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(2301,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_fun @ B @ A ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_fun @ B @ A ) @ tc_HOL_Obool ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__fun__UNIVD2) ).
thf(11318,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_fun @ B @ A ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_fun @ B @ A ) @ tc_HOL_Obool ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2301]) ).
thf(947,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/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__insert2) ).
thf(6263,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)],[947]) ).
thf(1646,axiom,
! [A: $i,B: $i] :
( ( c_Equiv__Relations_Oequiv @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A )
<=> ( c_Equiv__Relations_Oequivp @ B @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ B ) @ ( c_COMBC @ B @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_prod @ B @ B ) ) @ ( tc_fun @ B @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ B @ B ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ B ) @ ( c_member @ ( tc_prod @ B @ B ) ) ) ) @ ( c_Product__Type_OPair @ B @ B ) ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equivp__equiv) ).
thf(8887,plain,
! [A: $i,B: $i] :
( ( ( c_Equiv__Relations_Oequiv @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A )
=> ( c_Equiv__Relations_Oequivp @ B @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ B ) @ ( c_COMBC @ B @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_prod @ B @ B ) ) @ ( tc_fun @ B @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ B @ B ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ B ) @ ( c_member @ ( tc_prod @ B @ B ) ) ) ) @ ( c_Product__Type_OPair @ B @ B ) ) ) ) @ A ) ) )
& ( ( c_Equiv__Relations_Oequivp @ B @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ B ) @ ( c_COMBC @ B @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_prod @ B @ B ) ) @ ( tc_fun @ B @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ B @ B ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ B ) @ ( c_member @ ( tc_prod @ B @ B ) ) ) ) @ ( c_Product__Type_OPair @ B @ B ) ) ) ) @ A ) )
=> ( c_Equiv__Relations_Oequiv @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1646]) ).
thf(2206,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
<=> ? [E: $i] :
( ( A
= ( hAPP @ B @ E ) )
& ! [F: $i] :
( ( A
= ( hAPP @ B @ F ) )
=> ( F = E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__ex1__eq) ).
thf(10976,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
=> ? [E: $i] :
( ( A
= ( hAPP @ B @ E ) )
& ! [F: $i] :
( ( A
= ( hAPP @ B @ F ) )
=> ( F = E ) ) ) )
& ( ? [E: $i] :
( ( A
= ( hAPP @ B @ E ) )
& ! [F: $i] :
( ( A
= ( hAPP @ B @ F ) )
=> ( F = E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2206]) ).
thf(1031,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_List_Oset @ B ) @ ( c_List_Oremdups @ B @ A ) )
= ( hAPP @ ( c_List_Oset @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__remdups) ).
thf(6566,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)],[1031]) ).
thf(2608,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/sandbox/benchmark/theBenchmark.p',fact_prod_Orecs) ).
thf(12468,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)],[2608]) ).
thf(1628,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/sandbox/benchmark/theBenchmark.p',fact_add__lessD1) ).
thf(8828,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)],[1628]) ).
thf(870,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ D @ C @ B ) @ A ) )
=> ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1Set__nonempty) ).
thf(6014,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ D @ C @ B ) @ A ) )
=> ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(762,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/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I4_J) ).
thf(5582,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)],[762]) ).
thf(619,axiom,
( c_FunDef_Omax__strict
= ( c_Wellfounded_Omax__ext @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_FunDef_Opair__less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__strict__def) ).
thf(4992,plain,
( c_FunDef_Omax__strict
= ( c_Wellfounded_Omax__ext @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_FunDef_Opair__less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(976,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Relation_OField @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_ODomain @ B @ B ) @ A ) ) @ ( hAPP @ ( c_Relation_ORange @ B @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__def) ).
thf(6374,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Relation_OField @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_ODomain @ B @ B ) @ A ) ) @ ( hAPP @ ( c_Relation_ORange @ B @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(2657,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/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Orefl_H__def) ).
thf(12699,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)],[2657]) ).
thf(1019,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Equiv__Relations_Oequiv @ F @ E @ D )
=> ( ( c_Equiv__Relations_Ocongruent @ F @ ( tc_fun @ C @ tc_HOL_Obool ) @ D @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ E ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ F @ F @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) ) @ B )
= ( hAPP @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__equiv__class) ).
thf(6527,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Equiv__Relations_Oequiv @ F @ E @ D )
=> ( ( c_Equiv__Relations_Ocongruent @ F @ ( tc_fun @ C @ tc_HOL_Obool ) @ D @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ E ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ F @ F @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) ) @ B )
= ( hAPP @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).
thf(2606,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/sandbox/benchmark/theBenchmark.p',fact_all__code) ).
thf(12462,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)],[2606]) ).
thf(1471,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_Set_Oinsert @ E ) @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I5_J) ).
thf(8200,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_Set_Oinsert @ E ) @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1471]) ).
thf(2669,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/sandbox/benchmark/theBenchmark.p',fact_type__definition_OAbs__inject) ).
thf(12738,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)],[2669]) ).
thf(1691,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ E @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ D ) @ C ) ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ E @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__code_I3_J) ).
thf(9032,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ E @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ D ) @ C ) ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ E @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1691]) ).
thf(1096,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/sandbox/benchmark/theBenchmark.p',fact_o__apply) ).
thf(6808,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)],[1096]) ).
thf(2076,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__iff__psubset__eq) ).
thf(10507,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
| ( B = A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
| ( B = A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2076]) ).
thf(2308,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B ) @ A ) )
=> ( c_Wellfounded_Owf @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__exp) ).
thf(11350,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B ) @ A ) )
=> ( c_Wellfounded_Owf @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2308]) ).
thf(2055,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/sandbox/benchmark/theBenchmark.p',fact_part__equivpE) ).
thf(10431,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)],[2055]) ).
thf(1078,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/sandbox/benchmark/theBenchmark.p',fact_append__eq__appendI) ).
thf(6744,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)],[1078]) ).
thf(2125,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 ) ) @ ( c_List_Omeasures @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ D ) @ C ) ) @ ( c_List_Omeasures @ B @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ ( tc_fun @ B @ tc_Nat_Onat ) ) @ E ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_measures__lesseq) ).
thf(10694,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 ) ) @ ( c_List_Omeasures @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ D ) @ C ) ) @ ( c_List_Omeasures @ B @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ ( tc_fun @ B @ tc_Nat_Onat ) ) @ E ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2125]) ).
thf(500,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/sandbox/benchmark/theBenchmark.p',fact_all__set__conv__all__nth) ).
thf(4532,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)],[500]) ).
thf(2617,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/sandbox/benchmark/theBenchmark.p',fact_insert__absorb) ).
thf(12500,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)],[2617]) ).
thf(2262,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ E @ B ) @ A ) ) )
<=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ F ) @ A ) )
& ( D
= ( hAPP @ ( c_Set_Oimage @ C @ E @ B ) @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__image__iff) ).
thf(11175,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ E @ B ) @ A ) ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ F ) @ A ) )
& ( D
= ( hAPP @ ( c_Set_Oimage @ C @ E @ B ) @ F ) ) ) )
& ( ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ F ) @ A ) )
& ( D
= ( hAPP @ ( c_Set_Oimage @ C @ E @ B ) @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ E @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2262]) ).
thf(2114,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__mono) ).
thf(10658,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2114]) ).
thf(243,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ A @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ E ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SUPI) ).
thf(3534,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ A @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ E ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(907,axiom,
~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_infinite__UNIV__nat) ).
thf(6141,plain,
~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(6142,plain,
~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ),
inference(polarity_switch,[status(thm)],[6141]) ).
thf(2406,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ C @ C @ B ) @ A ) ) @ A ) )
=> ( ( hAPP @ ( c_Relation_OImage @ C @ C @ ( c_Transitive__Closure_Ortrancl @ C @ B ) ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__closed__trancl) ).
thf(11688,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ C @ C @ B ) @ A ) ) @ A ) )
=> ( ( hAPP @ ( c_Relation_OImage @ C @ C @ ( c_Transitive__Closure_Ortrancl @ C @ B ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2406]) ).
thf(1418,axiom,
! [A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_OCollect @ A ) @ ( hAPP @ ( c_COMBK @ tc_HOL_Obool @ A ) @ c_fFalse ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__def) ).
thf(8005,plain,
! [A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_OCollect @ A ) @ ( hAPP @ ( c_COMBK @ tc_HOL_Obool @ A ) @ c_fFalse ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1418]) ).
thf(1523,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( c_Fun_Oinj__on @ B @ E @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( c_Fun_Oinj__on @ B @ D @ ( hAPP @ ( c_Fun_Ocomp @ E @ D @ B @ C ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__comp) ).
thf(8417,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( c_Fun_Oinj__on @ B @ E @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( c_Fun_Oinj__on @ B @ D @ ( hAPP @ ( c_Fun_Ocomp @ E @ D @ B @ C ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1523]) ).
thf(2309,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ A ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) ) )
=> ( ( c_Transitive__Closure_Ortrancl @ C @ A )
= ( c_Transitive__Closure_Ortrancl @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__subset) ).
thf(11352,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ A ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) ) )
=> ( ( c_Transitive__Closure_Ortrancl @ C @ A )
= ( c_Transitive__Closure_Ortrancl @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2309]) ).
thf(1271,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__UN) ).
thf(7477,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1271]) ).
thf(113,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__0R) ).
thf(3072,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ 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)],[113]) ).
thf(1390,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/sandbox/benchmark/theBenchmark.p',fact_card__image__le) ).
thf(7905,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)],[1390]) ).
thf(1531,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/sandbox/benchmark/theBenchmark.p',fact_lexord__append__left__rightI) ).
thf(8450,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)],[1531]) ).
thf(1831,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I2_J) ).
thf(9573,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1831]) ).
thf(921,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl) ).
thf(6177,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(1399,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ A ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ounion) ).
thf(7935,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ A ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1399]) ).
thf(2530,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/sandbox/benchmark/theBenchmark.p',fact_congruent2__implies__congruent) ).
thf(12129,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)],[2530]) ).
thf(2650,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/sandbox/benchmark/theBenchmark.p',fact_pred__comp_Oequations) ).
thf(12649,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)],[2650]) ).
thf(1121,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/sandbox/benchmark/theBenchmark.p',fact_add__less__mono1) ).
thf(6918,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)],[1121]) ).
thf(492,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__absorb1) ).
thf(4500,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(383,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Oset @ ( tc_List_Olist @ C ) ) @ ( c_Enum_On__lists @ C @ B @ A ) )
= ( hAPP @ ( c_Set_OCollect @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ ( tc_List_Olist @ C ) @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_List_Olist @ C ) ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ C ) @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_List_Olist @ C ) ) @ c_fequal ) @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ C ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_List_Olist @ C ) ) @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( c_List_Oset @ C ) ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__n__lists) ).
thf(4075,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Oset @ ( tc_List_Olist @ C ) ) @ ( c_Enum_On__lists @ C @ B @ A ) )
= ( hAPP @ ( c_Set_OCollect @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ ( tc_List_Olist @ C ) @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_List_Olist @ C ) ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ C ) @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_List_Olist @ C ) ) @ c_fequal ) @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ C ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_List_Olist @ C ) ) @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( c_List_Oset @ C ) ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(1109,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( D
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ A ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__constant) ).
thf(6868,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( D
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).
thf(2463,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__subset__trans) ).
thf(11880,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2463]) ).
thf(1011,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ C @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ C ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ C ) @ c_fNot ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__diff__eq) ).
thf(6495,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ C @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ C ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ C ) @ c_fNot ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ E @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ E @ E ) @ D ) @ ( c_Groups_Oplus__class_Oplus @ E ) ) @ B ) ) @ A ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Odistrib) ).
thf(2808,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ E @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ E @ E ) @ D ) @ ( c_Groups_Oplus__class_Oplus @ E ) ) @ B ) ) @ A ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(342,axiom,
( ( hAPP @ ( c_Nat_Osize__class_Osize @ tc_HOL_Obool ) @ c_fTrue )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bool_Osize_I3_J) ).
thf(3905,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)],[342]) ).
thf(895,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( c_Relation_Orefl__on @ C @ ( hAPP @ B @ F ) @ ( hAPP @ A @ F ) ) )
=> ( c_Relation_Orefl__on @ C @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ D ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__UNION) ).
thf(6106,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( c_Relation_Orefl__on @ C @ ( hAPP @ B @ F ) @ ( hAPP @ A @ F ) ) )
=> ( c_Relation_Orefl__on @ C @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(2188,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__not__empty) ).
thf(10927,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2188]) ).
thf(778,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( c_Product__Type_Ofst @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) )
= A )
=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__eqD) ).
thf(5644,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( c_Product__Type_Ofst @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) )
= A )
=> ( C = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(2378,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__anti__mono) ).
thf(11603,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2378]) ).
thf(637,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/sandbox/benchmark/theBenchmark.p',fact_neq__if__length__neq) ).
thf(5069,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)],[637]) ).
thf(1002,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ C @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__quotient) ).
thf(6463,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ C @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(27,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__refl) ).
thf(2776,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)],[27]) ).
thf(2012,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ G @ F ) @ tc_HOL_Obool ) ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ F @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ G @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ G @ F @ C ) @ E ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ G @ F @ C ) @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__mono) ).
thf(10277,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ G @ F ) @ tc_HOL_Obool ) ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ F @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ G @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ G @ F @ C ) @ E ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ G @ F @ C ) @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2012]) ).
thf(2325,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/sandbox/benchmark/theBenchmark.p',fact_not__acc__down) ).
thf(11409,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)],[2325]) ).
thf(1919,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 @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) ) )
<=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ A @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UN) ).
thf(9901,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 @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ A @ E ) ) ) ) )
& ( ! [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 @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1919]) ).
thf(1720,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Relation_OField @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ A ) )
= ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oimage @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Relation_OField @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__Union) ).
thf(9120,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Relation_OField @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ A ) )
= ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oimage @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Relation_OField @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1720]) ).
thf(73,axiom,
~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Int_Oint ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Int_Oint @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_infinite__UNIV__int) ).
thf(2952,plain,
~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Int_Oint ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Int_Oint @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(2953,plain,
~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Int_Oint ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Int_Oint @ tc_HOL_Obool ) ) ) ),
inference(polarity_switch,[status(thm)],[2952]) ).
thf(1000,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
thf(6458,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)],[1000]) ).
thf(1695,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_SetInterval_Oord_OgreaterThanAtMost @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) ) @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ tc_Nat_Onat ) @ c_fNot ) ) @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ A @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OgreaterThanAtMost__empty) ).
thf(9045,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_SetInterval_Oord_OgreaterThanAtMost @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) ) @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ tc_Nat_Onat ) @ c_fNot ) ) @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ A @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1695]) ).
thf(222,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( B
= ( c_Inductive_Ocomplete__lattice__class_Ogfp @ C @ A ) )
=> ( ( c_Orderings_Oorder__class_Omono @ C @ C @ A )
=> ( B
= ( hAPP @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__gfp__unfold) ).
thf(3460,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( B
= ( c_Inductive_Ocomplete__lattice__class_Ogfp @ C @ A ) )
=> ( ( c_Orderings_Oorder__class_Omono @ C @ C @ A )
=> ( B
= ( hAPP @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(1092,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__Un__distrib) ).
thf(6796,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(1964,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/sandbox/benchmark/theBenchmark.p',fact_equivpE) ).
thf(10061,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)],[1964]) ).
thf(1925,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/sandbox/benchmark/theBenchmark.p',fact_insert__absorb2) ).
thf(9918,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)],[1925]) ).
thf(774,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ ( c_Complete__Lattice_OSup__class_OSup @ C @ B ) ) @ A ) )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__le__iff) ).
thf(5625,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ ( c_Complete__Lattice_OSup__class_OSup @ C @ B ) ) @ A ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ D ) @ A ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ D ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ ( c_Complete__Lattice_OSup__class_OSup @ C @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(1342,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/sandbox/benchmark/theBenchmark.p',fact_take__add) ).
thf(7726,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)],[1342]) ).
thf(2090,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/sandbox/benchmark/theBenchmark.p',fact_prod__fun__imageE) ).
thf(10562,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)],[2090]) ).
thf(1865,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_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ F ) @ E ) )
=> ( ! [I: $i,J: $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 ) @ I ) @ J ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) ) )
=> ! [K: $i,L: $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 ) @ I ) @ J ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ K ) @ L ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ I ) @ J ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ K ) @ L ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ D ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__induct2) ).
thf(9717,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_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ F ) @ E ) )
=> ( ! [I: $i,J: $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 ) @ I ) @ J ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) ) )
=> ! [K: $i,L: $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 ) @ I ) @ J ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ K ) @ L ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ I ) @ J ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ K ) @ L ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ D ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1865]) ).
thf(664,axiom,
( c_FunDef_Omin__strict
= ( c_Wellfounded_Omin__ext @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_FunDef_Opair__less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__strict__def) ).
thf(5173,plain,
( c_FunDef_Omin__strict
= ( c_Wellfounded_Omin__ext @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_FunDef_Opair__less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(965,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__Un__distrib) ).
thf(6323,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(2248,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ B ) ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__subset) ).
thf(11122,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ B ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2248]) ).
thf(1530,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Un__distrib1) ).
thf(8447,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1530]) ).
thf(970,axiom,
! [A: $i,B: $i] :
( ( B
!= ( c_List_Olist_ONil @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ A ) @ B ) )
=> ( ( c_List_OtakeWhile @ A @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ A ) @ c_fNot ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ A @ tc_HOL_Obool ) @ c_fequal ) @ ( c_List_Olast @ A @ B ) ) ) @ B )
= ( c_List_Obutlast @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile__not__last) ).
thf(6338,plain,
! [A: $i,B: $i] :
( ( B
!= ( c_List_Olist_ONil @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ A ) @ B ) )
=> ( ( c_List_OtakeWhile @ A @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ A ) @ c_fNot ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ A @ tc_HOL_Obool ) @ c_fequal ) @ ( c_List_Olast @ A @ B ) ) ) @ B )
= ( c_List_Obutlast @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(2022,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_Orderings_Oord__class_Oless__eq @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ F @ ( hAPP @ C @ A ) ) @ ( hAPP @ C @ B ) )
= ( hAPP @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Osubset__idem) ).
thf(10314,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_Orderings_Oord__class_Oless__eq @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ F @ ( hAPP @ C @ A ) ) @ ( hAPP @ C @ B ) )
= ( hAPP @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2022]) ).
thf(1201,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Oacyclic @ B @ A )
=> ( c_Relation_Oantisym @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__impl__antisym__rtrancl) ).
thf(7198,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)],[1201]) ).
thf(860,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 ) ) )
=> ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
& ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ ( hAPP @ ( c_Set_OCollect @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ B @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ D ) @ c_fequal ) @ A ) ) @ ( hAPP @ A @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pigeonhole__infinite) ).
thf(5982,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 ) ) )
=> ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
& ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ ( hAPP @ ( c_Set_OCollect @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ B @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ D ) @ c_fequal ) @ A ) ) @ ( hAPP @ A @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(1953,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__right__if1) ).
thf(10017,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1953]) ).
thf(677,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ B ) @ ( hAPP @ ( c_List_Orev @ B ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__rev) ).
thf(5224,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ B ) @ ( hAPP @ ( c_List_Orev @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ B ) @ ( hAPP @ ( c_List_Orev @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(785,axiom,
! [A: $i] :
( ( hAPP @ ( c_Set_Oimage @ A @ A @ ( c_Fun_Oid @ A ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__id) ).
thf(5669,plain,
! [A: $i] :
( ( hAPP @ ( c_Set_Oimage @ A @ A @ ( c_Fun_Oid @ A ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(1739,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/sandbox/benchmark/theBenchmark.p',fact_distinct__insert) ).
thf(9191,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)],[1739]) ).
thf(2552,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/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oin__idem) ).
thf(12221,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)],[2552]) ).
thf(716,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/sandbox/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
thf(5405,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)],[716]) ).
thf(419,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_List_Olist_ONil @ B ) )
=> ( ( c_List_Olast @ B @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ A ) @ C ) )
= ( c_List_Olast @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__ConsR) ).
thf(4215,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_List_Olist_ONil @ B ) )
=> ( ( c_List_Olast @ B @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ A ) @ C ) )
= ( c_List_Olast @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(1197,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ F ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ F ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ D ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__eq__cancel2) ).
thf(7182,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ F ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ F ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ D ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ F ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ F ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197]) ).
thf(2176,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/sandbox/benchmark/theBenchmark.p',fact_set__zip__leftD) ).
thf(10886,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)],[2176]) ).
thf(1663,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ C @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ C ) @ c_fdisj ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ B ) ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__disj__eq) ).
thf(8943,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ C @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ C ) @ c_fdisj ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ B ) ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1663]) ).
thf(1361,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/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).
thf(7781,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)],[1361]) ).
thf(207,axiom,
! [A: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__zminus) ).
thf(3402,plain,
! [A: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(680,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( c_Nitpick_Ocard_H @ B @ A )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ ( c_Hilbert__Choice_OEps @ ( tc_List_Olist @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ ( tc_List_Olist @ B ) @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_List_Olist @ B ) ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ B ) @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_List_Olist @ B ) ) @ c_fequal ) @ ( c_List_Oset @ B ) ) ) @ A ) ) ) @ ( c_List_Odistinct @ B ) ) ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( c_Nitpick_Ocard_H @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Ocard_H__def) ).
thf(5237,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( c_Nitpick_Ocard_H @ B @ A )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ ( c_Hilbert__Choice_OEps @ ( tc_List_Olist @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ ( tc_List_Olist @ B ) @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_List_Olist @ B ) ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ B ) @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_List_Olist @ B ) ) @ c_fequal ) @ ( c_List_Oset @ B ) ) ) @ A ) ) ) @ ( c_List_Odistinct @ B ) ) ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( c_Nitpick_Ocard_H @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(1566,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ ( c_Transitive__Closure_Otrancl @ C @ A ) ) )
<=> ? [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_member @ ( tc_prod @ C @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__power) ).
thf(8563,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ ( c_Transitive__Closure_Otrancl @ C @ A ) ) )
=> ? [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_member @ ( tc_prod @ C @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ D ) @ A ) ) ) ) )
& ( ? [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_member @ ( tc_prod @ C @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ D ) @ 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)],[1566]) ).
thf(468,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__infI1) ).
thf(4408,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(1959,axiom,
! [A: $i] : ( c_Wellfounded_Owf @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__empty) ).
thf(10039,plain,
! [A: $i] : ( c_Wellfounded_Owf @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1959]) ).
thf(1039,axiom,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) @ ( c_Relation_OId @ B ) ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__r__diff__Id) ).
thf(6602,plain,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) @ ( c_Relation_OId @ B ) ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).
thf(2416,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/sandbox/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded__le) ).
thf(11724,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)],[2416]) ).
thf(2332,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 ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ ( hAPP @ ( c_Fun_Othe__inv__into @ F @ E @ C @ D ) @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__into) ).
thf(11440,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 ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ ( hAPP @ ( c_Fun_Othe__inv__into @ F @ E @ C @ D ) @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2332]) ).
thf(1205,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_OCollect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool @ B ) @ ( c_HOL_OEx @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) @ ( hAPP @ ( c_COMBS @ D @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ C ) ) ) ) @ A ) ) ) ) )
<=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Set_OCollect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ D @ tc_HOL_Obool ) @ A ) @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__bex) ).
thf(7208,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_OCollect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool @ B ) @ ( c_HOL_OEx @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) @ ( hAPP @ ( c_COMBS @ D @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ C ) ) ) ) @ A ) ) ) ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Set_OCollect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ D @ tc_HOL_Obool ) @ A ) @ E ) ) ) ) ) )
& ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Set_OCollect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ D @ tc_HOL_Obool ) @ A ) @ E ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Set_OCollect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool @ B ) @ ( c_HOL_OEx @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) @ ( hAPP @ ( c_COMBS @ D @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ C ) ) ) ) @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1205]) ).
thf(1729,axiom,
! [A: $i,B: $i] : ( c_List_Olistrelp @ B @ A @ ( c_List_Olist_ONil @ B ) @ ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrelp_ONil) ).
thf(9152,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)],[1729]) ).
thf(1676,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__Diff__single) ).
thf(8988,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1676]) ).
thf(709,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ C @ B ) @ A ) )
<=> ( ( C
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( c_Product__Type_Ofst @ tc_Nat_Onat @ tc_Nat_Onat ) @ A ) ) @ B ) ) @ ( hAPP @ ( c_Product__Type_Osnd @ tc_Nat_Onat @ tc_Nat_Onat ) @ A ) ) )
& ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( c_Product__Type_Ofst @ tc_Nat_Onat @ tc_Nat_Onat ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( B
!= ( 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 ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Product__Type_Osnd @ tc_Nat_Onat @ tc_Nat_Onat ) @ A ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( c_Product__Type_Osnd @ tc_Nat_Onat @ 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 ) @ B ) @ ( hAPP @ ( c_Product__Type_Osnd @ tc_Nat_Onat @ tc_Nat_Onat ) @ A ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Product__Type_Osnd @ tc_Nat_Onat @ tc_Nat_Onat ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__rel__def) ).
thf(5348,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ C @ B ) @ A ) )
=> ( ( C
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( c_Product__Type_Ofst @ tc_Nat_Onat @ tc_Nat_Onat ) @ A ) ) @ B ) ) @ ( hAPP @ ( c_Product__Type_Osnd @ tc_Nat_Onat @ tc_Nat_Onat ) @ A ) ) )
& ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( c_Product__Type_Ofst @ tc_Nat_Onat @ tc_Nat_Onat ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( B
!= ( 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 ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Product__Type_Osnd @ tc_Nat_Onat @ tc_Nat_Onat ) @ A ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( c_Product__Type_Osnd @ tc_Nat_Onat @ 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 ) @ B ) @ ( hAPP @ ( c_Product__Type_Osnd @ tc_Nat_Onat @ tc_Nat_Onat ) @ A ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Product__Type_Osnd @ tc_Nat_Onat @ tc_Nat_Onat ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ) ) ) )
& ( ( ( C
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( c_Product__Type_Ofst @ tc_Nat_Onat @ tc_Nat_Onat ) @ A ) ) @ B ) ) @ ( hAPP @ ( c_Product__Type_Osnd @ tc_Nat_Onat @ tc_Nat_Onat ) @ A ) ) )
& ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( c_Product__Type_Ofst @ tc_Nat_Onat @ tc_Nat_Onat ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( B
!= ( 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 ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Product__Type_Osnd @ tc_Nat_Onat @ tc_Nat_Onat ) @ A ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( c_Product__Type_Osnd @ tc_Nat_Onat @ 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 ) @ B ) @ ( hAPP @ ( c_Product__Type_Osnd @ tc_Nat_Onat @ tc_Nat_Onat ) @ A ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Product__Type_Osnd @ tc_Nat_Onat @ tc_Nat_Onat ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(1752,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ C @ C @ C ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B ) @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_relpow_Osimps_I2_J) ).
thf(9268,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ C @ C @ C ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B ) @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1752]) ).
thf(489,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
<=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__empty__iff) ).
thf(4487,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( ( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(2501,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ G @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
<=> ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ C @ H ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF2__iff) ).
thf(12013,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ G @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ C @ H ) @ B ) @ A ) ) ) )
& ( ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ C @ H ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ G @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2501]) ).
thf(1682,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 ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( hAPP @ ( c_List_Oset @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ C @ B ) @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__update__memI) ).
thf(9003,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 ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( hAPP @ ( c_List_Oset @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ C @ B ) @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1682]) ).
thf(2236,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/sandbox/benchmark/theBenchmark.p',fact_IdI) ).
thf(11080,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)],[2236]) ).
thf(925,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ C @ B ) )
=> ( ( hAPP @ ( c_Set_OCollect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ A ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ A @ tc_HOL_Obool ) @ c_fequal ) @ B ) ) ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ C @ B ) )
=> ( ( hAPP @ ( c_Set_OCollect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ A ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ A @ tc_HOL_Obool ) @ c_fequal ) @ B ) ) ) @ C ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__conv__if) ).
thf(6194,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ C @ B ) )
=> ( ( hAPP @ ( c_Set_OCollect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ A ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ A @ tc_HOL_Obool ) @ c_fequal ) @ B ) ) ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ C @ B ) )
=> ( ( hAPP @ ( c_Set_OCollect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ A ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ A @ tc_HOL_Obool ) @ c_fequal ) @ B ) ) ) @ C ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(1133,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__UNIV__right) ).
thf(6971,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).
thf(215,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/sandbox/benchmark/theBenchmark.p',fact_listrel__eq__len) ).
thf(3439,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)],[215]) ).
thf(1,conjecture,
! [A: $i] :
( ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ B ) @ v_G ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ A @ B ) )
=> ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ B ) @ v_ts ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ B ) @ v_G ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ A @ B ) )
=> ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ B ) @ v_ts ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ A @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(2683,plain,
~ ! [A: $i] :
( ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ B ) @ v_G ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ A @ B ) )
=> ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ B ) @ v_ts ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(2686,plain,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ A ) @ v_G ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ sk1 @ A ) ),
inference(cnf,[status(esa)],[2683]) ).
thf(1331,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Set_Oinsert @ C ) ) @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__eq__UN) ).
thf(7697,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Set_Oinsert @ C ) ) @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1331]) ).
thf(10,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/sandbox/benchmark/theBenchmark.p',fact_zle__trans) ).
thf(2712,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)],[10]) ).
thf(1268,axiom,
! [A: $i,B: $i] : ( c_Relation_Orefl__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__rtrancl) ).
thf(7467,plain,
! [A: $i,B: $i] : ( c_Relation_Orefl__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1268]) ).
thf(2029,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ? [E: $i] : ( c_Fun_Obij__betw @ D @ B @ E @ C @ A )
<=> ( ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ C )
= ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_BIJ) ).
thf(10341,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( ? [E: $i] : ( c_Fun_Obij__betw @ D @ B @ E @ C @ A )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ C )
= ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A ) ) )
& ( ( ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ C )
= ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A ) )
=> ? [E: $i] : ( c_Fun_Obij__betw @ D @ B @ E @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2029]) ).
thf(1499,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_SetInterval_Oord_OatLeastLessThan @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) ) @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ tc_Nat_Onat ) @ c_fNot ) ) @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ A @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeastLessThan__empty) ).
thf(8320,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_SetInterval_Oord_OatLeastLessThan @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) ) @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ tc_Nat_Onat ) @ c_fNot ) ) @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ A @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1499]) ).
thf(719,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/sandbox/benchmark/theBenchmark.p',fact_nth__map) ).
thf(5425,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)],[719]) ).
thf(953,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/sandbox/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).
thf(6278,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)],[953]) ).
thf(2545,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/sandbox/benchmark/theBenchmark.p',fact_eqelem__imp__iff) ).
thf(12193,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)],[2545]) ).
thf(2014,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/sandbox/benchmark/theBenchmark.p',fact_not__in__set__insert) ).
thf(10282,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)],[2014]) ).
thf(2198,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/sandbox/benchmark/theBenchmark.p',fact_rtrancl__listrel1__ConsI1) ).
thf(10959,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)],[2198]) ).
thf(1611,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/sandbox/benchmark/theBenchmark.p',fact_distinct__remove1) ).
thf(8765,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)],[1611]) ).
thf(2484,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityI) ).
thf(11945,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2484]) ).
thf(1013,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Oset @ C ) @ ( hAPP @ ( c_List_Ofilter @ C @ B ) @ A ) )
= ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ C @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ C ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__filter) ).
thf(6505,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Oset @ C ) @ ( hAPP @ ( c_List_Ofilter @ C @ B ) @ A ) )
= ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ C @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ C ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(1798,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ C ) ) @ A ) @ ( c_List_Olists @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsp__lists__eq) ).
thf(9460,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ C ) ) @ A ) @ ( c_List_Olists @ C @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ C ) ) @ A ) @ ( c_List_Olists @ C @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1798]) ).
thf(758,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I3_J) ).
thf(5565,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(106,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/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2__lemma) ).
thf(3049,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)],[106]) ).
thf(300,axiom,
! [A: $i,B: $i] : ( c_Fun_Oinj__on @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) @ ( c_List_Orev @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__rev) ).
thf(3745,plain,
! [A: $i,B: $i] : ( c_Fun_Oinj__on @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) @ ( c_List_Orev @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(2234,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__mono) ).
thf(11072,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2234]) ).
thf(807,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ A ) )
=> ( ( A != B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I11_J) ).
thf(5755,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ A ) )
=> ( ( A != B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(270,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/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel1) ).
thf(3648,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)],[270]) ).
thf(2173,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/sandbox/benchmark/theBenchmark.p',fact_finite__converse) ).
thf(10869,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)],[2173]) ).
thf(2045,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 ) )
=> ( ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ D @ A ) @ ( hAPP @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oinsert__idem) ).
thf(10395,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 ) )
=> ( ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ D @ A ) @ ( hAPP @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2045]) ).
thf(195,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__int__def__symmetric) ).
thf(3365,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(1296,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/sandbox/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).
thf(7556,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)],[1296]) ).
thf(1698,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__vimage__eq) ).
thf(9052,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1698]) ).
thf(370,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/sandbox/benchmark/theBenchmark.p',fact_sublist__singleton) ).
thf(4026,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)],[370]) ).
thf(693,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Nat_Onat_Onat__case @ D @ C @ B @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__case__Suc) ).
thf(5288,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Nat_Onat_Onat__case @ D @ C @ B @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(1382,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ D @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ B ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__empty1) ).
thf(7873,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ D @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ B ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1382]) ).
thf(1170,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__disjoint) ).
thf(7096,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170]) ).
thf(2030,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/sandbox/benchmark/theBenchmark.p',fact_symD) ).
thf(10346,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)],[2030]) ).
thf(1790,axiom,
! [A: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__UNIV) ).
thf(9428,plain,
! [A: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1790]) ).
thf(2171,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Set_OCollect @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Set_OCollect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ B ) @ c_fNot ) @ A ) ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__not) ).
thf(10864,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Set_OCollect @ B ) @ A ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Set_OCollect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ B ) @ c_fNot ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Set_OCollect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ B ) @ c_fNot ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2171]) ).
thf(890,axiom,
! [A: $i,B: $i,C: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__fold1SetE) ).
thf(6089,plain,
! [A: $i,B: $i,C: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(1893,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/sandbox/benchmark/theBenchmark.p',fact_rtrancl__trans) ).
thf(9813,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)],[1893]) ).
thf(1072,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/sandbox/benchmark/theBenchmark.p',fact_drop__take) ).
thf(6727,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)],[1072]) ).
thf(1681,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Obij__betw @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__image__Compl__eq) ).
thf(9000,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Obij__betw @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1681]) ).
thf(284,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ ( hAPP @ A @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gfp__upperbound) ).
thf(3693,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ ( hAPP @ A @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(1185,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Fun_Othe__inv__into @ E @ D @ C @ B ) @ A )
= ( c_HOL_OThe @ E @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ E ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ E @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ E ) ) @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ D @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ c_fequal ) @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__def) ).
thf(7147,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Fun_Othe__inv__into @ E @ D @ C @ B ) @ A )
= ( c_HOL_OThe @ E @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ E ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ E @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ E ) ) @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ D @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ c_fequal ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185]) ).
thf(2257,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( c_Wellfounded_Owf @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__subset) ).
thf(11160,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( c_Wellfounded_Owf @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2257]) ).
thf(2193,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/sandbox/benchmark/theBenchmark.p',fact_SigmaE) ).
thf(10940,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)],[2193]) ).
thf(1512,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oimage @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) @ C ) ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oimage @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Inter__image) ).
thf(8370,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oimage @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) @ C ) ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oimage @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1512]) ).
thf(787,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/sandbox/benchmark/theBenchmark.p',fact_mult__eq__1__iff) ).
thf(5674,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)],[787]) ).
thf(2277,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ c_Nat_OSuc @ B )
= ( hAPP @ c_Nat_OSuc @ A ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__inject) ).
thf(11239,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)],[2277]) ).
thf(1256,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 @ B )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ D @ A ) ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Oremove) ).
thf(7422,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 @ B )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ D @ A ) ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1256]) ).
thf(2350,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_InterE) ).
thf(11513,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2350]) ).
thf(940,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/sandbox/benchmark/theBenchmark.p',fact_le__add2) ).
thf(6241,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)],[940]) ).
thf(2598,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/sandbox/benchmark/theBenchmark.p',fact_imageI) ).
thf(12421,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)],[2598]) ).
thf(1198,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/sandbox/benchmark/theBenchmark.p',fact_Cons__eq__appendI) ).
thf(7188,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)],[1198]) ).
thf(229,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Ozip @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ C @ B ) @ C ) @ ( c_Product__Type_Ofst @ C @ B ) ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ C @ B ) @ B ) @ ( c_Product__Type_Osnd @ C @ B ) ) @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__map__fst__snd) ).
thf(3481,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Ozip @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ C @ B ) @ C ) @ ( c_Product__Type_Ofst @ C @ B ) ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ C @ B ) @ B ) @ ( c_Product__Type_Osnd @ C @ B ) ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(623,axiom,
! [A: $i,B: $i] :
( ( B
!= ( c_List_Olist_ONil @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ ( c_List_Olast @ A @ B ) ) @ ( hAPP @ ( c_List_Oset @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__in__set) ).
thf(5005,plain,
! [A: $i,B: $i] :
( ( B
!= ( c_List_Olist_ONil @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ ( c_List_Olast @ A @ B ) ) @ ( hAPP @ ( c_List_Oset @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(1140,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/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc1) ).
thf(6996,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)],[1140]) ).
thf(1082,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Relation_ORange @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__rtrancl) ).
thf(6759,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Relation_ORange @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).
thf(2098,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate1D) ).
thf(10594,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2098]) ).
thf(1889,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/sandbox/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).
thf(9801,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)],[1889]) ).
thf(2537,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/sandbox/benchmark/theBenchmark.p',fact_neg__single__def) ).
thf(12165,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)],[2537]) ).
thf(2615,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/sandbox/benchmark/theBenchmark.p',fact_inj__on__contraD) ).
thf(12494,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)],[2615]) ).
thf(812,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/sandbox/benchmark/theBenchmark.p',fact_drop__all) ).
thf(5782,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)],[812]) ).
thf(666,axiom,
c_Wellfounded_Owf @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_FunDef_Opair__less,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__pair__less) ).
thf(5178,plain,
c_Wellfounded_Owf @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_FunDef_Opair__less,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(793,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/sandbox/benchmark/theBenchmark.p',fact_add__eq__if) ).
thf(5708,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)],[793]) ).
thf(2437,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ F @ E @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ F @ E @ D @ C ) @ ( hAPP @ ( hAPP @ E @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff1__fold__graph) ).
thf(11786,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ F @ E @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ F @ E @ D @ C ) @ ( hAPP @ ( hAPP @ E @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2437]) ).
thf(292,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_List_Oconcat @ C @ B )
= ( c_List_Oconcat @ C @ A ) )
=> ( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ ( tc_List_Olist @ C ) ) ) @ B )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ ( tc_List_Olist @ C ) ) ) @ A ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) @ D ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ B ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ C ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_Nat_Onat ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_Nat_Onat ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) @ ( tc_List_Olist @ C ) ) @ ( c_COMBB @ tc_Nat_Onat @ tc_HOL_Obool @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_List_Olist @ C ) ) @ c_fequal ) @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) ) ) ) @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) ) ) @ D ) ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat__injective) ).
thf(3717,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_List_Oconcat @ C @ B )
= ( c_List_Oconcat @ C @ A ) )
=> ( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ ( tc_List_Olist @ C ) ) ) @ B )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ ( tc_List_Olist @ C ) ) ) @ A ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) @ D ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ B ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ C ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_Nat_Onat ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_Nat_Onat ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) @ ( tc_List_Olist @ C ) ) @ ( c_COMBB @ tc_Nat_Onat @ tc_HOL_Obool @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_List_Olist @ C ) ) @ c_fequal ) @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) ) ) ) @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) ) ) @ D ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(717,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/sandbox/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel__disj) ).
thf(5412,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)],[717]) ).
thf(878,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= B ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I3_J) ).
thf(6046,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= B ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(1855,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DiffD2) ).
thf(9672,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1855]) ).
thf(1636,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/sandbox/benchmark/theBenchmark.p',fact_wfP__acyclicP) ).
thf(8851,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)],[1636]) ).
thf(938,axiom,
! [A: $i] : ( c_Relation_Otrans @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( c_Wellfounded_Ofinite__psubset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__finite__psubset) ).
thf(6236,plain,
! [A: $i] : ( c_Relation_Otrans @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( c_Wellfounded_Ofinite__psubset @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(1402,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Relation_OImage @ C @ C @ B ) @ A ) ) )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfE__pf) ).
thf(7944,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Relation_OImage @ C @ C @ B ) @ A ) ) )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1402]) ).
thf(1569,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessI) ).
thf(8578,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)],[1569]) ).
thf(2374,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__subset__iff) ).
thf(11588,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2374]) ).
thf(1232,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/sandbox/benchmark/theBenchmark.p',fact_append__eq__append__conv__if) ).
thf(7311,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)],[1232]) ).
thf(750,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_List_Olist_Olist__case @ F @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osimps_I5_J) ).
thf(5533,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_List_Olist_Olist__case @ F @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(605,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ B ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I4_J) ).
thf(4941,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ B ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(2640,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/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__rel__unique) ).
thf(12617,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)],[2640]) ).
thf(1793,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__disjoint2) ).
thf(9443,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1793]) ).
thf(906,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/sandbox/benchmark/theBenchmark.p',fact_o__assoc) ).
thf(6138,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)],[906]) ).
thf(374,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/sandbox/benchmark/theBenchmark.p',fact_nat__less__add__iff2) ).
thf(4047,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)],[374]) ).
thf(2028,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/sandbox/benchmark/theBenchmark.p',fact_finite__insert) ).
thf(10336,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)],[2028]) ).
thf(1147,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/sandbox/benchmark/theBenchmark.p',fact_fun__upd__apply) ).
thf(7018,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)],[1147]) ).
thf(2003,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/sandbox/benchmark/theBenchmark.p',fact_filter__eq__Cons__iff) ).
thf(10230,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)],[2003]) ).
thf(451,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Orefl__on @ C @ B @ A )
=> ( c_Relation_Orefl__on @ ( tc_List_Olist @ C ) @ ( c_List_Olists @ C @ B ) @ ( c_List_Olistrel @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__refl__on) ).
thf(4343,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Orefl__on @ C @ B @ A )
=> ( c_Relation_Orefl__on @ ( tc_List_Olist @ C ) @ ( c_List_Olists @ C @ B ) @ ( c_List_Olistrel @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(1635,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/sandbox/benchmark/theBenchmark.p',fact_zip__append2) ).
thf(8848,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)],[1635]) ).
thf(190,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_List_Olist_ONil @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ ( hAPP @ ( c_List_Ohd @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ A ) @ ( hAPP @ ( c_List_Otl @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__Suc) ).
thf(3350,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_List_Olist_ONil @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ ( hAPP @ ( c_List_Ohd @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ A ) @ ( hAPP @ ( c_List_Otl @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(1003,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/sandbox/benchmark/theBenchmark.p',fact_sequence__trans) ).
thf(6466,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)],[1003]) ).
thf(344,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/sandbox/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
thf(3915,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)],[344]) ).
thf(949,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ B ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__empty2) ).
thf(6268,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ B ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(1873,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/sandbox/benchmark/theBenchmark.p',fact_remove1__commute) ).
thf(9746,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)],[1873]) ).
thf(234,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
thf(3502,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(2360,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ D ) @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_weaken) ).
thf(11542,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ D ) @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2360]) ).
thf(2100,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singletonE) ).
thf(10599,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2100]) ).
thf(2318,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityD1) ).
thf(11382,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2318]) ).
thf(1559,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/sandbox/benchmark/theBenchmark.p',fact_le__diff__conv) ).
thf(8539,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)],[1559]) ).
thf(2471,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__greatest) ).
thf(11907,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2471]) ).
thf(1044,axiom,
! [A: $i,B: $i] :
( ( c_List_Osublist @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) )
= ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__empty) ).
thf(6623,plain,
! [A: $i,B: $i] :
( ( c_List_Osublist @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) )
= ( c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).
thf(1452,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/sandbox/benchmark/theBenchmark.p',fact_inj__on__imageI2) ).
thf(8133,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)],[1452]) ).
thf(531,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Orev @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ ( hAPP @ ( c_List_Orev @ C ) @ A ) ) @ ( hAPP @ ( c_List_Orev @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__append) ).
thf(4679,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Orev @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ ( hAPP @ ( c_List_Orev @ C ) @ A ) ) @ ( hAPP @ ( c_List_Orev @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(1211,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oimage @ C @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__image__eq) ).
thf(7235,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oimage @ C @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1211]) ).
thf(1711,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Un__distrib2) ).
thf(9096,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1711]) ).
thf(1732,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/sandbox/benchmark/theBenchmark.p',fact_diff__diff__left) ).
thf(9159,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)],[1732]) ).
thf(1947,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/sandbox/benchmark/theBenchmark.p',fact_takeWhile__eq__filter) ).
thf(9994,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)],[1947]) ).
thf(1343,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/sandbox/benchmark/theBenchmark.p',fact_fun__upd__other) ).
thf(7729,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)],[1343]) ).
thf(1116,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ tc_Nat_Onat ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ) )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__less) ).
thf(6904,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ tc_Nat_Onat ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ) )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).
thf(2459,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ H ) @ G ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ E @ G ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ H @ ( tc_fun @ B @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) @ F ) @ E ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP2__I) ).
thf(11863,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ H ) @ G ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ E @ G ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ H @ ( tc_fun @ B @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) @ F ) @ E ) @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2459]) ).
thf(1449,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ A ) )
= ( hAPP @ ( c_List_Olist_Olist__case @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) @ E @ ( c_List_Olist_ONil @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) ) @ ( tc_fun @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) ) @ ( tc_fun @ ( tc_fun @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) ) @ ( tc_fun @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) ) ) @ E ) @ ( c_COMBB @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_prod @ E @ D ) @ ( tc_fun @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) ) @ E ) @ ( c_List_Olist_OCons @ ( tc_prod @ E @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ D @ ( tc_prod @ E @ D ) ) @ ( c_Product__Type_OPair @ E @ D ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) ) @ ( c_List_Ozip @ E @ D ) ) @ A ) ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__Cons) ).
thf(8122,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ A ) )
= ( hAPP @ ( c_List_Olist_Olist__case @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) @ E @ ( c_List_Olist_ONil @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) ) @ ( tc_fun @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) ) @ ( tc_fun @ ( tc_fun @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) ) @ ( tc_fun @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) ) ) @ E ) @ ( c_COMBB @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) @ ( tc_List_Olist @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_prod @ E @ D ) @ ( tc_fun @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) ) @ E ) @ ( c_List_Olist_OCons @ ( tc_prod @ E @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ D @ ( tc_prod @ E @ D ) ) @ ( c_Product__Type_OPair @ E @ D ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) ) @ ( c_List_Ozip @ E @ D ) ) @ A ) ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1449]) ).
thf(170,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__int__def) ).
thf(3281,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(697,axiom,
! [A: $i,B: $i] : ( c_Fun_Obij__betw @ B @ B @ ( c_Fun_Oid @ B ) @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__id) ).
thf(5301,plain,
! [A: $i,B: $i] : ( c_Fun_Obij__betw @ B @ B @ ( c_Fun_Oid @ B ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(416,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ D @ C ) @ B ) @ A ) )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__list__update) ).
thf(4198,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ D @ C ) @ B ) @ A ) )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(2417,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ tc_HOL_Obool ) ) @ ( c_List_Olistrel1 @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_List_Olist @ B ) @ ( c_List_Olistrel1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1__rtrancl__subset__rtrancl__listrel1) ).
thf(11731,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ tc_HOL_Obool ) ) @ ( c_List_Olistrel1 @ 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)],[2417]) ).
thf(1799,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/sandbox/benchmark/theBenchmark.p',fact_dropWhile__append1) ).
thf(9465,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)],[1799]) ).
thf(1780,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( c_Relation_OId @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ C @ C @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) @ B ) ) @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Int__subset) ).
thf(9396,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( c_Relation_OId @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ C @ C @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) @ B ) ) @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1780]) ).
thf(398,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Product__Type_Ofst @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Opartition @ C @ B @ A ) )
= ( hAPP @ ( c_List_Ofilter @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partition__filter1) ).
thf(4137,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Product__Type_Ofst @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Opartition @ C @ B @ A ) )
= ( hAPP @ ( c_List_Ofilter @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(1081,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/sandbox/benchmark/theBenchmark.p',fact_dropWhile__append2) ).
thf(6754,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)],[1081]) ).
thf(1423,axiom,
! [A: $i,B: $i] :
( ( c_List_Oremove1 @ B @ A @ ( c_List_Olist_ONil @ B ) )
= ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remove1_Osimps_I1_J) ).
thf(8025,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)],[1423]) ).
thf(1561,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Osingle__valued @ E @ D @ ( hAPP @ ( c_Relation_Oconverse @ D @ E ) @ C ) )
=> ( ( hAPP @ ( c_Relation_OImage @ D @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ D @ E @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_OImage @ D @ E @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__Int__eq) ).
thf(8546,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Osingle__valued @ E @ D @ ( hAPP @ ( c_Relation_Oconverse @ D @ E ) @ C ) )
=> ( ( hAPP @ ( c_Relation_OImage @ D @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ D @ E @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_OImage @ D @ E @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1561]) ).
thf(1595,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ B ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ A ) )
& ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ B ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__append) ).
thf(8699,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ A ) )
& ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ B ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ A ) )
& ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ B ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1595]) ).
thf(2473,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/sandbox/benchmark/theBenchmark.p',fact_trancl__converseD) ).
thf(11912,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)],[2473]) ).
thf(1548,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Diff__cancel) ).
thf(8504,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1548]) ).
thf(43,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/sandbox/benchmark/theBenchmark.p',fact_self__quotient__aux2) ).
thf(2825,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)],[43]) ).
thf(2154,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ E @ B ) @ A ) ) )
=> ( c_Fun_Oinj__on @ E @ C @ ( c_Hilbert__Choice_Oinv__into @ C @ E @ A @ B ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__inv__into) ).
thf(10807,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ E @ B ) @ A ) ) )
=> ( c_Fun_Oinj__on @ E @ C @ ( c_Hilbert__Choice_Oinv__into @ C @ E @ A @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2154]) ).
thf(2083,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__inter__insert) ).
thf(10530,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2083]) ).
thf(445,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/sandbox/benchmark/theBenchmark.p',fact_nat__dvd__1__iff__1) ).
thf(4322,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)],[445]) ).
thf(2680,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/sandbox/benchmark/theBenchmark.p',fact_r__into__trancl_H) ).
thf(12785,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)],[2680]) ).
thf(404,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Oassoc) ).
thf(4156,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(688,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/sandbox/benchmark/theBenchmark.p',fact_nth__length__takeWhile) ).
thf(5269,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)],[688]) ).
thf(1041,axiom,
! [A: $i,B: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) )
= ( c_SetInterval_Oord_OatLeastLessThan @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) ) @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ tc_Nat_Onat ) @ c_fNot ) ) @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( 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/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeastLessThan__empty__iff2) ).
thf(6608,plain,
! [A: $i,B: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) )
= ( c_SetInterval_Oord_OatLeastLessThan @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) ) @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ tc_Nat_Onat ) @ c_fNot ) ) @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( 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 ) ) ) )
& ( ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) )
= ( c_SetInterval_Oord_OatLeastLessThan @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) ) @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ tc_Nat_Onat ) @ c_fNot ) ) @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(805,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/sandbox/benchmark/theBenchmark.p',fact_card__length) ).
thf(5750,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)],[805]) ).
thf(2575,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/sandbox/benchmark/theBenchmark.p',fact_Ball__set__list__all) ).
thf(12324,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)],[2575]) ).
thf(2448,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__subset) ).
thf(11831,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2448]) ).
thf(958,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Relation_ODomain @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__rtrancl) ).
thf(6291,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Relation_ODomain @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(1779,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/sandbox/benchmark/theBenchmark.p',fact_equivI) ).
thf(9394,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)],[1779]) ).
thf(1152,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/sandbox/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).
thf(7043,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)],[1152]) ).
thf(607,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( class_Lattices_Osemilattice__inf @ E )
& ( class_Lattices_Osemilattice__inf @ D ) )
=> ( ( c_Orderings_Oorder__class_Omono @ D @ E @ C )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ E ) @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mono__inf) ).
thf(4948,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( class_Lattices_Osemilattice__inf @ E )
& ( class_Lattices_Osemilattice__inf @ D ) )
=> ( ( c_Orderings_Oorder__class_Omono @ D @ E @ C )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ E ) @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(482,axiom,
! [A: $i,B: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( c_Complete__Lattice_OInf__class_OInf @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ B @ B @ ( c_Lattices_Osemilattice__inf__class_Oinf @ B ) ) @ ( c_Orderings_Otop__class_Otop @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fold__inf) ).
thf(4467,plain,
! [A: $i,B: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( c_Complete__Lattice_OInf__class_OInf @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ B @ B @ ( c_Lattices_Osemilattice__inf__class_Oinf @ B ) ) @ ( c_Orderings_Otop__class_Otop @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(627,axiom,
! [A: $i,B: $i] : ( c_Fun_Oinj__on @ B @ B @ ( c_COMBI @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__id2) ).
thf(5024,plain,
! [A: $i,B: $i] : ( c_Fun_Oinj__on @ B @ B @ ( c_COMBI @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(2095,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Equiv__Relations_Oequiv @ C @ B @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ C ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__type) ).
thf(10584,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Equiv__Relations_Oequiv @ C @ B @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ C ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2095]) ).
thf(816,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ tc_Nat_Onat ) @ A ) @ B )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
<=> ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
& ( ( hAPP @ A @ D )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( D != E )
=> ( ( hAPP @ A @ E )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__eq__Suc0__iff) ).
thf(5797,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ tc_Nat_Onat ) @ A ) @ B )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
& ( ( hAPP @ A @ D )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( D != E )
=> ( ( hAPP @ A @ E )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) )
& ( ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
& ( ( hAPP @ A @ D )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( D != E )
=> ( ( hAPP @ A @ E )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ tc_Nat_Onat ) @ A ) @ B )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(707,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__0__right) ).
thf(5342,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)],[707]) ).
thf(1509,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__equals__eq2) ).
thf(8357,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1509]) ).
thf(690,axiom,
! [A: $i] :
( ( hAPP @ ( c_List_Omap @ A @ A ) @ ( c_COMBI @ A ) )
= ( c_Fun_Oid @ ( tc_List_Olist @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_List_Omap_Oidentity) ).
thf(5274,plain,
! [A: $i] :
( ( hAPP @ ( c_List_Omap @ A @ A ) @ ( c_COMBI @ A ) )
= ( c_Fun_Oid @ ( tc_List_Olist @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(1666,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__Un) ).
thf(8951,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1666]) ).
thf(1630,axiom,
! [A: $i,B: $i] : ( c_Relation_Otrans @ B @ ( c_Relation_OId__on @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__Id__on) ).
thf(8834,plain,
! [A: $i,B: $i] : ( c_Relation_Otrans @ B @ ( c_Relation_OId__on @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1630]) ).
thf(968,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I8_J) ).
thf(6332,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(1721,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Osym @ B @ A )
=> ( ( c_Relation_Otrans @ B @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ B @ B @ B ) @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) ) @ A ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sym__trans__comp__subset) ).
thf(9123,plain,
! [A: $i,B: $i] :
( ( c_Relation_Osym @ B @ A )
=> ( ( c_Relation_Otrans @ B @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ B @ B @ B ) @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) ) @ A ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1721]) ).
thf(1246,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_OCollect @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_HOL_OEx @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBS @ D @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool @ D ) ) @ c_fequal ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__eq) ).
thf(7386,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_OCollect @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_HOL_OEx @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBS @ D @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool @ D ) ) @ c_fequal ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1246]) ).
thf(337,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ E ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ E ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__subset) ).
thf(3891,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ E ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ E ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(2582,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/sandbox/benchmark/theBenchmark.p',fact_conversep_Ointros) ).
thf(12351,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)],[2582]) ).
thf(161,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__commute) ).
thf(3248,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)],[161]) ).
thf(1576,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__Un__distrib1) ).
thf(8610,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1576]) ).
thf(216,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ ( hAPP @ ( c_List_Orev @ B ) @ A ) )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__rev) ).
thf(3442,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ ( hAPP @ ( c_List_Orev @ B ) @ A ) )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(164,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/sandbox/benchmark/theBenchmark.p',fact_zle__antisym) ).
thf(3263,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)],[164]) ).
thf(2181,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Obij__betw @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ A )
= ( hAPP @ ( c_Set_Oimage @ C @ D @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__vimage__eq__inv__image) ).
thf(10903,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Obij__betw @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ A )
= ( hAPP @ ( c_Set_Oimage @ C @ D @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2181]) ).
thf(1213,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__insert) ).
thf(7241,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1213]) ).
thf(2197,axiom,
! [A: $i,B: $i,C: $i] :
( C
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__Cons__self) ).
thf(10955,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)],[2197]) ).
thf(1084,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/sandbox/benchmark/theBenchmark.p',fact_map__is__Nil__conv) ).
thf(6766,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)],[1084]) ).
thf(1312,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Int__distrib2) ).
thf(7620,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1312]) ).
thf(1976,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/sandbox/benchmark/theBenchmark.p',fact_wf__iff__acyclic__if__finite) ).
thf(10121,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)],[1976]) ).
thf(763,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/sandbox/benchmark/theBenchmark.p',fact_length__pos__if__in__set) ).
thf(5585,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)],[763]) ).
thf(1945,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Oacyclic @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( c_Wellfounded_Oacyclic @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__subset) ).
thf(9989,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Oacyclic @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( c_Wellfounded_Oacyclic @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1945]) ).
thf(2191,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( c_Fun_Oinj__on @ E @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__inj__on) ).
thf(10935,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( c_Fun_Oinj__on @ E @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2191]) ).
thf(143,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/sandbox/benchmark/theBenchmark.p',fact_zless__linear) ).
thf(3195,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)],[143]) ).
thf(1222,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Diff__distrib1) ).
thf(7277,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1222]) ).
thf(99,axiom,
class_Groups_Ocomm__monoid__mult @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).
thf(3029,plain,
class_Groups_Ocomm__monoid__mult @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(453,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ ( tc_prod @ F @ E ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ F @ E ) @ D ) @ C ) ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Ozip @ F @ E ) @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ F @ D ) @ B ) @ ( hAPP @ ( c_Product__Type_Ofst @ F @ E ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ E @ C ) @ B ) @ ( hAPP @ ( c_Product__Type_Osnd @ F @ E ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_update__zip) ).
thf(4348,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ ( tc_prod @ F @ E ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ F @ E ) @ D ) @ C ) ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Ozip @ F @ E ) @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ F @ D ) @ B ) @ ( hAPP @ ( c_Product__Type_Ofst @ F @ E ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ E @ C ) @ B ) @ ( hAPP @ ( c_Product__Type_Osnd @ F @ E ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(581,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/sandbox/benchmark/theBenchmark.p',fact_nth__map__upt) ).
thf(4866,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)],[581]) ).
thf(1026,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Ounion__inter) ).
thf(6552,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).
thf(1712,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/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc2) ).
thf(9099,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)],[1712]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ D ) @ C ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) ) ) @ ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) ) )
= ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( 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 ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ 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 ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult) ).
thf(2814,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ D ) @ C ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) ) ) @ ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) ) )
= ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( 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 ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ 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 ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(472,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/sandbox/benchmark/theBenchmark.p',fact_lexord__append__leftD) ).
thf(4422,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)],[472]) ).
thf(2110,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/sandbox/benchmark/theBenchmark.p',fact_acyclic__insert) ).
thf(10630,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)],[2110]) ).
thf(1373,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/sandbox/benchmark/theBenchmark.p',fact_remove1__remdups) ).
thf(7825,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)],[1373]) ).
thf(168,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__1__right) ).
thf(3275,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)],[168]) ).
thf(1544,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/sandbox/benchmark/theBenchmark.p',fact_le__trans) ).
thf(8494,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)],[1544]) ).
thf(1900,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/sandbox/benchmark/theBenchmark.p',fact_part__equivp__refl__symp__transp) ).
thf(9828,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)],[1900]) ).
thf(2440,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/sandbox/benchmark/theBenchmark.p',fact_rtrancl__trancl__absorb) ).
thf(11798,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)],[2440]) ).
thf(1679,axiom,
! [A: $i,B: $i,C: $i] : ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__empty) ).
thf(8996,plain,
! [A: $i,B: $i,C: $i] : ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1679]) ).
thf(1833,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/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq2) ).
thf(9597,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)],[1833]) ).
thf(127,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( c_List_Ohd @ tc_Nat_Onat ) @ ( c_List_Oupt @ B @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__upt) ).
thf(3131,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( c_List_Ohd @ tc_Nat_Onat ) @ ( c_List_Oupt @ B @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(610,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( c_Complete__Lattice_OSup__class_OSup @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__insert) ).
thf(4956,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( c_Complete__Lattice_OSup__class_OSup @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(2268,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_OPow @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_PowD) ).
thf(11203,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_OPow @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2268]) ).
thf(1643,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__INT__distrib) ).
thf(8875,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1643]) ).
thf(122,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( c_Nat_Onat_Onat__case @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Nat_OSuc ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Orderings_Oord__class_Omin @ tc_Nat_Onat ) ) @ A ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__Suc2) ).
thf(3116,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( c_Nat_Onat_Onat__case @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Nat_OSuc ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Orderings_Oord__class_Omin @ tc_Nat_Onat ) ) @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(1249,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/sandbox/benchmark/theBenchmark.p',fact_drop__drop) ).
thf(7401,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)],[1249]) ).
thf(1441,axiom,
! [A: $i,B: $i] :
( ( c_List_Olists @ B @ A )
= ( hAPP @ ( c_Set_OCollect @ ( tc_List_Olist @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ B ) @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_List_Olist @ B ) ) @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ ( c_List_Oset @ B ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists__eq__set) ).
thf(8089,plain,
! [A: $i,B: $i] :
( ( c_List_Olists @ B @ A )
= ( hAPP @ ( c_Set_OCollect @ ( tc_List_Olist @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ B ) @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_List_Olist @ B ) ) @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ ( c_List_Oset @ B ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1441]) ).
thf(1479,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/sandbox/benchmark/theBenchmark.p',fact_listrel1I) ).
thf(8225,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)],[1479]) ).
thf(951,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oimage @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) @ C ) ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oimage @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Union__image) ).
thf(6274,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oimage @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) @ C ) ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oimage @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(2219,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/sandbox/benchmark/theBenchmark.p',fact_converse__iff) ).
thf(11025,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)],[2219]) ).
thf(282,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/sandbox/benchmark/theBenchmark.p',fact_mult__less__mono2) ).
thf(3689,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)],[282]) ).
thf(1827,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Relation_OImage @ D @ C @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ tc_HOL_Obool ) @ B ) ) ) @ A )
= ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool @ C ) @ ( c_HOL_OEx @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_COMBS @ D @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ A ) ) ) ) @ ( hAPP @ ( c_COMBC @ D @ C @ tc_HOL_Obool ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__Collect__split) ).
thf(9561,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Relation_OImage @ D @ C @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ tc_HOL_Obool ) @ B ) ) ) @ A )
= ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool @ C ) @ ( c_HOL_OEx @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_COMBS @ D @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ A ) ) ) ) @ ( hAPP @ ( c_COMBC @ D @ C @ tc_HOL_Obool ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1827]) ).
thf(1962,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__subset__Compl__iff) ).
thf(10053,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1962]) ).
thf(1707,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ C ) ) )
=> ( c_Fun_Oinj__on @ tc_Nat_Onat @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__diff__nat) ).
thf(9084,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ C ) ) )
=> ( c_Fun_Oinj__on @ tc_Nat_Onat @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1707]) ).
thf(2663,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/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oidem) ).
thf(12718,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)],[2663]) ).
thf(422,axiom,
class_Lattices_Osemilattice__inf @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__inf) ).
thf(4224,plain,
class_Lattices_Osemilattice__inf @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(1583,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Omax__extp @ D @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ D @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ D @ D ) ) ) ) @ ( c_Product__Type_OPair @ D @ D ) ) ) ) @ C ) @ B @ A )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ ( c_Wellfounded_Omax__ext @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__extp__max__ext__eq) ).
thf(8647,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Wellfounded_Omax__extp @ D @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ D @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ D @ D ) ) ) ) @ ( c_Product__Type_OPair @ D @ D ) ) ) ) @ C ) @ B @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ ( c_Wellfounded_Omax__ext @ D @ C ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ ( c_Wellfounded_Omax__ext @ D @ C ) ) )
=> ( c_Wellfounded_Omax__extp @ D @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ D @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ D @ D ) ) ) ) @ ( c_Product__Type_OPair @ D @ D ) ) ) ) @ C ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1583]) ).
thf(2510,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/sandbox/benchmark/theBenchmark.p',fact_RangeP_Oequations) ).
thf(12046,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)],[2510]) ).
thf(556,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/sandbox/benchmark/theBenchmark.p',fact_finite__maxlen) ).
thf(4761,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)],[556]) ).
thf(2295,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1D2) ).
thf(11299,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2295]) ).
thf(1723,axiom,
! [A: $i,B: $i] :
( ( c_Relation_OId__on @ B @ A )
= ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ B @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ B @ tc_HOL_Obool @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ tc_HOL_Obool @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ B ) @ ( c_COMBC @ B @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ B ) @ c_fconj ) ) @ c_fequal ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__def_H) ).
thf(9128,plain,
! [A: $i,B: $i] :
( ( c_Relation_OId__on @ B @ A )
= ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ B @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ B @ tc_HOL_Obool @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ tc_HOL_Obool @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ B ) @ ( c_COMBC @ B @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ B ) @ c_fconj ) ) @ c_fequal ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1723]) ).
thf(319,axiom,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
thf(3821,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(2000,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ B ) @ A ) ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__take__subset) ).
thf(10221,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ B ) @ A ) ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2000]) ).
thf(1357,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/sandbox/benchmark/theBenchmark.p',fact_comp__inj__on) ).
thf(7771,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)],[1357]) ).
thf(2335,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/sandbox/benchmark/theBenchmark.p',fact_rtrancl__listrel1__ConsI2) ).
thf(11448,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)],[2335]) ).
thf(2339,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI2) ).
thf(11458,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2339]) ).
thf(1771,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Oinv__image @ D @ C ) @ B ) @ A )
= ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ C @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ C ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ D ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ D ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ D ) @ ( tc_fun @ C @ ( tc_prod @ D @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ D @ D ) ) @ ( tc_fun @ ( tc_fun @ C @ D ) @ ( tc_fun @ C @ ( tc_prod @ D @ D ) ) ) @ C ) @ ( c_COMBB @ D @ ( tc_prod @ D @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ D @ ( tc_prod @ D @ D ) ) @ C ) @ ( c_Product__Type_OPair @ D @ D ) ) @ A ) ) ) @ A ) ) ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__image__def) ).
thf(9360,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Oinv__image @ D @ C ) @ B ) @ A )
= ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ C @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ C ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ D ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ D ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ D ) @ ( tc_fun @ C @ ( tc_prod @ D @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ D @ D ) ) @ ( tc_fun @ ( tc_fun @ C @ D ) @ ( tc_fun @ C @ ( tc_prod @ D @ D ) ) ) @ C ) @ ( c_COMBB @ D @ ( tc_prod @ D @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ D @ ( tc_prod @ D @ D ) ) @ C ) @ ( c_Product__Type_OPair @ D @ D ) ) @ A ) ) ) @ A ) ) ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1771]) ).
thf(1475,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ E @ D @ C ) @ B ) @ A )
= ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ E @ C ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ E @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ E ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool @ C ) @ ( c_HOL_OEx @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ E ) @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_COMBS @ D @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ E @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ E @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ E @ D ) ) ) ) @ ( c_Product__Type_OPair @ E @ D ) ) ) ) @ B ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( hAPP @ ( c_COMBC @ D @ C @ ( tc_prod @ D @ C ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__def) ).
thf(8214,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ E @ D @ C ) @ B ) @ A )
= ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ E @ C ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ E @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ E ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool @ C ) @ ( c_HOL_OEx @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ E ) @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_COMBS @ D @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ E @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ E @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ E @ D ) ) ) ) @ ( c_Product__Type_OPair @ E @ D ) ) ) ) @ B ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( hAPP @ ( c_COMBC @ D @ C @ ( tc_prod @ D @ C ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1475]) ).
thf(308,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ G @ ( hAPP @ ( c_Product__Type_Osnd @ F @ E ) @ D ) ) @ ( hAPP @ ( c_Product__Type_Ofst @ F @ E ) @ D ) ) )
=> ( ! [H: $i,I: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ G @ I ) @ H ) )
=> ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ B @ H ) @ I ) ) ) )
=> ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ F @ E @ A ) @ B ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_exE__realizer) ).
thf(3776,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ G @ ( hAPP @ ( c_Product__Type_Osnd @ F @ E ) @ D ) ) @ ( hAPP @ ( c_Product__Type_Ofst @ F @ E ) @ D ) ) )
=> ( ! [H: $i,I: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ G @ I ) @ H ) )
=> ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ B @ H ) @ I ) ) ) )
=> ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ F @ E @ A ) @ B ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(1132,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/sandbox/benchmark/theBenchmark.p',fact_image__compose) ).
thf(6968,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)],[1132]) ).
thf(659,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ C @ C @ B @ ( c_Fun_Oid @ C ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_id__o) ).
thf(5150,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ C @ C @ B @ ( c_Fun_Oid @ C ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(2444,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/sandbox/benchmark/theBenchmark.p',fact_in__set__conv__decomp) ).
thf(11812,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)],[2444]) ).
thf(1950,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_ODomain @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_ODomain @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__mono) ).
thf(10010,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_ODomain @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_ODomain @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1950]) ).
thf(369,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_List_Osublist @ C @ B @ A )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ C @ tc_Nat_Onat ) @ C ) @ ( c_Product__Type_Ofst @ C @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_List_Ofilter @ ( tc_prod @ C @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_prod @ C @ tc_Nat_Onat ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_prod @ C @ tc_Nat_Onat ) ) @ ( c_member @ tc_Nat_Onat ) ) @ ( c_Product__Type_Osnd @ C @ tc_Nat_Onat ) ) ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ C @ tc_Nat_Onat ) @ B ) @ ( c_List_Oupt @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__def) ).
thf(4023,plain,
! [A: $i,B: $i,C: $i] :
( ( c_List_Osublist @ C @ B @ A )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ C @ tc_Nat_Onat ) @ C ) @ ( c_Product__Type_Ofst @ C @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_List_Ofilter @ ( tc_prod @ C @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_prod @ C @ tc_Nat_Onat ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_prod @ C @ tc_Nat_Onat ) ) @ ( c_member @ tc_Nat_Onat ) ) @ ( c_Product__Type_Osnd @ C @ tc_Nat_Onat ) ) ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ C @ tc_Nat_Onat ) @ B ) @ ( c_List_Oupt @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(2102,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_InterD) ).
thf(10606,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2102]) ).
thf(118,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/sandbox/benchmark/theBenchmark.p',fact_int__one__le__iff__zero__less) ).
thf(3089,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)],[118]) ).
thf(1142,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/sandbox/benchmark/theBenchmark.p',fact_equiv__def) ).
thf(7000,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)],[1142]) ).
thf(505,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/sandbox/benchmark/theBenchmark.p',fact_all__nth__imp__all__set) ).
thf(4568,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)],[505]) ).
thf(191,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ D ) @ A ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ C ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ A @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ D ) @ A ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ C ) ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__head__upt__Suc) ).
thf(3353,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ D ) @ A ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ C ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ A @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ D ) @ A ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ C ) ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(1422,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__Int__distrib) ).
thf(8022,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1422]) ).
thf(2385,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__absorb2) ).
thf(11628,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2385]) ).
thf(647,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Product__Type_Osnd @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Opartition @ C @ B @ A ) )
= ( hAPP @ ( c_List_Ofilter @ C @ ( hAPP @ ( c_Fun_Ocomp @ tc_HOL_Obool @ tc_HOL_Obool @ C @ c_fNot ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partition__filter2) ).
thf(5108,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Product__Type_Osnd @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Opartition @ C @ B @ A ) )
= ( hAPP @ ( c_List_Ofilter @ C @ ( hAPP @ ( c_Fun_Ocomp @ tc_HOL_Obool @ tc_HOL_Obool @ C @ c_fNot ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(1484,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/sandbox/benchmark/theBenchmark.p',fact_snoc__listrel1__snoc__iff) ).
thf(8242,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)],[1484]) ).
thf(474,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Orderings_Oorder @ D )
& ( class_Orderings_Oorder @ C ) )
=> ( ( c_Orderings_Oorder__class_Omono @ C @ D @ B )
=> ( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ A ) )
& ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ E ) @ F ) ) ) )
=> ( ( c_Orderings_Oord__class_OLeast @ D @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ C @ D @ B ) @ A ) ) )
= ( hAPP @ B @ ( c_Orderings_Oord__class_OLeast @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Least__mono) ).
thf(4428,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Orderings_Oorder @ D )
& ( class_Orderings_Oorder @ C ) )
=> ( ( c_Orderings_Oorder__class_Omono @ C @ D @ B )
=> ( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ A ) )
& ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ E ) @ F ) ) ) )
=> ( ( c_Orderings_Oord__class_OLeast @ D @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ C @ D @ B ) @ A ) ) )
= ( hAPP @ B @ ( c_Orderings_Oord__class_OLeast @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(2067,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/sandbox/benchmark/theBenchmark.p',fact_acc_OaccI) ).
thf(10469,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)],[2067]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ A @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__insert) ).
thf(2745,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ A @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(1645,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/sandbox/benchmark/theBenchmark.p',fact_same__append__eq) ).
thf(8880,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)],[1645]) ).
thf(1320,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/sandbox/benchmark/theBenchmark.p',fact_Domain__converse) ).
thf(7665,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)],[1320]) ).
thf(2428,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/sandbox/benchmark/theBenchmark.p',fact_finite__imageD) ).
thf(11760,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)],[2428]) ).
thf(2263,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ E ) @ B ) ) @ ( hAPP @ ( c_List_Oset @ E ) @ A ) ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_List_Omap @ E @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ E @ D ) @ C ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__map__eq__map) ).
thf(11183,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ E ) @ B ) ) @ ( hAPP @ ( c_List_Oset @ E ) @ A ) ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_List_Omap @ E @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ E @ D ) @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( 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)],[2263]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ D ) ) @ C ) @ ( hAPP @ ( c_List_Oset @ ( tc_List_Olist @ D ) ) @ ( c_Enum_On__lists @ D @ B @ A ) ) ) )
=> ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__n__lists__elem) ).
thf(2989,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ D ) ) @ C ) @ ( hAPP @ ( c_List_Oset @ ( tc_List_Olist @ D ) ) @ ( c_Enum_On__lists @ D @ B @ A ) ) ) )
=> ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(1540,axiom,
! [A: $i,B: $i] :
( ( c_Set_Othe__elem @ B @ A )
= ( c_HOL_OThe @ B @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool @ B ) @ ( hAPP @ c_fequal @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__elem__def) ).
thf(8483,plain,
! [A: $i,B: $i] :
( ( c_Set_Othe__elem @ B @ A )
= ( c_HOL_OThe @ B @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool @ B ) @ ( hAPP @ c_fequal @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1540]) ).
thf(155,axiom,
! [A: $i,B: $i] :
( ( c_Enum_On__lists @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ ( tc_List_Olist @ B ) ) @ ( c_List_Olist_ONil @ B ) ) @ ( c_List_Olist_ONil @ ( tc_List_Olist @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__lists_Osimps_I1_J) ).
thf(3231,plain,
! [A: $i,B: $i] :
( ( c_Enum_On__lists @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ ( tc_List_Olist @ B ) ) @ ( c_List_Olist_ONil @ B ) ) @ ( c_List_Olist_ONil @ ( tc_List_Olist @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(1485,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/sandbox/benchmark/theBenchmark.p',fact_Cons__eq__append__conv) ).
thf(8257,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)],[1485]) ).
thf(1613,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__Diff) ).
thf(8770,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1613]) ).
thf(1652,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/sandbox/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).
thf(8907,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)],[1652]) ).
thf(803,axiom,
! [A: $i,B: $i] :
( ( B
!= ( c_List_Olist_ONil @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ A ) @ ( c_List_Obutlast @ A @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ A ) @ ( c_List_Olast @ A @ B ) ) @ ( c_List_Olist_ONil @ A ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__butlast__last__id) ).
thf(5744,plain,
! [A: $i,B: $i] :
( ( B
!= ( c_List_Olist_ONil @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ A ) @ ( c_List_Obutlast @ A @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ A ) @ ( c_List_Olast @ A @ B ) ) @ ( c_List_Olist_ONil @ A ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(2337,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/sandbox/benchmark/theBenchmark.p',fact_zip__Cons__Cons) ).
thf(11453,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)],[2337]) ).
thf(2670,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/sandbox/benchmark/theBenchmark.p',fact_image__eqI) ).
thf(12745,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)],[2670]) ).
thf(1911,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__mp) ).
thf(9877,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1911]) ).
thf(1188,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Nitpick_Oprod @ D @ C @ B @ A )
= ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Oprod__def) ).
thf(7156,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Nitpick_Oprod @ D @ C @ B @ A )
= ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188]) ).
thf(2494,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/sandbox/benchmark/theBenchmark.p',fact_rel__compE) ).
thf(11986,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)],[2494]) ).
thf(2409,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/sandbox/benchmark/theBenchmark.p',fact_converseE) ).
thf(11696,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)],[2409]) ).
thf(943,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/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
thf(6253,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)],[943]) ).
thf(2276,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/sandbox/benchmark/theBenchmark.p',fact_list__ex__simps_I1_J) ).
thf(11232,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)],[2276]) ).
thf(392,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ ( c_Complete__Lattice_OInf__class_OInf @ C @ A ) ) )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Inf__iff) ).
thf(4119,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ ( c_Complete__Lattice_OInf__class_OInf @ C @ A ) ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ D ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ ( c_Complete__Lattice_OInf__class_OInf @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(237,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/sandbox/benchmark/theBenchmark.p',fact_takeWhile__eq__take) ).
thf(3517,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)],[237]) ).
thf(198,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__mult @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Groups_Oone__class_Oone @ D ) ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ D ) ) @ B )
= ( c_Groups_Oone__class_Oone @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__1) ).
thf(3374,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__mult @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Groups_Oone__class_Oone @ D ) ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ D ) ) @ B )
= ( c_Groups_Oone__class_Oone @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(1573,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
<=> ( ( c_Fun_Oinj__on @ E @ D @ C @ B )
& ( c_Fun_Oinj__on @ E @ D @ C @ A )
& ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ A ) @ B ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__Un) ).
thf(8590,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( c_Fun_Oinj__on @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( c_Fun_Oinj__on @ E @ D @ C @ B )
& ( c_Fun_Oinj__on @ E @ D @ C @ A )
& ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ A ) @ B ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
& ( ( ( c_Fun_Oinj__on @ E @ D @ C @ B )
& ( c_Fun_Oinj__on @ E @ D @ C @ A )
& ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ A ) @ B ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) )
=> ( c_Fun_Oinj__on @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1573]) ).
thf(266,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oorder__class_Omono @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ C )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mono__Int) ).
thf(3638,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oorder__class_Omono @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ C )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(1804,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__assoc) ).
thf(9480,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1804]) ).
thf(2684,plain,
~ ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ sk1 @ sk2 ),
inference(cnf,[status(esa)],[2683]) ).
thf(12803,plain,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ A ) @ v_G ) )
| ( ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ sk1 @ A )
!= ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[2686,2684]) ).
thf(12804,plain,
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ sk2 ) @ v_G ) ),
inference(pattern_uni,[status(thm)],[12803:[bind(A,$thf( sk2 ))]]) ).
thf(1650,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/sandbox/benchmark/theBenchmark.p',fact_single__valued__rel__comp) ).
thf(8902,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)],[1650]) ).
thf(999,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/sandbox/benchmark/theBenchmark.p',fact_prod_Osimps_I2_J) ).
thf(6455,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)],[999]) ).
thf(516,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Groups_Ocomm__monoid__add @ F )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ E @ F ) @ C ) @ D )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ B @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ F @ B ) @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ E @ F ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ B ) @ ( c_Set_OCollect @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ B ) @ ( hAPP @ ( c_COMBS @ E @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ E ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ E @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ E ) ) @ D ) ) ) ) @ ( hAPP @ ( c_COMBC @ E @ B @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ E ) @ c_fequal ) @ A ) ) ) ) ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ B @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__image__gen) ).
thf(4617,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Groups_Ocomm__monoid__add @ F )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ E @ F ) @ C ) @ D )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ B @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ F @ B ) @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ E @ F ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ B ) @ ( c_Set_OCollect @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ B ) @ ( hAPP @ ( c_COMBS @ E @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ E ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ E @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ E ) ) @ D ) ) ) ) @ ( hAPP @ ( c_COMBC @ E @ B @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ E ) @ c_fequal ) @ A ) ) ) ) ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ B @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(2432,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_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnI1) ).
thf(11773,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_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2432]) ).
thf(2077,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Predicate_Oconversep @ C @ B @ ( c_Predicate_Oconversep @ B @ C @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_conversep__conversep) ).
thf(10516,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)],[2077]) ).
thf(2302,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/sandbox/benchmark/theBenchmark.p',fact_acc__downwards__aux) ).
thf(11321,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)],[2302]) ).
thf(1497,axiom,
! [A: $i] :
( ( c_List_Oremdups @ A @ ( c_List_Olist_ONil @ A ) )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remdups_Osimps_I1_J) ).
thf(8310,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)],[1497]) ).
thf(910,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Relation_OImage @ C @ B @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__empty) ).
thf(6149,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Relation_OImage @ C @ B @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(1158,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/sandbox/benchmark/theBenchmark.p',fact_less__diff__conv) ).
thf(7060,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)],[1158]) ).
thf(1045,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/sandbox/benchmark/theBenchmark.p',fact_rtrancl__converse) ).
thf(6626,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)],[1045]) ).
thf(2358,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ComplE) ).
thf(11538,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2358]) ).
thf(2457,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__lower) ).
thf(11859,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2457]) ).
thf(25,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_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ B ) ) @ ( hAPP @ c_Int_Onat @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__relations_I3_J) ).
thf(2767,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_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ B ) ) @ ( hAPP @ c_Int_Onat @ 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_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ B ) ) @ ( hAPP @ c_Int_Onat @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(1535,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/sandbox/benchmark/theBenchmark.p',fact_List_Omap_Ocomp) ).
thf(8468,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)],[1535]) ).
thf(1038,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_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ F ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ F ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ F ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ D ) ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__subset__cancel2) ).
thf(6599,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_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ F ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ F ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ F ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ D ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ F ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ F ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ F ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(490,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/sandbox/benchmark/theBenchmark.p',fact_take__butlast) ).
thf(4492,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)],[490]) ).
thf(702,axiom,
! [A: $i,B: $i] :
( ( ( c_SetInterval_Oord_OatLeastAtMost @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) )
<=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeastatMost__empty__iff) ).
thf(5323,plain,
! [A: $i,B: $i] :
( ( ( ( c_SetInterval_Oord_OatLeastAtMost @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) )
=> ~ ( 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 ) )
=> ( ( c_SetInterval_Oord_OatLeastAtMost @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(714,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ A ) )
<=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__inf) ).
thf(5397,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A )
= B ) )
& ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A )
= B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(773,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/sandbox/benchmark/theBenchmark.p',fact_length__filter__map) ).
thf(5622,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)],[773]) ).
thf(736,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/sandbox/benchmark/theBenchmark.p',fact_mult__eq__if) ).
thf(5480,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)],[736]) ).
thf(152,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1) ).
thf(3216,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(1482,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 ) @ 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oremove) ).
thf(8235,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 ) @ 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1482]) ).
thf(1088,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/sandbox/benchmark/theBenchmark.p',fact_le__iff__add) ).
thf(6781,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)],[1088]) ).
thf(1126,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__eq__0__iff) ).
thf(6936,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) ) ) )
& ( ( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
| ~ ( 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)],[1126]) ).
thf(1511,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ A ) )
= ( c_Nat_Onat_Onat__case @ ( tc_List_Olist @ D ) @ ( c_List_Olist_ONil @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( c_List_Otake @ D ) ) @ A ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__Cons) ).
thf(8367,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ A ) )
= ( c_Nat_Onat_Onat__case @ ( tc_List_Olist @ D ) @ ( c_List_Olist_ONil @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( c_List_Otake @ D ) ) @ A ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1511]) ).
thf(2202,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/sandbox/benchmark/theBenchmark.p',fact_wf__not__refl) ).
thf(10967,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)],[2202]) ).
thf(225,axiom,
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ ( c_SetInterval_Oord__class_OgreaterThan @ tc_Nat_Onat ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__greaterThan__UNIV) ).
thf(3470,plain,
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ ( c_SetInterval_Oord__class_OgreaterThan @ tc_Nat_Onat ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(1817,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/sandbox/benchmark/theBenchmark.p',fact_insert__Nil) ).
thf(9529,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)],[1817]) ).
thf(2421,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ C @ A ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate1D) ).
thf(11741,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ C @ A ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2421]) ).
thf(1123,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I1_J) ).
thf(6923,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).
thf(2113,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/sandbox/benchmark/theBenchmark.p',fact_zip__same) ).
thf(10650,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)],[2113]) ).
thf(829,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ F @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ F @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ F @ E @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ F @ E @ D ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__distrib2) ).
thf(5851,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ F @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ F @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ F @ E @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ F @ E @ D ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(272,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/sandbox/benchmark/theBenchmark.p',fact_upt__conv__Cons) ).
thf(3657,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)],[272]) ).
thf(2542,axiom,
! [A: $i,B: $i] :
( ? [C: $i] : ( hBOOL @ ( hAPP @ B @ C ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Hilbert__Choice_OEps @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tfl__some) ).
thf(12180,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)],[2542]) ).
thf(1154,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/sandbox/benchmark/theBenchmark.p',fact_fun__upd__idem) ).
thf(7047,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)],[1154]) ).
thf(2495,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__mono) ).
thf(11991,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2495]) ).
thf(296,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeast @ C ) @ B ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeast @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast__subset__iff) ).
thf(3734,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeast @ C ) @ B ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeast @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeast @ C ) @ B ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeast @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(821,axiom,
c_FunDef_Oreduction__pair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) ) @ c_FunDef_Omax__strict ) @ c_FunDef_Omax__weak ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__rpair__set) ).
thf(5829,plain,
c_FunDef_Oreduction__pair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) ) @ c_FunDef_Omax__strict ) @ c_FunDef_Omax__weak ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(1909,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 ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnCI) ).
thf(9869,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 ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1909]) ).
thf(94,axiom,
class_Orderings_Oord @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).
thf(3014,plain,
class_Orderings_Oord @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(1477,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/sandbox/benchmark/theBenchmark.p',fact_less__SucI) ).
thf(8220,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)],[1477]) ).
thf(797,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/sandbox/benchmark/theBenchmark.p',fact_take__1__Cons) ).
thf(5727,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)],[797]) ).
thf(1940,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ E ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__inj__on__le) ).
thf(9973,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ E ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1940]) ).
thf(324,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_Ovimage @ B @ B @ ( c_COMBI @ B ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__ident) ).
thf(3835,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_Ovimage @ B @ B @ ( c_COMBI @ B ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(2455,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A ) )
<=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ B @ F ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__subset__iff) ).
thf(11849,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ B @ F ) ) @ A ) ) ) )
& ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ B @ F ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2455]) ).
thf(2116,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/sandbox/benchmark/theBenchmark.p',fact_list__all__simps_I1_J) ).
thf(10665,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)],[2116]) ).
thf(1867,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnionI) ).
thf(9725,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1867]) ).
thf(1693,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/sandbox/benchmark/theBenchmark.p',fact_diff__add__inverse) ).
thf(9039,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)],[1693]) ).
thf(2194,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Fun_Obij__betw @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ D ) )
=> ( ( ( hAPP @ ( c_Set_Oimage @ G @ F @ E ) @ B )
= A )
=> ( c_Fun_Obij__betw @ G @ F @ E @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__subset) ).
thf(10945,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Fun_Obij__betw @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ D ) )
=> ( ( ( hAPP @ ( c_Set_Oimage @ G @ F @ E ) @ B )
= A )
=> ( c_Fun_Obij__betw @ G @ F @ E @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2194]) ).
thf(433,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ B ) @ ( hAPP @ ( c_Product__Type_Ofst @ C @ B ) @ A ) ) @ ( hAPP @ ( c_Product__Type_Osnd @ C @ B ) @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__collapse) ).
thf(4265,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ B ) @ ( hAPP @ ( c_Product__Type_Ofst @ C @ B ) @ A ) ) @ ( hAPP @ ( c_Product__Type_Osnd @ C @ B ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(480,axiom,
! [A: $i,B: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ B )
=> ( ( c_Orderings_Oorder__class_Omono @ B @ B @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B ) @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ B @ A ) ) @ ( hAPP @ A @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gfp__lemma2) ).
thf(4460,plain,
! [A: $i,B: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ B )
=> ( ( c_Orderings_Oorder__class_Omono @ B @ B @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B ) @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ B @ A ) ) @ ( hAPP @ A @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(1102,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ C ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ C ) @ A ) ) ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ D ) ) @ B ) ) )
=> ( c_Relation_Orefl__on @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__onI) ).
thf(6828,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ C ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ C ) @ A ) ) ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ D ) ) @ B ) ) )
=> ( c_Relation_Orefl__on @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).
thf(2128,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ C )
= B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ ( hAPP @ ( c_Set_Oimage @ E @ F @ ( c_Hilbert__Choice_Oinv__into @ F @ E @ C @ D ) ) @ A ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__inv__into__cancel) ).
thf(10702,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ C )
= B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ ( hAPP @ ( c_Set_Oimage @ E @ F @ ( c_Hilbert__Choice_Oinv__into @ F @ E @ C @ D ) ) @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2128]) ).
thf(495,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_List_Olistset @ C @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( c_List_Oset__Cons @ C @ B @ ( c_List_Olistset @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listset_Osimps_I2_J) ).
thf(4507,plain,
! [A: $i,B: $i,C: $i] :
( ( c_List_Olistset @ C @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( c_List_Oset__Cons @ C @ B @ ( c_List_Olistset @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(2414,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__iff) ).
thf(11716,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2414]) ).
thf(2652,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/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Opos__union__def) ).
thf(12657,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)],[2652]) ).
thf(466,axiom,
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeast @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast__0) ).
thf(4400,plain,
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeast @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(1267,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_OPow @ B ) @ A )
= ( hAPP @ ( c_Set_OCollect @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__def) ).
thf(7464,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_OPow @ B ) @ A )
= ( hAPP @ ( c_Set_OCollect @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1267]) ).
thf(1507,axiom,
! [A: $i,B: $i] : ( c_Relation_Otrans @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__rtrancl) ).
thf(8352,plain,
! [A: $i,B: $i] : ( c_Relation_Otrans @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1507]) ).
thf(1009,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__Un__eq) ).
thf(6487,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(1564,axiom,
! [A: $i] : ( c_Fun_Oinj__on @ A @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__singleton) ).
thf(8558,plain,
! [A: $i] : ( c_Fun_Oinj__on @ A @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1564]) ).
thf(2347,axiom,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
thf(11495,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2347]) ).
thf(1282,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__triv) ).
thf(7509,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1282]) ).
thf(2621,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/sandbox/benchmark/theBenchmark.p',fact_list__ex1__iff) ).
thf(12517,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)],[2621]) ).
thf(979,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ G @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) @ F ) @ ( c_COMBB @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ G @ tc_HOL_Obool ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ F ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) @ D ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__INT__distrib2) ).
thf(6382,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ G @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) @ F ) @ ( c_COMBB @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ G @ tc_HOL_Obool ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ F ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) @ D ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(1036,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Compl) ).
thf(6594,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).
thf(1880,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI) ).
thf(9768,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1880]) ).
thf(1984,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/sandbox/benchmark/theBenchmark.p',fact_pair__in__Id__conv) ).
thf(10157,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)],[1984]) ).
thf(1303,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hAPP @ ( c_Set_Oimage @ D @ B @ A ) @ C )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ ( tc_fun @ B @ tc_HOL_Obool ) @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ B @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ D ) @ ( c_Set_Oinsert @ B ) ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__eq__fold__image) ).
thf(7588,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hAPP @ ( c_Set_Oimage @ D @ B @ A ) @ C )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ ( tc_fun @ B @ tc_HOL_Obool ) @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ B @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ D ) @ ( c_Set_Oinsert @ B ) ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1303]) ).
thf(2356,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IntD1) ).
thf(11533,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2356]) ).
thf(1493,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/sandbox/benchmark/theBenchmark.p',fact_fun__upd__def) ).
thf(8293,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)],[1493]) ).
thf(1789,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ B ) @ ( c_Product__Type_Ocurry @ D @ C @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__curry) ).
thf(9425,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ B ) @ ( c_Product__Type_Ocurry @ D @ C @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1789]) ).
thf(1782,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/sandbox/benchmark/theBenchmark.p',fact_distinct__take) ).
thf(9401,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)],[1782]) ).
thf(464,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hAPP @ ( c_Product__Type_Osnd @ G @ F ) @ ( hAPP @ ( c_Product__Type_Omap__pair @ E @ G @ D @ F @ C @ B ) @ A ) )
= ( hAPP @ B @ ( hAPP @ ( c_Product__Type_Osnd @ E @ D ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__prod__fun) ).
thf(4396,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hAPP @ ( c_Product__Type_Osnd @ G @ F ) @ ( hAPP @ ( c_Product__Type_Omap__pair @ E @ G @ D @ F @ C @ B ) @ A ) )
= ( hAPP @ B @ ( hAPP @ ( c_Product__Type_Osnd @ E @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(2511,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ B ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Hilbert__Choice_OEps @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_someI) ).
thf(12051,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)],[2511]) ).
thf(1054,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/sandbox/benchmark/theBenchmark.p',fact_nat__le__linear) ).
thf(6657,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)],[1054]) ).
thf(2424,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ D ) @ tc_HOL_Obool ) ) @ C ) @ A ) )
=> ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_thin) ).
thf(11748,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ D ) @ tc_HOL_Obool ) ) @ C ) @ A ) )
=> ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2424]) ).
thf(879,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 ) ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__0__I) ).
thf(6054,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 ) ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(861,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__partition2) ).
thf(5985,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(887,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ A ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_irrefl__tranclI) ).
thf(6081,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ A ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(2184,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Typedef_Otype__definition @ E @ D @ C @ B @ A )
=> ( ( hAPP @ ( c_Set_Oimage @ D @ E @ B ) @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_OAbs__image) ).
thf(10913,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Typedef_Otype__definition @ E @ D @ C @ B @ A )
=> ( ( hAPP @ ( c_Set_Oimage @ D @ E @ B ) @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2184]) ).
thf(2078,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 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IntI) ).
thf(10519,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 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2078]) ).
thf(2062,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ B ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__empty__eq2) ).
thf(10454,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ B ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ B ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2062]) ).
thf(537,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Nat_Onat @ 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 ) ) @ B ) @ D ) ) @ c_FunDef_Opair__less ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ A ) @ C ) ) @ c_FunDef_Omax__strict ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ B ) @ A ) ) @ C ) ) @ c_FunDef_Omax__strict ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smax__insertI) ).
thf(4696,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Nat_Onat @ 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 ) ) @ B ) @ D ) ) @ c_FunDef_Opair__less ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ A ) @ C ) ) @ c_FunDef_Omax__strict ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ B ) @ A ) ) @ C ) ) @ c_FunDef_Omax__strict ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(855,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/sandbox/benchmark/theBenchmark.p',fact_list__ex__append) ).
thf(5957,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)],[855]) ).
thf(617,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ D ) @ C ) @ ( c_List_OtakeWhile @ D @ B @ A ) )
= ( c_List_OtakeWhile @ ( tc_prod @ E @ D ) @ ( hAPP @ ( c_Fun_Ocomp @ D @ tc_HOL_Obool @ ( tc_prod @ E @ D ) @ B ) @ ( c_Product__Type_Osnd @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ D ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__takeWhile__snd) ).
thf(4988,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ D ) @ C ) @ ( c_List_OtakeWhile @ D @ B @ A ) )
= ( c_List_OtakeWhile @ ( tc_prod @ E @ D ) @ ( hAPP @ ( c_Fun_Ocomp @ D @ tc_HOL_Obool @ ( tc_prod @ E @ D ) @ B ) @ ( c_Product__Type_Osnd @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ D ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(1742,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Equiv__Relations_Ocongruent @ D @ C @ B @ A )
<=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ E ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ D @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ C ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ C ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBB @ C @ tc_HOL_Obool @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ c_fequal ) @ A ) ) ) @ A ) ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_congruent__def) ).
thf(9204,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Equiv__Relations_Ocongruent @ D @ C @ B @ A )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ E ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ D @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ C ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ C ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBB @ C @ tc_HOL_Obool @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ c_fequal ) @ A ) ) ) @ A ) ) @ E ) ) ) )
& ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ E ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ D @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ C ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ C ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBB @ C @ tc_HOL_Obool @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ c_fequal ) @ A ) ) ) @ A ) ) @ E ) ) )
=> ( c_Equiv__Relations_Ocongruent @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1742]) ).
thf(722,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/sandbox/benchmark/theBenchmark.p',fact_card_Oeq__fold__g) ).
thf(5433,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)],[722]) ).
thf(1174,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ B ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) ) ) @ ( hAPP @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Oinsert__remove) ).
thf(7107,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ B ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) ) ) @ ( hAPP @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).
thf(2300,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ A ) @ c_Int_OInteg ) )
=> ~ ! [B: $i] :
( A
!= ( hAPP @ c_Int_ORep__Integ @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Rep__Integ__cases) ).
thf(11314,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ A ) @ c_Int_OInteg ) )
=> ~ ! [B: $i] :
( A
!= ( hAPP @ c_Int_ORep__Integ @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2300]) ).
thf(1365,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__left__absorb) ).
thf(7792,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1365]) ).
thf(1469,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_OPow @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_Set_OPow @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__INT__eq) ).
thf(8190,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_OPow @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_Set_OPow @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1469]) ).
thf(1714,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_Fun_Ocomp @ C @ ( tc_fun @ E @ tc_HOL_Obool ) @ F @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ C @ A ) @ D ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__o) ).
thf(9103,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_Fun_Ocomp @ C @ ( tc_fun @ E @ tc_HOL_Obool ) @ F @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ C @ A ) @ D ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1714]) ).
thf(1363,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/sandbox/benchmark/theBenchmark.p',fact_drop__zip) ).
thf(7786,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)],[1363]) ).
thf(841,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Oset @ C ) @ ( hAPP @ ( c_List_OremoveAll @ C @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__removeAll) ).
thf(5892,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Oset @ C ) @ ( hAPP @ ( c_List_OremoveAll @ C @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(2139,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__iff) ).
thf(10746,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2139]) ).
thf(2434,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Obij__betw @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( hAPP @ ( c_Set_OCollect @ D ) @ A ) )
= ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ tc_HOL_Obool @ C ) @ A ) @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__image__Collect__eq) ).
thf(11778,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Obij__betw @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( hAPP @ ( c_Set_OCollect @ D ) @ A ) )
= ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ tc_HOL_Obool @ C ) @ A ) @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2434]) ).
thf(1184,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ ( tc_fun @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ D ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ C ) @ ( c_Set_Oinsert @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__def) ).
thf(7144,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ ( tc_fun @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ D ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ C ) @ ( c_Set_Oinsert @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).
thf(446,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/sandbox/benchmark/theBenchmark.p',fact_n__less__n__mult__m) ).
thf(4329,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)],[446]) ).
thf(2659,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Obij__betw @ F @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ E @ F @ B @ ( c_Hilbert__Choice_Oinv__into @ F @ E @ C @ D ) ) @ A )
= ( hAPP @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__inv__into__eq) ).
thf(12706,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Obij__betw @ F @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ E @ F @ B @ ( c_Hilbert__Choice_Oinv__into @ F @ E @ C @ D ) ) @ A )
= ( hAPP @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2659]) ).
thf(2231,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 @ E ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ D ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP1__I) ).
thf(11064,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 @ E ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ D ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2231]) ).
thf(2393,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__subset) ).
thf(11656,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2393]) ).
thf(145,axiom,
( ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint )
!= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__0__neq__1) ).
thf(3199,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)],[145]) ).
thf(840,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ ( hAPP @ ( c_Set_OCollect @ D ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Set_OCollect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool @ B ) @ ( c_HOL_OEx @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) @ ( hAPP @ ( c_COMBS @ D @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) @ C ) ) ) @ A ) ) ) ) )
<=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ C @ E ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Set_OCollect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ D @ tc_HOL_Obool ) @ A ) @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__bounded__ex) ).
thf(5888,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ ( hAPP @ ( c_Set_OCollect @ D ) @ C ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Set_OCollect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool @ B ) @ ( c_HOL_OEx @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) @ ( hAPP @ ( c_COMBS @ D @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) @ C ) ) ) @ A ) ) ) ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ C @ E ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Set_OCollect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ D @ tc_HOL_Obool ) @ A ) @ E ) ) ) ) ) )
& ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ C @ E ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Set_OCollect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ D @ tc_HOL_Obool ) @ A ) @ E ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Set_OCollect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool @ B ) @ ( c_HOL_OEx @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) @ ( hAPP @ ( c_COMBS @ D @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) @ C ) ) ) @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(749,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/sandbox/benchmark/theBenchmark.p',fact_drop__eq__Nil) ).
thf(5526,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)],[749]) ).
thf(640,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ ( c_List_Oremdups @ B @ ( c_List_Oconcat @ B @ A ) ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_List_Olist @ B ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ ( tc_List_Olist @ B ) ) @ A ) ) @ ( c_List_Oset @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__remdups__concat) ).
thf(5084,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ ( c_List_Oremdups @ B @ ( c_List_Oconcat @ B @ A ) ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_List_Olist @ B ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ ( tc_List_Olist @ B ) ) @ A ) ) @ ( c_List_Oset @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(114,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( 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 ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ E ) @ A ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ D ) @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ E ) @ A ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ C ) @ B ) ) )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ E ) @ A ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ D ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__add__nat__ivl) ).
thf(3075,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( 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 ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ E ) @ A ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ D ) @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ E ) @ A ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ C ) @ B ) ) )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ E ) @ A ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ D ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(382,axiom,
! [A: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ tc_Nat_Onat ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__size) ).
thf(4072,plain,
! [A: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ tc_Nat_Onat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(1480,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ C @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ C ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__def) ).
thf(8229,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ C @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ C ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1480]) ).
thf(1993,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ C ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ B @ F ) )
=> ( hBOOL @ ( hAPP @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_Set_OCollect @ E ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( c_Set_OCollect @ E ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Collect__mono) ).
thf(10189,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ C ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ B @ F ) )
=> ( hBOOL @ ( hAPP @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_Set_OCollect @ E ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( c_Set_OCollect @ E ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1993]) ).
thf(204,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__zadd__distrib) ).
thf(3393,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(2292,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/sandbox/benchmark/theBenchmark.p',fact_finite__imageI) ).
thf(11293,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)],[2292]) ).
thf(2479,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/sandbox/benchmark/theBenchmark.p',fact_wf__insert) ).
thf(11926,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)],[2479]) ).
thf(1371,axiom,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ ( c_Nat_Ocompow @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__is__UN__rel__pow) ).
thf(7818,plain,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ ( c_Nat_Ocompow @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1371]) ).
thf(1241,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__insert__distrib) ).
thf(7369,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1241]) ).
thf(704,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_List_Opartition @ D @ C @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ ( tc_List_Olist @ D ) @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) ) @ ( tc_fun @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) ) @ ( tc_List_Olist @ D ) ) @ ( c_COMBS @ ( tc_List_Olist @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) ) @ ( tc_List_Olist @ D ) ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( tc_List_Olist @ D ) ) @ ( hAPP @ ( c_If @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ C @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_List_Olist @ D ) @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( tc_List_Olist @ D ) ) @ ( c_Product__Type_OPair @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ D ) @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( tc_fun @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) ) @ ( tc_List_Olist @ D ) ) @ ( c_COMBB @ ( tc_List_Olist @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( tc_List_Olist @ D ) ) ) @ ( c_Product__Type_OPair @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) ) @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) ) ) ) @ ( c_List_Opartition @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partition_Osimps_I2_J) ).
thf(5333,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_List_Opartition @ D @ C @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ ( tc_List_Olist @ D ) @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) ) @ ( tc_fun @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) ) @ ( tc_List_Olist @ D ) ) @ ( c_COMBS @ ( tc_List_Olist @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) ) @ ( tc_List_Olist @ D ) ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( tc_List_Olist @ D ) ) @ ( hAPP @ ( c_If @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ C @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_List_Olist @ D ) @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( tc_List_Olist @ D ) ) @ ( c_Product__Type_OPair @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ D ) @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( tc_fun @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) ) @ ( tc_List_Olist @ D ) ) @ ( c_COMBB @ ( tc_List_Olist @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( tc_List_Olist @ D ) ) ) @ ( c_Product__Type_OPair @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) ) @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) ) ) ) @ ( c_List_Opartition @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(2010,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
=> ~ ( ( hBOOL @ ( hAPP @ C @ A ) )
=> ~ ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1E) ).
thf(10271,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
=> ~ ( ( hBOOL @ ( hAPP @ C @ A ) )
=> ~ ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2010]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_List_Olist_ONil @ B ) )
=> ( ( hAPP @ ( c_List_Otl @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ ( hAPP @ ( c_List_Otl @ B ) @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tl__append2) ).
thf(3163,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_List_Olist_ONil @ B ) )
=> ( ( hAPP @ ( c_List_Otl @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ ( hAPP @ ( c_List_Otl @ B ) @ C ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(1173,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ C @ B ) @ ( hAPP @ ( c_Relation_Oconverse @ B @ C ) @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__converse) ).
thf(7104,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)],[1173]) ).
thf(220,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Nitpick_Ofold__graph_H @ D @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_H_Oequations_I1_J) ).
thf(3453,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Nitpick_Ofold__graph_H @ D @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(2186,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ G @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
<=> ? [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ C @ H ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP2__iff) ).
thf(10918,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ G @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ? [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ C @ H ) @ B ) @ A ) ) ) )
& ( ? [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ C @ H ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ G @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2186]) ).
thf(924,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/sandbox/benchmark/theBenchmark.p',fact_not__less__eq) ).
thf(6189,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)],[924]) ).
thf(1670,axiom,
! [A: $i,B: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_OPow @ B ) @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__Pow__eq) ).
thf(8972,plain,
! [A: $i,B: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_OPow @ B ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1670]) ).
thf(56,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__0L) ).
thf(2880,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ 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)],[56]) ).
thf(577,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( c_Orderings_Oorder__class_Omono @ C @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ A ) @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ A ) @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ C @ B ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ A ) @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_coinduct) ).
thf(4847,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( c_Orderings_Oorder__class_Omono @ C @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ A ) @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ A ) @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ C @ B ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ A ) @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(1243,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_List_Oconcat @ D @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ ( tc_List_Olist @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ C ) @ ( c_List_Olist_OCons @ D ) ) @ B ) ) @ ( c_List_Olist_ONil @ D ) ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ D ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat__map__singleton) ).
thf(7376,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_List_Oconcat @ D @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ ( tc_List_Olist @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ C ) @ ( c_List_Olist_OCons @ D ) ) @ B ) ) @ ( c_List_Olist_ONil @ D ) ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ D ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1243]) ).
thf(1892,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__lower2) ).
thf(9811,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1892]) ).
thf(756,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( c_Product__Type_Osnd @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) )
= A )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__eqD) ).
thf(5558,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( c_Product__Type_Osnd @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) )
= A )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(375,axiom,
! [A: $i,B: $i] :
( ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ B @ tc_HOL_Obool ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_COMBI @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__def) ).
thf(4050,plain,
! [A: $i,B: $i] :
( ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ B @ tc_HOL_Obool ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_COMBI @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(2570,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/sandbox/benchmark/theBenchmark.p',fact_exE__some) ).
thf(12296,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)],[2570]) ).
thf(2525,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Quotient_ORespects @ C @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__respects) ).
thf(12105,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Quotient_ORespects @ C @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Quotient_ORespects @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2525]) ).
thf(2320,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/sandbox/benchmark/theBenchmark.p',fact_splitD) ).
thf(11389,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)],[2320]) ).
thf(544,axiom,
! [A: $i,B: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ B )
=> ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Complete__Lattice_Ocomplete__lattice) ).
thf(4724,plain,
! [A: $i,B: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ B )
=> ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__Un__disjoint) ).
thf(2925,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(2407,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/sandbox/benchmark/theBenchmark.p',fact_tranclD2) ).
thf(11691,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)],[2407]) ).
thf(2451,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__absorb2) ).
thf(11838,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2451]) ).
thf(397,axiom,
! [A: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oempty) ).
thf(4134,plain,
! [A: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(2413,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( c_Set_OCollect @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
<=> ! [C: $i] :
~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).
thf(11709,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( c_Set_OCollect @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ! [C: $i] :
~ ( hBOOL @ ( hAPP @ A @ C ) ) )
& ( ! [C: $i] :
~ ( hBOOL @ ( hAPP @ A @ C ) )
=> ( ( hAPP @ ( c_Set_OCollect @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2413]) ).
thf(1146,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__cartesian__product) ).
thf(7015,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).
thf(1582,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/sandbox/benchmark/theBenchmark.p',fact_less__eq) ).
thf(8642,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)],[1582]) ).
thf(347,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ C @ B @ C @ A ) @ ( c_Fun_Oid @ C ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__id) ).
thf(3923,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ C @ B @ C @ A ) @ ( c_Fun_Oid @ C ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(173,axiom,
! [A: $i] :
( ( hAPP @ ( c_List_Otl @ A ) @ ( c_List_Olist_ONil @ A ) )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tl_Osimps_I1_J) ).
thf(3290,plain,
! [A: $i] :
( ( hAPP @ ( c_List_Otl @ A ) @ ( c_List_Olist_ONil @ A ) )
= ( c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(1301,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/sandbox/benchmark/theBenchmark.p',fact_lexord__trans) ).
thf(7581,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)],[1301]) ).
thf(1609,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( c_Equiv__Relations_Oequiv @ I @ H @ G )
=> ( ( c_Equiv__Relations_Oequiv @ F @ E @ D )
=> ( ( c_Equiv__Relations_Ocongruent2 @ I @ F @ ( tc_fun @ C @ tc_HOL_Obool ) @ G @ D @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ E ) )
=> ( c_Equiv__Relations_Ocongruent @ I @ ( tc_fun @ C @ tc_HOL_Obool ) @ G @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ I ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ F @ F @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) ) ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_congruent2__implies__congruent__UN) ).
thf(8759,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( c_Equiv__Relations_Oequiv @ I @ H @ G )
=> ( ( c_Equiv__Relations_Oequiv @ F @ E @ D )
=> ( ( c_Equiv__Relations_Ocongruent2 @ I @ F @ ( tc_fun @ C @ tc_HOL_Obool ) @ G @ D @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ E ) )
=> ( c_Equiv__Relations_Ocongruent @ I @ ( tc_fun @ C @ tc_HOL_Obool ) @ G @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ I ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ F @ F @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) ) ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1609]) ).
thf(993,axiom,
! [A: $i] : ( c_Relation_Osym @ A @ ( c_Relation_OId @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sym__Id) ).
thf(6438,plain,
! [A: $i] : ( c_Relation_Osym @ A @ ( c_Relation_OId @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(2633,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Equiv__Relations_Oequivp @ D @ C )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ B @ E ) )
=> ( hBOOL @ ( hAPP @ A @ E ) ) )
=> ( ? [E: $i] : ( hBOOL @ ( hAPP @ B @ E ) )
=> ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ ( c_Quotient_ORespects @ D @ C ) ) )
& ( hBOOL @ ( hAPP @ A @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bex__reg__right) ).
thf(12582,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Equiv__Relations_Oequivp @ D @ C )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ B @ E ) )
=> ( hBOOL @ ( hAPP @ A @ E ) ) )
=> ( ? [E: $i] : ( hBOOL @ ( hAPP @ B @ E ) )
=> ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ ( c_Quotient_ORespects @ D @ C ) ) )
& ( hBOOL @ ( hAPP @ A @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2633]) ).
thf(2668,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/sandbox/benchmark/theBenchmark.p',fact_insert__image) ).
thf(12735,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)],[2668]) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Groups_Ocomm__monoid__add @ F )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ D ) )
=> ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ G ) @ D ) )
=> ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ H ) @ D ) )
=> ( ( G != H )
=> ( ( ( hAPP @ C @ G )
= ( hAPP @ C @ H ) )
=> ( ( hAPP @ B @ ( hAPP @ C @ G ) )
= ( c_Groups_Ozero__class_Ozero @ F ) ) ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ A @ F ) @ B ) @ ( hAPP @ ( c_Set_Oimage @ E @ A @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ E @ F ) @ ( hAPP @ ( c_Fun_Ocomp @ A @ F @ E @ B ) @ C ) ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__reindex__nonzero) ).
thf(3152,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Groups_Ocomm__monoid__add @ F )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ D ) )
=> ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ G ) @ D ) )
=> ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ H ) @ D ) )
=> ( ( G != H )
=> ( ( ( hAPP @ C @ G )
= ( hAPP @ C @ H ) )
=> ( ( hAPP @ B @ ( hAPP @ C @ G ) )
= ( c_Groups_Ozero__class_Ozero @ F ) ) ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ A @ F ) @ B ) @ ( hAPP @ ( c_Set_Oimage @ E @ A @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ E @ F ) @ ( hAPP @ ( c_Fun_Ocomp @ A @ F @ E @ B ) @ C ) ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(1069,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/sandbox/benchmark/theBenchmark.p',fact_symp__def) ).
thf(6717,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)],[1069]) ).
thf(2136,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ B ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Pow__iff) ).
thf(10734,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2136]) ).
thf(406,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_List_Oset @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ D @ C ) @ B ) @ A ) )
= ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool @ ( tc_prod @ D @ C ) ) @ ( c_HOL_OEx @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_prod @ D @ C ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( tc_prod @ D @ C ) ) @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_prod @ D @ C ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( tc_prod @ D @ C ) ) @ ( c_COMBB @ ( tc_prod @ D @ C ) @ tc_HOL_Obool @ tc_Nat_Onat ) ) @ c_fequal ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ C @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ D @ C ) ) @ ( hAPP @ ( c_List_Onth @ D ) @ B ) ) ) @ ( hAPP @ ( c_List_Onth @ C ) @ A ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ B ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__zip) ).
thf(4162,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_List_Oset @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ D @ C ) @ B ) @ A ) )
= ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool @ ( tc_prod @ D @ C ) ) @ ( c_HOL_OEx @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_prod @ D @ C ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( tc_prod @ D @ C ) ) @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_prod @ D @ C ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( tc_prod @ D @ C ) ) @ ( c_COMBB @ ( tc_prod @ D @ C ) @ tc_HOL_Obool @ tc_Nat_Onat ) ) @ c_fequal ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ C @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ D @ C ) ) @ ( hAPP @ ( c_List_Onth @ D ) @ B ) ) ) @ ( hAPP @ ( c_List_Onth @ C ) @ A ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ B ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(1388,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/sandbox/benchmark/theBenchmark.p',fact_map__comp__map) ).
thf(7899,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)],[1388]) ).
thf(927,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__left__absorb) ).
thf(6204,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(2222,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/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__comp) ).
thf(11036,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)],[2222]) ).
thf(1761,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/sandbox/benchmark/theBenchmark.p',fact_fun__upd__upd) ).
thf(9309,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)],[1761]) ).
thf(824,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/sandbox/benchmark/theBenchmark.p',fact_nat__diff__add__eq2) ).
thf(5834,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)],[824]) ).
thf(111,axiom,
class_Groups_Ocomm__monoid__mult @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
thf(3068,plain,
class_Groups_Ocomm__monoid__mult @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(371,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( B = A )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__iff) ).
thf(4033,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( ( B = A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ A ) @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ A ) @ B ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(2600,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/sandbox/benchmark/theBenchmark.p',fact_pos__single__def) ).
thf(12430,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)],[2600]) ).
thf(1624,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Set_Ovimage @ F @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ ( c_Set_Ovimage @ F @ E @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__UN) ).
thf(8817,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Set_Ovimage @ F @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ ( c_Set_Ovimage @ F @ E @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1624]) ).
thf(1464,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_OPow @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) )
= ( hAPP @ ( c_Set_OCollect @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ tc_HOL_Obool @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_HOL_OEx @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_COMBS @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ c_fconj ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_COMBB @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ c_fequal ) ) @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ tc_HOL_Obool @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_member @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) @ ( c_Set_OPow @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__Compl) ).
thf(8173,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_OPow @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) )
= ( hAPP @ ( c_Set_OCollect @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ tc_HOL_Obool @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_HOL_OEx @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_COMBS @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ c_fconj ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_COMBB @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ c_fequal ) ) @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ tc_HOL_Obool @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_member @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) @ ( c_Set_OPow @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1464]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( class_Groups_Ocomm__monoid__add @ H )
=> ( ( c_Fun_Oinj__on @ G @ F @ E @ D )
=> ( ( C
= ( hAPP @ ( c_Set_Oimage @ G @ F @ E ) @ D ) )
=> ( ! [I: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ I ) @ D ) )
=> ( ( hAPP @ B @ I )
= ( hAPP @ A @ ( hAPP @ E @ I ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ F @ H ) @ A ) @ C )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ G @ H ) @ B ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__reindex__cong) ).
thf(2750,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( class_Groups_Ocomm__monoid__add @ H )
=> ( ( c_Fun_Oinj__on @ G @ F @ E @ D )
=> ( ( C
= ( hAPP @ ( c_Set_Oimage @ G @ F @ E ) @ D ) )
=> ( ! [I: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ I ) @ D ) )
=> ( ( hAPP @ B @ I )
= ( hAPP @ A @ ( hAPP @ E @ I ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ F @ H ) @ A ) @ C )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ G @ H ) @ B ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(633,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/sandbox/benchmark/theBenchmark.p',fact_n__less__m__mult__n) ).
thf(5045,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)],[633]) ).
thf(1335,axiom,
! [A: $i,B: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__derivs_Oequations_I1_J) ).
thf(7707,plain,
! [A: $i,B: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1335]) ).
thf(2576,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/sandbox/benchmark/theBenchmark.p',fact_CollectE) ).
thf(12330,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)],[2576]) ).
thf(2482,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__by__empty) ).
thf(11939,plain,
! [A: $i,B: $i,C: $i] :
( ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2482]) ).
thf(1966,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/sandbox/benchmark/theBenchmark.p',fact_wf__irrefl) ).
thf(10070,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)],[1966]) ).
thf(553,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oorder__class_Omono @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ C )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mono__Un) ).
thf(4751,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oorder__class_Omono @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ C )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(2278,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
? [E: $i] :
( ( c_Fun_Oinj__on @ D @ ( tc_prod @ C @ D ) @ E @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ ( tc_prod @ C @ D ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ex__inj__on__UNION__Sigma) ).
thf(11242,plain,
! [A: $i,B: $i,C: $i,D: $i] :
? [E: $i] :
( ( c_Fun_Oinj__on @ D @ ( tc_prod @ C @ D ) @ E @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ ( tc_prod @ C @ D ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2278]) ).
thf(801,axiom,
! [A: $i,B: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ B )
=> ( ( c_Complete__Lattice_OInf__class_OInf @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__singleton) ).
thf(5738,plain,
! [A: $i,B: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ B )
=> ( ( c_Complete__Lattice_OInf__class_OInf @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(2299,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/sandbox/benchmark/theBenchmark.p',fact_SigmaI) ).
thf(11312,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)],[2299]) ).
thf(2647,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/sandbox/benchmark/theBenchmark.p',fact_DomainP_Ointros) ).
thf(12638,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)],[2647]) ).
thf(1874,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ B ) )
=> ( ( hAPP @ ( c_List_Ofilter @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ ( c_List_Osublist @ C @ B @ A ) ) ) ) @ B )
= ( c_List_Osublist @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__in__sublist) ).
thf(9749,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ B ) )
=> ( ( hAPP @ ( c_List_Ofilter @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ ( c_List_Osublist @ C @ B @ A ) ) ) ) @ B )
= ( c_List_Osublist @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1874]) ).
thf(2304,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/sandbox/benchmark/theBenchmark.p',fact_insert__commute) ).
thf(11325,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)],[2304]) ).
thf(2574,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/sandbox/benchmark/theBenchmark.p',fact_equalityCE) ).
thf(12311,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)],[2574]) ).
thf(1087,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ D ) @ B ) @ A ) ) )
=> ~ ! [E: $i] :
( ( C
= ( hAPP @ ( c_Relation_OImage @ D @ D @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotientE) ).
thf(6777,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ D ) @ B ) @ A ) ) )
=> ~ ! [E: $i] :
( ( C
= ( hAPP @ ( c_Relation_OImage @ D @ D @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).
thf(2247,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/sandbox/benchmark/theBenchmark.p',fact_in__set__zipE) ).
thf(11119,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)],[2247]) ).
thf(1369,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I3_J) ).
thf(7807,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1369]) ).
thf(2086,axiom,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_List_Omember @ B ) @ ( c_List_Olist_ONil @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_member__rec_I2_J) ).
thf(10551,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)],[2086]) ).
thf(710,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/sandbox/benchmark/theBenchmark.p',fact_lexord__append__leftI) ).
thf(5384,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)],[710]) ).
thf(290,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/sandbox/benchmark/theBenchmark.p',fact_listrel_ONil) ).
thf(3712,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)],[290]) ).
thf(1796,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__eq) ).
thf(9452,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1796]) ).
thf(1626,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__Int__subset) ).
thf(8823,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1626]) ).
thf(1455,axiom,
! [A: $i] : ( c_Relation_Oantisym @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisym__empty) ).
thf(8141,plain,
! [A: $i] : ( c_Relation_Oantisym @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1455]) ).
thf(2241,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OField @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_OField @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mono__Field) ).
thf(11104,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OField @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_OField @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2241]) ).
thf(1234,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Otrans @ B @ A )
=> ( ( c_Transitive__Closure_Otrancl @ B @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__id) ).
thf(7336,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)],[1234]) ).
thf(102,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ B ) ) @ ( hAPP @ c_Int_Onat @ 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 ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__nat__conj) ).
thf(3036,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ B ) ) @ ( hAPP @ c_Int_Onat @ 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 ) @ 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 @ tc_Int_Oint ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ B ) ) @ ( hAPP @ c_Int_Onat @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(2252,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ C ) )
<=> ( ( ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__class__eq__iff) ).
thf(11136,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ E @ D @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ C ) )
=> ( ( ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ D ) ) ) )
& ( ( ( ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2252]) ).
thf(809,axiom,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
thf(5772,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(1392,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/sandbox/benchmark/theBenchmark.p',fact_le__add__diff) ).
thf(7909,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)],[1392]) ).
thf(2500,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/sandbox/benchmark/theBenchmark.p',fact_takeWhile__append2) ).
thf(12008,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)],[2500]) ).
thf(973,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/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
thf(6347,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)],[973]) ).
thf(695,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
thf(5296,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(1012,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ D @ C ) @ B ) @ A )
= ( c_List_Olist_ONil @ D ) )
<=> ( C
= ( c_List_Olist_ONil @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__nonempty) ).
thf(6498,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ D @ C ) @ B ) @ A )
= ( c_List_Olist_ONil @ D ) )
=> ( C
= ( c_List_Olist_ONil @ D ) ) )
& ( ( C
= ( c_List_Olist_ONil @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ D @ C ) @ B ) @ A )
= ( c_List_Olist_ONil @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(2507,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ B ) @ A ) )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__1) ).
thf(12036,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ B ) @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2507]) ).
thf(2524,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/sandbox/benchmark/theBenchmark.p',fact_type__definition_ORep__inverse) ).
thf(12101,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)],[2524]) ).
thf(1592,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/sandbox/benchmark/theBenchmark.p',fact_add__le__mono1) ).
thf(8686,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)],[1592]) ).
thf(599,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/sandbox/benchmark/theBenchmark.p',fact_diff__self__eq__0) ).
thf(4924,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)],[599]) ).
thf(1692,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A )
!= ( c_List_Olist_ONil @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osimps_I3_J) ).
thf(9035,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)],[1692]) ).
thf(2201,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_Owf @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Wellfounded_Omin__ext @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__ext__wf) ).
thf(10965,plain,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_Owf @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Wellfounded_Omin__ext @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2201]) ).
thf(1860,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ H @ ( tc_fun @ G @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ E ) @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ H ) @ A ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ D @ A ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF2__D) ).
thf(9700,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ H @ ( tc_fun @ G @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ E ) @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ H ) @ A ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ D @ A ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1860]) ).
thf(2032,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/sandbox/benchmark/theBenchmark.p',fact_Transitive__Closure_Otrancl__into__trancl) ).
thf(10350,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)],[2032]) ).
thf(571,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( class_Rings_Osemiring__0 @ G )
=> ( ( c_Fun_Oinj__on @ ( tc_prod @ F @ E ) @ G @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ F @ E @ G ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ E @ G ) @ ( tc_fun @ E @ G ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ G @ G ) @ ( tc_fun @ ( tc_fun @ E @ G ) @ ( tc_fun @ E @ G ) ) @ F ) @ ( c_COMBB @ G @ G @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ G @ ( tc_fun @ G @ G ) @ F ) @ ( c_Groups_Otimes__class_Otimes @ G ) ) @ D ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) @ A ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ G ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ F @ G ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ E @ G ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ G @ G ) @ ( c_Fun_Oid @ G ) ) @ ( hAPP @ ( c_Set_OCollect @ G ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ tc_HOL_Obool @ G ) @ ( c_HOL_OEx @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ F @ tc_HOL_Obool ) @ G ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ tc_HOL_Obool @ F ) @ ( c_HOL_OEx @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ G @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ ( tc_fun @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ ( tc_fun @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ G ) @ ( c_COMBS @ F @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ ( tc_fun @ E @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) ) @ ( tc_fun @ F @ ( tc_fun @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ G ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_COMBS @ E @ tc_HOL_Obool @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ F @ ( tc_fun @ E @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) ) @ G ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ E ) @ c_fconj ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ G @ ( tc_fun @ F @ ( tc_fun @ E @ G ) ) @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ E @ G ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ F @ ( tc_fun @ E @ G ) ) @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ G ) @ ( c_COMBB @ ( tc_fun @ E @ G ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ E @ G ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ G ) @ ( c_COMBB @ G @ tc_HOL_Obool @ E ) ) @ c_fequal ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ E @ G ) @ ( tc_fun @ E @ G ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ G @ G ) @ ( tc_fun @ ( tc_fun @ E @ G ) @ ( tc_fun @ E @ G ) ) @ F ) @ ( c_COMBB @ G @ G @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ G @ ( tc_fun @ G @ G ) @ F ) @ ( c_Groups_Otimes__class_Otimes @ G ) ) @ D ) ) ) @ C ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ F ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ F @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ F ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ E @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ E ) ) @ A ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__mult__setsum__if__inj) ).
thf(4825,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( class_Rings_Osemiring__0 @ G )
=> ( ( c_Fun_Oinj__on @ ( tc_prod @ F @ E ) @ G @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ F @ E @ G ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ E @ G ) @ ( tc_fun @ E @ G ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ G @ G ) @ ( tc_fun @ ( tc_fun @ E @ G ) @ ( tc_fun @ E @ G ) ) @ F ) @ ( c_COMBB @ G @ G @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ G @ ( tc_fun @ G @ G ) @ F ) @ ( c_Groups_Otimes__class_Otimes @ G ) ) @ D ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) @ A ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ G ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ F @ G ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ E @ G ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ G @ G ) @ ( c_Fun_Oid @ G ) ) @ ( hAPP @ ( c_Set_OCollect @ G ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ tc_HOL_Obool @ G ) @ ( c_HOL_OEx @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ F @ tc_HOL_Obool ) @ G ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ tc_HOL_Obool @ F ) @ ( c_HOL_OEx @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ G @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ ( tc_fun @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ ( tc_fun @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ G ) @ ( c_COMBS @ F @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ ( tc_fun @ E @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) ) @ ( tc_fun @ F @ ( tc_fun @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ G ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_COMBS @ E @ tc_HOL_Obool @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ F @ ( tc_fun @ E @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) ) @ G ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ E ) @ c_fconj ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ G @ ( tc_fun @ F @ ( tc_fun @ E @ G ) ) @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ E @ G ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ F @ ( tc_fun @ E @ G ) ) @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ G ) @ ( c_COMBB @ ( tc_fun @ E @ G ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ E @ G ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ G ) @ ( c_COMBB @ G @ tc_HOL_Obool @ E ) ) @ c_fequal ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ E @ G ) @ ( tc_fun @ E @ G ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ G @ G ) @ ( tc_fun @ ( tc_fun @ E @ G ) @ ( tc_fun @ E @ G ) ) @ F ) @ ( c_COMBB @ G @ G @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ G @ ( tc_fun @ G @ G ) @ F ) @ ( c_Groups_Otimes__class_Otimes @ G ) ) @ D ) ) ) @ C ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ F ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ F @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ F ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ E @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ E ) ) @ A ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(1107,axiom,
! [A: $i,B: $i] : ( c_Relation_Oantisym @ B @ ( c_Relation_OId__on @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisym__Id__on) ).
thf(6863,plain,
! [A: $i,B: $i] : ( c_Relation_Oantisym @ B @ ( c_Relation_OId__on @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).
thf(2596,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/sandbox/benchmark/theBenchmark.p',fact_type__definition_ORep__inject) ).
thf(12411,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)],[2596]) ).
thf(2042,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_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ B ) @ C ) @ A ) ) ) @ ( hAPP @ ( c_List_Oset @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ B ) @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__drop__subset__set__drop) ).
thf(10388,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_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ B ) @ C ) @ A ) ) ) @ ( hAPP @ ( c_List_Oset @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ B ) @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2042]) ).
thf(2180,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/sandbox/benchmark/theBenchmark.p',fact_Id__on__iff) ).
thf(10895,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)],[2180]) ).
thf(2043,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ C @ D @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__inv__f__f) ).
thf(10390,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ C @ D @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2043]) ).
thf(159,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Groups_Ocomm__monoid__add @ F )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ E @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ F ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ F ) @ E ) @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ F ) ) @ C ) ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ F ) @ ( tc_fun @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) @ D ) @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ E @ F ) ) @ ( hAPP @ ( c_COMBC @ E @ D @ F ) @ C ) ) ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__commute) ).
thf(3243,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Groups_Ocomm__monoid__add @ F )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ E @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ F ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ F ) @ E ) @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ F ) ) @ C ) ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ F ) @ ( tc_fun @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) @ D ) @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ E @ F ) ) @ ( hAPP @ ( c_COMBC @ E @ D @ F ) @ C ) ) ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(872,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Relation_Osingle__valued @ F @ E @ ( hAPP @ ( c_Relation_Oconverse @ E @ F ) @ D ) )
=> ( ( C
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Relation_OImage @ E @ F @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) @ B ) @ ( c_Relation_OImage @ E @ F @ D ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__INT__eq) ).
thf(6021,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Relation_Osingle__valued @ F @ E @ ( hAPP @ ( c_Relation_Oconverse @ E @ F ) @ D ) )
=> ( ( C
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Relation_OImage @ E @ F @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) @ B ) @ ( c_Relation_OImage @ E @ F @ D ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(1768,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) )
<=> ( hBOOL @ ( c_Nat_Onat_Onat__case @ tc_HOL_Obool @ c_fFalse @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I2_J) ).
thf(9347,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) )
=> ( hBOOL @ ( c_Nat_Onat_Onat__case @ tc_HOL_Obool @ c_fFalse @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( c_Nat_Onat_Onat__case @ tc_HOL_Obool @ c_fFalse @ ( 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 ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1768]) ).
thf(2436,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/sandbox/benchmark/theBenchmark.p',fact_f__the__inv__into__f) ).
thf(11783,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)],[2436]) ).
thf(2093,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/sandbox/benchmark/theBenchmark.p',fact_fold__graph__imp__finite) ).
thf(10574,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)],[2093]) ).
thf(2487,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/sandbox/benchmark/theBenchmark.p',fact_inj__on__the__inv__into) ).
thf(11954,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)],[2487]) ).
thf(522,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_Olist__update @ C @ B ) @ D ) @ A ) ) @ D )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__list__update__eq) ).
thf(4643,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_Olist__update @ C @ B ) @ D ) @ A ) ) @ D )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(1647,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ D @ E @ C ) @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ E @ D @ ( hAPP @ ( c_Relation_Oconverse @ D @ E ) @ C ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__subset__eq) ).
thf(8892,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ D @ E @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ E @ D @ ( hAPP @ ( c_Relation_Oconverse @ D @ E ) @ C ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ A ) ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ E @ D @ ( hAPP @ ( c_Relation_Oconverse @ D @ E ) @ C ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ A ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ D @ E @ C ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1647]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ B ) @ ( hAPP @ ( c_List_Otl @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__Suc) ).
thf(2965,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ B ) @ ( hAPP @ ( c_List_Otl @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(2377,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/sandbox/benchmark/theBenchmark.p',fact_sym__def) ).
thf(11596,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)],[2377]) ).
thf(1529,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/sandbox/benchmark/theBenchmark.p',fact_o__eq__dest) ).
thf(8443,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)],[1529]) ).
thf(775,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/sandbox/benchmark/theBenchmark.p',fact_wf__mlex) ).
thf(5629,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)],[775]) ).
thf(497,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__commute) ).
thf(4519,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)],[497]) ).
thf(2253,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/sandbox/benchmark/theBenchmark.p',fact_member__rec_I1_J) ).
thf(11143,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)],[2253]) ).
thf(1661,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/sandbox/benchmark/theBenchmark.p',fact_wf__less) ).
thf(8939,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)],[1661]) ).
thf(1375,axiom,
! [A: $i,B: $i] :
( ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ B @ tc_HOL_Obool ) @ A )
= ( hAPP @ ( c_Set_OCollect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ tc_HOL_Obool @ B ) @ ( c_HOL_OAll @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ B ) @ ( hAPP @ ( c_COMBS @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ c_fimplies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A ) ) ) ) @ ( c_member @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__eq) ).
thf(7830,plain,
! [A: $i,B: $i] :
( ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ B @ tc_HOL_Obool ) @ A )
= ( hAPP @ ( c_Set_OCollect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ tc_HOL_Obool @ B ) @ ( c_HOL_OAll @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ B ) @ ( hAPP @ ( c_COMBS @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ c_fimplies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A ) ) ) ) @ ( c_member @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1375]) ).
thf(656,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ A @ ( tc_prod @ B @ A ) ) @ ( c_Product__Type_OPair @ B @ A ) )
= ( c_Fun_Oid @ ( tc_prod @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__Pair) ).
thf(5137,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ A @ ( tc_prod @ B @ A ) ) @ ( c_Product__Type_OPair @ B @ A ) )
= ( c_Fun_Oid @ ( tc_prod @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(2063,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__rev__mp) ).
thf(10459,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2063]) ).
thf(587,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
| ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).
thf(4892,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
| ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(1155,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/sandbox/benchmark/theBenchmark.p',fact_fun__upd__comp) ).
thf(7051,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)],[1155]) ).
thf(819,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/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel1) ).
thf(5819,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)],[819]) ).
thf(1327,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/sandbox/benchmark/theBenchmark.p',fact_card__insert__le) ).
thf(7688,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)],[1327]) ).
thf(2190,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1I2) ).
thf(10933,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2190]) ).
thf(1927,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/sandbox/benchmark/theBenchmark.p',fact_map__pair__imageI) ).
thf(9923,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)],[1927]) ).
thf(259,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/sandbox/benchmark/theBenchmark.p',fact_dropWhile__eq__drop) ).
thf(3606,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)],[259]) ).
thf(1353,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ J @ I @ H ) @ G )
= F )
=> ( ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B )
= A )
=> ( ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ J @ E ) @ ( tc_prod @ I @ D ) @ ( c_Product__Type_Omap__pair @ J @ I @ E @ D @ H @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ J @ E ) @ G ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ J ) @ B ) ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ I @ D ) @ F ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ I ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair__surj__on) ).
thf(7758,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ J @ I @ H ) @ G )
= F )
=> ( ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B )
= A )
=> ( ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ J @ E ) @ ( tc_prod @ I @ D ) @ ( c_Product__Type_Omap__pair @ J @ I @ E @ D @ H @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ J @ E ) @ G ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ J ) @ B ) ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ I @ D ) @ F ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ I ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1353]) ).
thf(1688,axiom,
! [A: $i,B: $i] : ( c_Relation_Osym @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sym__Un__converse) ).
thf(9024,plain,
! [A: $i,B: $i] : ( c_Relation_Osym @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1688]) ).
thf(2311,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( c_Wellfounded_Owf @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__Int1) ).
thf(11357,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( c_Wellfounded_Owf @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2311]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Otl @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ ( hAPP @ ( c_List_Otl @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tl__take) ).
thf(2718,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Otl @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ ( hAPP @ ( c_List_Otl @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(929,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Oinj__on @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ B ) @ ( hAPP @ ( c_List_Omap @ C @ B ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) )
=> ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__mapD) ).
thf(6210,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Oinj__on @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ B ) @ ( hAPP @ ( c_List_Omap @ C @ B ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) )
=> ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(485,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mult__distrib2) ).
thf(4475,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)],[485]) ).
thf(1193,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Union2) ).
thf(7170,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193]) ).
thf(1917,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Equiv__Relations_Oequiv @ G @ F @ E )
=> ( ( c_Equiv__Relations_Ocongruent @ G @ ( tc_fun @ D @ tc_HOL_Obool ) @ E @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ G ) @ F ) @ E ) ) )
=> ( ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ F ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ C @ H ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ G @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ C ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__equiv__class__type) ).
thf(9896,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Equiv__Relations_Oequiv @ G @ F @ E )
=> ( ( c_Equiv__Relations_Ocongruent @ G @ ( tc_fun @ D @ tc_HOL_Obool ) @ E @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ G ) @ F ) @ E ) ) )
=> ( ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ F ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ C @ H ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ G @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ C ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1917]) ).
thf(380,axiom,
class_Orderings_Oorder @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
thf(4065,plain,
class_Orderings_Oorder @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(791,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/sandbox/benchmark/theBenchmark.p',fact_take__eq__Nil) ).
thf(5695,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)],[791]) ).
thf(2080,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__UNIV) ).
thf(10523,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2080]) ).
thf(1230,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Diff__distrib2) ).
thf(7305,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1230]) ).
thf(1656,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/sandbox/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).
thf(8924,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)],[1656]) ).
thf(1897,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oord @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funE) ).
thf(9822,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oord @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1897]) ).
thf(133,axiom,
class_Orderings_Oorder @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).
thf(3151,plain,
class_Orderings_Oorder @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(2364,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_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ E ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ E ) @ A ) ) ) )
=> ( ( D = C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__subset__Sigma__aux) ).
thf(11555,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_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ E ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ E ) @ A ) ) ) )
=> ( ( D = C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2364]) ).
thf(1709,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/sandbox/benchmark/theBenchmark.p',fact_take__drop) ).
thf(9090,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)],[1709]) ).
thf(1436,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__assoc) ).
thf(8078,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1436]) ).
thf(754,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ ( c_Complete__Lattice_OInf__class_OInf @ C @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__lower) ).
thf(5545,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ ( c_Complete__Lattice_OInf__class_OInf @ C @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(1748,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/sandbox/benchmark/theBenchmark.p',fact_append__self__conv) ).
thf(9252,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)],[1748]) ).
thf(1998,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/sandbox/benchmark/theBenchmark.p',fact_filter__remove1) ).
thf(10216,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)],[1998]) ).
thf(696,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/sandbox/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).
thf(5298,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)],[696]) ).
thf(1689,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__empty) ).
thf(9026,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1689]) ).
thf(1696,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/sandbox/benchmark/theBenchmark.p',fact_distinct__dropWhile) ).
thf(9048,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)],[1696]) ).
thf(2401,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UnI) ).
thf(11677,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2401]) ).
thf(539,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 ) ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ D @ C ) @ B ) @ A )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__beyond) ).
thf(4700,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 ) ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ D @ C ) @ B ) @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(1607,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/sandbox/benchmark/theBenchmark.p',fact_wfP__def) ).
thf(8751,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)],[1607]) ).
thf(74,axiom,
( ( hAPP @ c_Int_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__0) ).
thf(2954,plain,
( ( hAPP @ c_Int_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(1671,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ ( c_Set_Oimage @ C @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ F @ C ) @ ( tc_prod @ E @ B ) @ ( c_Product__Type_Omap__pair @ F @ E @ C @ B @ D @ A ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_prod @ F @ C ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_prod @ E @ B ) @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair__surj) ).
thf(8975,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ ( c_Set_Oimage @ C @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ F @ C ) @ ( tc_prod @ E @ B ) @ ( c_Product__Type_Omap__pair @ F @ E @ C @ B @ D @ A ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_prod @ F @ C ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_prod @ E @ B ) @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1671]) ).
thf(340,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__neq) ).
thf(3899,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(65,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( hAPP @ c_Nat_OSuc @ ( hAPP @ c_Int_Onat @ A ) )
= ( hAPP @ c_Int_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__nat__eq__nat__zadd1) ).
thf(2922,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( hAPP @ c_Nat_OSuc @ ( hAPP @ c_Int_Onat @ A ) )
= ( hAPP @ c_Int_Onat @ ( 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)],[65]) ).
thf(2354,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_OwfP @ C @ B )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp__wfPD) ).
thf(11528,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)],[2354]) ).
thf(154,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/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
thf(3229,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)],[154]) ).
thf(1215,axiom,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__psubset__empty) ).
thf(7254,plain,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1215]) ).
thf(2667,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/sandbox/benchmark/theBenchmark.p',fact_in__set__insert) ).
thf(12732,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)],[2667]) ).
thf(1463,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ D @ C ) @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBK__1) ).
thf(8170,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)],[1463]) ).
thf(93,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ocomm__monoid__add @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ B @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Oempty) ).
thf(3011,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ocomm__monoid__add @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ B @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(1289,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ G @ F @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ ( tc_prod @ G @ E ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ G @ E ) @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_Relation_Orel__comp @ G @ F @ E ) @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__UNION__distrib) ).
thf(7533,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ G @ F @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ ( tc_prod @ G @ E ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ G @ E ) @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_Relation_Orel__comp @ G @ F @ E ) @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1289]) ).
thf(1541,axiom,
! [A: $i,B: $i] :
~ ( c_List_Olist__ex @ B @ A @ ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__ex__simps_I2_J) ).
thf(8486,plain,
! [A: $i,B: $i] :
~ ( c_List_Olist__ex @ B @ A @ ( c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1541]) ).
thf(1379,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 @ ( c_Finite__Set_Ofinite @ G ) @ A ) )
=> ( ! [I: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ I ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( ( hAPP @ D @ I )
= E ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Ounion__inter__neutral) ).
thf(7849,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 @ ( c_Finite__Set_Ofinite @ G ) @ A ) )
=> ( ! [I: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ I ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( ( hAPP @ D @ I )
= E ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1379]) ).
thf(1029,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Relation_ODomain @ B @ B ) @ ( c_Relation_OId__on @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Id__on) ).
thf(6560,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)],[1029]) ).
thf(2496,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite_Oequations_I1_J) ).
thf(11993,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2496]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ A @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Oinsert) ).
thf(2910,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ A @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(2519,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/sandbox/benchmark/theBenchmark.p',fact_in__set__sublistD) ).
thf(12078,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)],[2519]) ).
thf(1585,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_OCollect @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool @ D ) @ ( c_HOL_OAll @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_COMBS @ C @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ C ) @ c_fimplies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) ) ) ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ ( c_Set_OCollect @ D ) ) @ ( hAPP @ ( c_COMBC @ D @ C @ tc_HOL_Obool ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__ball__eq) ).
thf(8655,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_OCollect @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool @ D ) @ ( c_HOL_OAll @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_COMBS @ C @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ C ) @ c_fimplies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) ) ) ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ ( c_Set_OCollect @ D ) ) @ ( hAPP @ ( c_COMBC @ D @ C @ tc_HOL_Obool ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1585]) ).
thf(554,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__le2) ).
thf(4753,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(510,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/sandbox/benchmark/theBenchmark.p',fact_listrel_OCons) ).
thf(4589,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)],[510]) ).
thf(2281,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ D @ C ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ ( hAPP @ ( c_List_Oset @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__update__subset__insert) ).
thf(11253,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ D @ C ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ ( hAPP @ ( c_List_Oset @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2281]) ).
thf(2282,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__f__f) ).
thf(11255,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2282]) ).
thf(1007,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ D ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ C @ D @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ D @ D ) @ C ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ D ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUPR__fold__sup) ).
thf(6482,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ D ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ C @ D @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ D @ D ) @ C ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ D ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(2322,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/sandbox/benchmark/theBenchmark.p',fact_wf__eq__minimal) ).
thf(11395,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)],[2322]) ).
thf(1766,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ D @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( hAPP @ ( c_Relation_ORange @ D @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeP__Range__eq) ).
thf(9340,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ D @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( hAPP @ ( c_Relation_ORange @ D @ C ) @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( hAPP @ ( c_Relation_ORange @ D @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ D @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1766]) ).
thf(2138,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__not__insert) ).
thf(10742,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2138]) ).
thf(1657,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Orderings_Oorder @ D )
& ( class_Enum_Oenum @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ D ) ) @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) ) @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__ex @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ C ) @ c_fNot ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ C @ D @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ c_fequal ) @ B ) ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__fun_I2_J) ).
thf(8927,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Orderings_Oorder @ D )
& ( class_Enum_Oenum @ C ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ D ) ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) ) @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__ex @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ C ) @ c_fNot ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ C @ D @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ c_fequal ) @ B ) ) @ A ) ) ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) ) @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__ex @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ C ) @ c_fNot ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ C @ D @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ c_fequal ) @ B ) ) @ A ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ D ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1657]) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ C ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( ( hAPP @ A @ F )
= ( c_Groups_Ozero__class_Ozero @ E ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ C )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__mono__zero__right) ).
thf(3169,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ C ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( ( hAPP @ A @ F )
= ( c_Groups_Ozero__class_Ozero @ E ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ C )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(2439,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__equals__eq) ).
thf(11791,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2439]) ).
thf(2642,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/sandbox/benchmark/theBenchmark.p',fact_equivp__symp) ).
thf(12623,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)],[2642]) ).
thf(626,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/sandbox/benchmark/theBenchmark.p',fact_length__remove1) ).
thf(5017,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)],[626]) ).
thf(242,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ C ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ B ) ) @ C ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__add__mult__distrib) ).
thf(3531,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)],[242]) ).
thf(265,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/sandbox/benchmark/theBenchmark.p',fact_drop__1__Cons) ).
thf(3635,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)],[265]) ).
thf(2546,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/sandbox/benchmark/theBenchmark.p',fact_accp_Osimps) ).
thf(12200,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)],[2546]) ).
thf(2577,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/sandbox/benchmark/theBenchmark.p',fact_in__listsp__conv__set) ).
thf(12333,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)],[2577]) ).
thf(881,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I6_J) ).
thf(6064,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(1618,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/sandbox/benchmark/theBenchmark.p',fact_diff__cancel2) ).
thf(8795,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)],[1618]) ).
thf(942,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/sandbox/benchmark/theBenchmark.p',fact_comp__inj__on__iff) ).
thf(6250,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)],[942]) ).
thf(504,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/sandbox/benchmark/theBenchmark.p',fact_append__eq__conv__conj) ).
thf(4557,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)],[504]) ).
thf(1519,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_Olist__update @ C @ B ) @ D ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ ( hAPP @ c_Nat_OSuc @ D ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upd__conv__take__nth__drop) ).
thf(8397,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_Olist__update @ C @ B ) @ D ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ ( hAPP @ c_Nat_OSuc @ D ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1519]) ).
thf(694,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_List_Olist__ex @ C @ B @ ( hAPP @ ( c_List_Orev @ C ) @ A ) )
<=> ( c_List_Olist__ex @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__ex__rev) ).
thf(5291,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_List_Olist__ex @ C @ B @ ( hAPP @ ( c_List_Orev @ C ) @ A ) )
=> ( c_List_Olist__ex @ C @ B @ A ) )
& ( ( c_List_Olist__ex @ C @ B @ A )
=> ( c_List_Olist__ex @ C @ B @ ( hAPP @ ( c_List_Orev @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(1577,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/sandbox/benchmark/theBenchmark.p',fact_lexord__Nil__left) ).
thf(8613,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)],[1577]) ).
thf(650,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ C ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ C ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ tc_HOL_Obool ) ) @ ( c_List_Olistrel @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olists @ C @ A ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olists @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__subset) ).
thf(5117,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ C ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ C ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ tc_HOL_Obool ) ) @ ( c_List_Olistrel @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olists @ C @ A ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olists @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(181,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__add @ D )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ D ) @ A ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ ( hAPP @ c_Nat_OSuc @ C ) ) )
= ( c_Groups_Ozero__class_Ozero @ D ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ D ) @ A ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ ( hAPP @ c_Nat_OSuc @ C ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ D ) @ A ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ C ) ) ) @ ( hAPP @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__op__ivl__Suc) ).
thf(3318,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__add @ D )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ D ) @ A ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ ( hAPP @ c_Nat_OSuc @ C ) ) )
= ( c_Groups_Ozero__class_Ozero @ D ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ D ) @ A ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ ( hAPP @ c_Nat_OSuc @ C ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ D ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ D ) @ A ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ C ) ) ) @ ( hAPP @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(1219,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__single__insert) ).
thf(7269,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1219]) ).
thf(2338,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ E @ C ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ E @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Int__subset) ).
thf(11456,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ E @ C ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ E @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2338]) ).
thf(2233,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 ) @ ( hAPP @ B @ ( hAPP @ c_Nat_OSuc @ D ) ) ) @ ( hAPP @ B @ D ) ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) )
=> ( ( c_Wellfounded_Owf @ C @ ( c_Transitive__Closure_Otrancl @ C @ A ) )
=> ? [D: $i] :
! [E: $i] :
( ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ E ) )
= ( hAPP @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__weak__decr__stable) ).
thf(11069,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 ) @ ( hAPP @ B @ ( hAPP @ c_Nat_OSuc @ D ) ) ) @ ( hAPP @ B @ D ) ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) )
=> ( ( c_Wellfounded_Owf @ C @ ( c_Transitive__Closure_Otrancl @ C @ A ) )
=> ? [D: $i] :
! [E: $i] :
( ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ E ) )
= ( hAPP @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2233]) ).
thf(1734,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__card__mono) ).
thf(9164,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1734]) ).
thf(1108,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__disjoint) ).
thf(6865,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).
thf(2613,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/sandbox/benchmark/theBenchmark.p',fact_exists__code) ).
thf(12489,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)],[2613]) ).
thf(456,axiom,
! [A: $i,B: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ B )
=> ( ( c_Complete__Lattice_OInf__class_OInf @ B @ A )
= ( c_Complete__Lattice_OSup__class_OSup @ B @ ( hAPP @ ( c_Set_OCollect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool @ B ) @ ( c_HOL_OAll @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) @ B ) @ ( hAPP @ ( c_COMBS @ B @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ B ) @ c_fimplies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ B ) ) @ A ) ) ) ) @ ( c_Orderings_Oord__class_Oless__eq @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__Sup) ).
thf(4370,plain,
! [A: $i,B: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ B )
=> ( ( c_Complete__Lattice_OInf__class_OInf @ B @ A )
= ( c_Complete__Lattice_OSup__class_OSup @ B @ ( hAPP @ ( c_Set_OCollect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool @ B ) @ ( c_HOL_OAll @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) @ B ) @ ( hAPP @ ( c_COMBS @ B @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ B ) @ c_fimplies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ B ) ) @ A ) ) ) ) @ ( c_Orderings_Oord__class_Oless__eq @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(593,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/sandbox/benchmark/theBenchmark.p',fact_one__less__mult) ).
thf(4910,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)],[593]) ).
thf(1633,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ E @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ E @ D ) @ C ) @ B ) ) @ C ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ E @ D ) @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__overwrite) ).
thf(8842,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ E @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ E @ D ) @ C ) @ B ) ) @ C ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ E @ D ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1633]) ).
thf(1077,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Obij__betw @ F @ E @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( c_Set_Oimage @ F @ E @ D ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__image__INT) ).
thf(6741,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Obij__betw @ F @ E @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( c_Set_Oimage @ F @ E @ D ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).
thf(1164,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A )
= ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ C @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ C ) @ c_fdisj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ C @ tc_HOL_Obool ) @ c_fequal ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__compr) ).
thf(7078,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A )
= ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ C @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ C ) @ c_fdisj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ C @ tc_HOL_Obool ) @ c_fequal ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164]) ).
thf(378,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ D @ C ) @ B ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ D @ B ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I11_J) ).
thf(4059,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ D @ C ) @ B ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ D @ B ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(2517,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ B @ A ) @ ( c_Divides_Odivmod__nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__rel__divmod__nat) ).
thf(12073,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)],[2517]) ).
thf(2348,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2D1) ).
thf(11499,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2348]) ).
thf(2571,axiom,
hBOOL @ c_fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fTrue__1) ).
thf(12300,plain,
hBOOL @ c_fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2571]) ).
thf(2412,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) )
<=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__iff) ).
thf(11704,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2412]) ).
thf(891,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/sandbox/benchmark/theBenchmark.p',fact_diff__less__mono2) ).
thf(6092,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)],[891]) ).
thf(1175,axiom,
! [A: $i,B: $i] :
( ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( ( c_Divides_Odivmod__nat @ A @ B )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ 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 ) ) )
=> ( ( c_Divides_Odivmod__nat @ A @ B )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ tc_Nat_Onat @ tc_Nat_Onat @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ c_Nat_OSuc ) ) @ ( c_Divides_Odivmod__nat @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__if) ).
thf(7110,plain,
! [A: $i,B: $i] :
( ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( ( c_Divides_Odivmod__nat @ A @ B )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ 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 ) ) )
=> ( ( c_Divides_Odivmod__nat @ A @ B )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ tc_Nat_Onat @ tc_Nat_Onat @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ c_Nat_OSuc ) ) @ ( c_Divides_Odivmod__nat @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1175]) ).
thf(312,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding__idem @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ B ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ B ) ) @ ( hAPP @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__idem_Oinsert__idem) ).
thf(3795,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding__idem @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ B ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ B ) ) @ ( hAPP @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(652,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/sandbox/benchmark/theBenchmark.p',fact_take__0) ).
thf(5122,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)],[652]) ).
thf(2555,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/sandbox/benchmark/theBenchmark.p',fact_sympE) ).
thf(12232,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)],[2555]) ).
thf(1913,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/sandbox/benchmark/theBenchmark.p',fact_takeWhile__map) ).
thf(9881,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)],[1913]) ).
thf(1345,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__empty1) ).
thf(7735,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1345]) ).
thf(278,axiom,
! [A: $i] :
( ( c_List_Olists @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_List_Olist @ A ) ) @ ( c_List_Olist_ONil @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_List_Olist @ A ) @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists__empty) ).
thf(3679,plain,
! [A: $i] :
( ( c_List_Olists @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_List_Olist @ A ) ) @ ( c_List_Olist_ONil @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_List_Olist @ A ) @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(1866,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Set_Oimage @ D @ E @ ( c_Hilbert__Choice_Oinv__into @ E @ D @ B @ C ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__image__cancel) ).
thf(9722,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Set_Oimage @ D @ E @ ( c_Hilbert__Choice_Oinv__into @ E @ D @ B @ C ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1866]) ).
thf(258,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofun__left__comm__idem @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ D @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofold__insert__idem) ).
thf(3603,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofun__left__comm__idem @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ D @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(687,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).
thf(5266,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)],[687]) ).
thf(1840,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/sandbox/benchmark/theBenchmark.p',fact_distinct__takeWhile) ).
thf(9618,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)],[1840]) ).
thf(1638,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/sandbox/benchmark/theBenchmark.p',fact_Suc__less__eq) ).
thf(8856,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)],[1638]) ).
thf(2210,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ D @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_OemptyI) ).
thf(11003,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ D @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2210]) ).
thf(1644,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 @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__card__le__card__Diff) ).
thf(8878,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 @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1644]) ).
thf(2526,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/sandbox/benchmark/theBenchmark.p',fact_ord_OatLeastLessThan__iff) ).
thf(12110,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)],[2526]) ).
thf(1806,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_Olist__update @ D @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ B ) ) @ E ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ D @ C ) @ E ) @ A ) ) @ B ) ) )
& ( ~ ( 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_Olist__update @ D @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ B ) ) @ E ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ D @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ E ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__append) ).
thf(9488,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_Olist__update @ D @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ B ) ) @ E ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ D @ C ) @ E ) @ A ) ) @ B ) ) )
& ( ~ ( 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_Olist__update @ D @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ B ) ) @ E ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ D @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ E ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1806]) ).
thf(1048,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/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__graph__determ) ).
thf(6635,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)],[1048]) ).
thf(1862,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ D ) )
=> ( ( ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__equiv__class__iff) ).
thf(9705,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ D ) )
=> ( ( ( ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
=> ( 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 @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ C ) )
=> ( ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1862]) ).
thf(1474,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ B ) )
=> ( ( hAPP @ ( c_List_Oset @ C ) @ ( c_List_Oremove1 @ C @ A @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__remove1__eq) ).
thf(8211,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ B ) )
=> ( ( hAPP @ ( c_List_Oset @ C ) @ ( c_List_Oremove1 @ C @ A @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1474]) ).
thf(1616,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__Int__eq) ).
thf(8783,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1616]) ).
thf(886,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/sandbox/benchmark/theBenchmark.p',fact_trans__less__add1) ).
thf(6079,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)],[886]) ).
thf(2563,axiom,
! [A: $i] : ( class_Nat_Osize @ ( tc_Hoare__Mirabelle_Otriple @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Hoare____Mirabelle__Otriple__Nat_Osize) ).
thf(12260,plain,
! [A: $i] : ( class_Nat_Osize @ ( tc_Hoare__Mirabelle_Otriple @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2563]) ).
thf(1414,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/sandbox/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded) ).
thf(7989,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)],[1414]) ).
thf(1381,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/sandbox/benchmark/theBenchmark.p',fact_add__diff__assoc2) ).
thf(7870,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)],[1381]) ).
thf(367,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__UN__finite__eq) ).
thf(4016,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(1333,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Set_OPow @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ B @ tc_HOL_Obool ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__Pow__Union) ).
thf(7703,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Set_OPow @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ B @ tc_HOL_Obool ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1333]) ).
thf(1987,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) )
=> ? [C: $i] :
( A
= ( hAPP @ c_Nat_OSuc @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__D) ).
thf(10171,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) )
=> ? [C: $i] :
( A
= ( hAPP @ c_Nat_OSuc @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1987]) ).
thf(1040,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Int__crazy) ).
thf(6605,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(1678,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( c_Fun_Oinj__on @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ B ) @ ( hAPP @ ( c_List_Omap @ C @ B ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__mapI) ).
thf(8994,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( c_Fun_Oinj__on @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ B ) @ ( hAPP @ ( c_List_Omap @ C @ B ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1678]) ).
thf(1236,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_SetInterval_Oord_OgreaterThanLessThan @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) ) @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ tc_Nat_Onat ) @ c_fNot ) ) @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ A @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OgreaterThanLessThan__empty) ).
thf(7353,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_SetInterval_Oord_OgreaterThanLessThan @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) ) @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ tc_Nat_Onat ) @ c_fNot ) ) @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ A @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1236]) ).
thf(597,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/sandbox/benchmark/theBenchmark.p',fact_length__filter__le) ).
thf(4920,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)],[597]) ).
thf(2127,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/sandbox/benchmark/theBenchmark.p',fact_SigmaD2) ).
thf(10699,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)],[2127]) ).
thf(458,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/sandbox/benchmark/theBenchmark.p',fact_upt__conv__Nil) ).
thf(4375,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)],[458]) ).
thf(1608,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__eq__Union) ).
thf(8756,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1608]) ).
thf(1895,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__refl) ).
thf(9817,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1895]) ).
thf(1085,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofun__left__comm @ E @ D @ C )
=> ( c_Finite__Set_Ofun__left__comm @ B @ D @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ D @ D ) @ B ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofun__left__comm__apply) ).
thf(6773,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofun__left__comm @ E @ D @ C )
=> ( c_Finite__Set_Ofun__left__comm @ B @ D @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ D @ D ) @ B ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).
thf(761,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/sandbox/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel1) ).
thf(5579,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)],[761]) ).
thf(744,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ D @ D @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ D @ D @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) ) @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__inf__insert) ).
thf(5512,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ D @ D @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ D @ D @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) ) @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(1935,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OCollect @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__subsets) ).
thf(9949,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OCollect @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1935]) ).
thf(1209,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ A ) )
= ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ C @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ C ) @ c_fimplies ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ C ) @ c_fNot ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ C @ tc_HOL_Obool ) @ c_fequal ) @ B ) ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__Collect) ).
thf(7229,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ A ) )
= ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ C @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ C ) @ c_fimplies ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ C ) @ c_fNot ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ C @ tc_HOL_Obool ) @ c_fequal ) @ B ) ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1209]) ).
thf(2169,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/sandbox/benchmark/theBenchmark.p',fact_butlast__drop) ).
thf(10858,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)],[2169]) ).
thf(2460,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Obij__betw @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
<=> ( ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
& ( ( hAPP @ ( c_Set_Oimage @ C @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__def) ).
thf(11865,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Fun_Obij__betw @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
& ( ( hAPP @ ( c_Set_Oimage @ C @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) )
& ( ( ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
& ( ( hAPP @ ( c_Set_Oimage @ C @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( c_Fun_Obij__betw @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2460]) ).
thf(818,axiom,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).
thf(5815,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(299,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__0) ).
thf(3742,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)],[299]) ).
thf(2685,plain,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ sk2 ) @ v_ts ),
inference(cnf,[status(esa)],[2683]) ).
thf(12808,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ sk2 ) @ v_ts ) )
!= ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ sk2 ) @ v_G ) ) ),
inference(paramod_ordered,[status(thm)],[2685,12804]) ).
thf(12809,plain,
( ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ sk2 ) @ v_ts )
!= ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ sk2 ) @ v_G ) ),
inference(simp,[status(thm)],[12808]) ).
thf(1504,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__commute) ).
thf(8334,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1504]) ).
thf(112,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0) ).
thf(3069,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(1166,axiom,
! [A: $i] :
( ( c_List_Obutlast @ A @ ( c_List_Olist_ONil @ A ) )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_butlast_Osimps_I1_J) ).
thf(7084,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)],[1166]) ).
thf(336,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( c_List_Orev @ C ) @ B )
= ( hAPP @ ( c_List_Orev @ C ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__is__rev__conv) ).
thf(3884,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ C ) @ B )
= ( hAPP @ ( c_List_Orev @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( c_List_Orev @ C ) @ B )
= ( hAPP @ ( c_List_Orev @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(732,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/sandbox/benchmark/theBenchmark.p',fact_lexord__irreflexive) ).
thf(5470,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)],[732]) ).
thf(1942,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 @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ F @ F ) @ tc_HOL_Obool ) @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ E ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ F @ F ) @ tc_HOL_Obool ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__Suc__I2) ).
thf(9981,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 @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ F @ F ) @ tc_HOL_Obool ) @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ E ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ F @ F ) @ tc_HOL_Obool ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1942]) ).
thf(197,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__mult @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__Un__disjoint) ).
thf(3371,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__mult @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(2242,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_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnI2) ).
thf(11106,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_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2242]) ).
thf(1437,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__card__ge__0) ).
thf(8081,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1437]) ).
thf(128,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 ) ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ B ) ) @ ( hAPP @ c_Int_Onat @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__eq__zle) ).
thf(3134,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 ) ) @ A ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ B ) ) @ ( hAPP @ c_Int_Onat @ 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_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ B ) ) @ ( hAPP @ c_Int_Onat @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(2662,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/sandbox/benchmark/theBenchmark.p',fact_enum__all) ).
thf(12715,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)],[2662]) ).
thf(1329,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/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
thf(7692,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)],[1329]) ).
thf(1412,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ D @ D @ D ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__add) ).
thf(7984,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ D @ D @ D ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1412]) ).
thf(2550,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/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Oneg__single__def) ).
thf(12215,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)],[2550]) ).
thf(570,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= B )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
thf(4821,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)],[570]) ).
thf(84,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( class_Groups_Ocomm__monoid__add @ G )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ F @ G ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ F @ ( tc_fun @ D @ tc_HOL_Obool ) @ G ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ G ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ G ) @ F ) @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ G ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ F ) @ ( c_Set_OCollect @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( c_COMBS @ D @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ C ) ) ) ) @ A ) ) ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ G ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ ( tc_fun @ F @ tc_HOL_Obool ) @ G ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ G ) @ ( tc_fun @ ( tc_fun @ F @ tc_HOL_Obool ) @ G ) @ D ) @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ F @ G ) ) @ ( hAPP @ ( c_COMBC @ F @ D @ G ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) @ D ) @ ( c_Set_OCollect @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_COMBS @ F @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ F ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ F @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ F ) ) @ E ) ) ) ) @ ( hAPP @ ( c_COMBC @ F @ D @ tc_HOL_Obool ) @ A ) ) ) ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__setsum__restrict) ).
thf(2986,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( class_Groups_Ocomm__monoid__add @ G )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ F @ G ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ F @ ( tc_fun @ D @ tc_HOL_Obool ) @ G ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ G ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ G ) @ F ) @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ G ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ F ) @ ( c_Set_OCollect @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( c_COMBS @ D @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ C ) ) ) ) @ A ) ) ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ G ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ ( tc_fun @ F @ tc_HOL_Obool ) @ G ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ G ) @ ( tc_fun @ ( tc_fun @ F @ tc_HOL_Obool ) @ G ) @ D ) @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ F @ G ) ) @ ( hAPP @ ( c_COMBC @ F @ D @ G ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) @ D ) @ ( c_Set_OCollect @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_COMBS @ F @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ F ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ F @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ F ) ) @ E ) ) ) ) @ ( hAPP @ ( c_COMBC @ F @ D @ tc_HOL_Obool ) @ A ) ) ) ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(1598,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Ototal__on @ C @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ A ) @ ( c_Relation_OId @ C ) ) )
<=> ( c_Relation_Ototal__on @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_total__on__diff__Id) ).
thf(8714,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Relation_Ototal__on @ C @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ A ) @ ( c_Relation_OId @ C ) ) )
=> ( c_Relation_Ototal__on @ C @ B @ A ) )
& ( ( c_Relation_Ototal__on @ C @ B @ A )
=> ( c_Relation_Ototal__on @ C @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ A ) @ ( c_Relation_OId @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1598]) ).
thf(2058,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/sandbox/benchmark/theBenchmark.p',fact_map__fun__upd) ).
thf(10441,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)],[2058]) ).
thf(767,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/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel2) ).
thf(5594,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)],[767]) ).
thf(1214,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_List_Omeasures @ E @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ ( tc_fun @ E @ tc_Nat_Onat ) ) @ B ) @ A ) ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ B @ D ) ) @ ( hAPP @ B @ C ) ) )
| ( ( ( hAPP @ B @ D )
= ( hAPP @ B @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_List_Omeasures @ E @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__measures_I2_J) ).
thf(7244,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_List_Omeasures @ E @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ ( tc_fun @ E @ tc_Nat_Onat ) ) @ B ) @ A ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ B @ D ) ) @ ( hAPP @ B @ C ) ) )
| ( ( ( hAPP @ B @ D )
= ( hAPP @ B @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_List_Omeasures @ E @ A ) ) ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ B @ D ) ) @ ( hAPP @ B @ C ) ) )
| ( ( ( hAPP @ B @ D )
= ( hAPP @ B @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_List_Omeasures @ E @ A ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_List_Omeasures @ E @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ ( tc_fun @ E @ tc_Nat_Onat ) ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1214]) ).
thf(2235,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 ) @ A ) )
<=> ( ( c_Fun_Oinj__on @ E @ D @ C @ A )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ ( hAPP @ C @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__insert) ).
thf(11074,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 ) @ A ) )
=> ( ( c_Fun_Oinj__on @ E @ D @ C @ A )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ ( hAPP @ C @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) ) ) )
& ( ( ( c_Fun_Oinj__on @ E @ D @ C @ A )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ ( hAPP @ C @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) ) )
=> ( c_Fun_Oinj__on @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2235]) ).
thf(279,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Lattices_Osemilattice__inf @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ E ) @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__mono) ).
thf(3682,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Lattices_Osemilattice__inf @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ E ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(373,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/sandbox/benchmark/theBenchmark.p',fact_card__infinite) ).
thf(4044,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)],[373]) ).
thf(826,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__upper) ).
thf(5843,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(1405,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/sandbox/benchmark/theBenchmark.p',fact_add__le__mono) ).
thf(7957,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)],[1405]) ).
thf(1797,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ E @ D @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ E @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ E @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ E @ D ) ) ) ) @ ( 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 ) @ A ) ) @ ( hAPP @ ( c_Relation_Oconverse @ E @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_conversep__converse__eq) ).
thf(9455,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ E @ D @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ E @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ E @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ E @ D ) ) ) ) @ ( 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 ) @ A ) ) @ ( hAPP @ ( c_Relation_Oconverse @ E @ D ) @ C ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ E ) @ B ) @ A ) ) @ ( hAPP @ ( c_Relation_Oconverse @ E @ D ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ E @ D @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ E @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ E @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ E @ D ) ) ) ) @ ( c_Product__Type_OPair @ E @ D ) ) ) ) @ C ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1797]) ).
thf(1591,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/sandbox/benchmark/theBenchmark.p',fact_diff__diff__cancel) ).
thf(8683,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)],[1591]) ).
thf(915,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__insert__distrib) ).
thf(6163,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(789,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oorder @ E )
=> ( ( c_Orderings_Oorder__class_Omono @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ C )
=> ( c_Orderings_Oorder__class_Omono @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ C ) ) @ B ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_coinduct3__mono__lemma) ).
thf(5690,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oorder @ E )
=> ( ( c_Orderings_Oorder__class_Omono @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ C )
=> ( c_Orderings_Oorder__class_Omono @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ C ) ) @ B ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(985,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Hilbert__Choice_OEps @ ( tc_prod @ D @ C ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) @ ( hAPP @ c_fequal @ B ) ) ) ) @ ( hAPP @ c_fequal @ A ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Eps__split__eq) ).
thf(6402,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Hilbert__Choice_OEps @ ( tc_prod @ D @ C ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) @ ( hAPP @ c_fequal @ B ) ) ) ) @ ( hAPP @ c_fequal @ A ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(101,axiom,
! [A: $i,B: $i] :
( ( B
!= ( c_List_Olist_ONil @ A ) )
=> ( ( c_List_Olast @ A @ ( hAPP @ ( c_List_Orev @ A ) @ B ) )
= ( hAPP @ ( c_List_Ohd @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__rev) ).
thf(3033,plain,
! [A: $i,B: $i] :
( ( B
!= ( c_List_Olist_ONil @ A ) )
=> ( ( c_List_Olast @ A @ ( hAPP @ ( c_List_Orev @ A ) @ B ) )
= ( hAPP @ ( c_List_Ohd @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(217,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Product__Type_Ofst @ C @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ C @ B @ C ) @ ( c_COMBK @ C @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__def) ).
thf(3445,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Product__Type_Ofst @ C @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ C @ B @ C ) @ ( c_COMBK @ C @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(1068,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I2_J) ).
thf(6709,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).
thf(2133,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/sandbox/benchmark/theBenchmark.p',fact_List_Oset_Osimps_I2_J) ).
thf(10721,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)],[2133]) ).
thf(136,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__add @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ D ) @ C ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ D @ tc_Nat_Onat ) @ C ) @ c_Nat_OSuc ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__shift__bounds__Suc__ivl) ).
thf(3166,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__add @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ D ) @ C ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ D @ tc_Nat_Onat ) @ C ) @ c_Nat_OSuc ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(1231,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Relation_OImage @ D @ C @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( c_Relation_OImage @ D @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ D ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__eq__UN) ).
thf(7308,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Relation_OImage @ D @ C @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( c_Relation_OImage @ D @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ D ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1231]) ).
thf(440,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ C ) @ B ) ) @ ( c_List_Olists @ D @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ D ) ) @ B ) @ ( c_List_Olists @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cons__in__lists__iff) ).
thf(4295,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ C ) @ B ) ) @ ( c_List_Olists @ D @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ D ) ) @ B ) @ ( c_List_Olists @ D @ A ) ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ D ) ) @ B ) @ ( c_List_Olists @ D @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ C ) @ B ) ) @ ( c_List_Olists @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(2648,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ c_Int_ORep__Integ @ B )
= ( hAPP @ c_Int_ORep__Integ @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Rep__Integ__inject) ).
thf(12640,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)],[2648]) ).
thf(1623,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/sandbox/benchmark/theBenchmark.p',fact_upt__Suc) ).
thf(8810,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)],[1623]) ).
thf(820,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/sandbox/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).
thf(5826,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)],[820]) ).
thf(436,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ B @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= ( c_Fun_Oid @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funpow_Osimps_I1_J) ).
thf(4280,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ B @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= ( c_Fun_Oid @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(837,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/sandbox/benchmark/theBenchmark.p',fact_trancl__unfold__right) ).
thf(5879,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)],[837]) ).
thf(53,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/sandbox/benchmark/theBenchmark.p',fact_zle__linear) ).
thf(2873,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)],[53]) ).
thf(851,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__empty__right) ).
thf(5937,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(166,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_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ A ) ) @ ( hAPP @ c_Int_Onat @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mono__iff) ).
thf(3269,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_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ A ) ) @ ( hAPP @ c_Int_Onat @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ A ) ) @ ( hAPP @ c_Int_Onat @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(1046,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/sandbox/benchmark/theBenchmark.p',fact_Range__converse) ).
thf(6629,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)],[1046]) ).
thf(991,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_List_Olistsp @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) @ ( c_List_Olistsp @ C @ B ) ) @ ( c_List_Olistsp @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsp__inf__eq) ).
thf(6432,plain,
! [A: $i,B: $i,C: $i] :
( ( c_List_Olistsp @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) @ ( c_List_Olistsp @ C @ B ) ) @ ( c_List_Olistsp @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(2074,axiom,
! [A: $i,B: $i] :
( ( ( class_Enum_Oenum @ B )
& ( class_Enum_Oenum @ A ) )
=> ( class_Enum_Oenum @ ( tc_prod @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_prod__Enum_Oenum) ).
thf(10502,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)],[2074]) ).
thf(399,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/sandbox/benchmark/theBenchmark.p',fact_nat__less__add__iff1) ).
thf(4140,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)],[399]) ).
thf(1745,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ D )
= A ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) )
=> ( ( D != E )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( c_Finite__Set_Ocard @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__partition) ).
thf(9217,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ D )
= A ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) )
=> ( ( D != E )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( c_Finite__Set_Ocard @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1745]) ).
thf(1617,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ A ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) ) @ B ) ) )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ A ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_below__fold1__iff) ).
thf(8788,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ A ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) ) @ B ) ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ A ) @ D ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ A ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ A ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) ) @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1617]) ).
thf(578,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Osemilattice__inf @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ B ) @ A ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Oidem) ).
thf(4849,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Osemilattice__inf @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ B ) @ A ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(376,axiom,
! [A: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ A )
=> ( ( c_Complete__Lattice_OSup__class_OSup @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__empty) ).
thf(4053,plain,
! [A: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ A )
=> ( ( c_Complete__Lattice_OSup__class_OSup @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(2533,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/sandbox/benchmark/theBenchmark.p',fact_ord_OatLeastAtMost__iff) ).
thf(12147,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)],[2533]) ).
thf(1439,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/sandbox/benchmark/theBenchmark.p',fact_Suc__lessD) ).
thf(8085,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)],[1439]) ).
thf(2578,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/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__eq) ).
thf(12340,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)],[2578]) ).
thf(1457,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__commute) ).
thf(8145,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1457]) ).
thf(144,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/sandbox/benchmark/theBenchmark.p',fact_int__0__less__1) ).
thf(3198,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)],[144]) ).
thf(989,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__absorb) ).
thf(6427,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(1354,axiom,
! [A: $i] :
( ( hAPP @ ( c_Relation_ODomain @ A @ A ) @ ( c_Relation_OId @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Id) ).
thf(7762,plain,
! [A: $i] :
( ( hAPP @ ( c_Relation_ODomain @ A @ A ) @ ( c_Relation_OId @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1354]) ).
thf(877,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Int__distrib) ).
thf(6043,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(620,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/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__base) ).
thf(4994,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)],[620]) ).
thf(2254,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 ) @ C ) @ A ) )
=> ( ( c_Fun_Oinj__on @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ E ) @ B ) ) @ ( hAPP @ ( c_List_Oset @ E ) @ A ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__inj__on) ).
thf(11152,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 ) @ C ) @ A ) )
=> ( ( c_Fun_Oinj__on @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ E ) @ B ) ) @ ( hAPP @ ( c_List_Oset @ E ) @ A ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2254]) ).
thf(233,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ D @ B ) @ B ) @ ( c_Product__Type_Osnd @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ D @ B ) @ C ) @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__snd__zip) ).
thf(3499,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ D @ B ) @ B ) @ ( c_Product__Type_Osnd @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ D @ B ) @ C ) @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(302,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( c_Complete__Lattice_OInf__class_OInf @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__binary) ).
thf(3750,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( c_Complete__Lattice_OInf__class_OInf @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(1604,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__complement) ).
thf(8736,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1604]) ).
thf(1239,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) ) @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__INT__eq) ).
thf(7361,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1239]) ).
thf(728,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/sandbox/benchmark/theBenchmark.p',fact_map__Suc__upt) ).
thf(5460,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)],[728]) ).
thf(1389,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/sandbox/benchmark/theBenchmark.p',fact_diff__add__assoc) ).
thf(7902,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)],[1389]) ).
thf(1314,axiom,
! [A: $i,B: $i] : ( c_Relation_Osym @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sym__Int__converse) ).
thf(7625,plain,
! [A: $i,B: $i] : ( c_Relation_Osym @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1314]) ).
thf(257,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Ocommute) ).
thf(3600,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(862,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/sandbox/benchmark/theBenchmark.p',fact_listrel1I2) ).
thf(5988,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)],[862]) ).
thf(811,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofun__left__comm__idem @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ ( hAPP @ ( hAPP @ D @ A ) @ B ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofold__insert__idem2) ).
thf(5779,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofun__left__comm__idem @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ ( hAPP @ ( hAPP @ D @ A ) @ B ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(1778,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/sandbox/benchmark/theBenchmark.p',fact_le__add__diff__inverse) ).
thf(9391,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)],[1778]) ).
thf(2504,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ B @ C @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__imp__surj__inv) ).
thf(12025,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ B @ C @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2504]) ).
thf(908,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Relation_ORange @ C @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Relation_ORange @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Union) ).
thf(6143,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Relation_ORange @ C @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Relation_ORange @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(1293,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ C @ tc_HOL_Obool ) @ c_fequal ) @ B ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__def) ).
thf(7545,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ C @ tc_HOL_Obool ) @ c_fequal ) @ B ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1293]) ).
thf(1467,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 @ ( c_Finite__Set_Ofinite @ G ) @ A ) )
=> ( ( hAPP @ ( hAPP @ F @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Ounion__inter) ).
thf(8181,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 @ ( c_Finite__Set_Ofinite @ G ) @ A ) )
=> ( ( hAPP @ ( hAPP @ F @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1467]) ).
thf(630,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__infI) ).
thf(5038,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(552,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/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__le__cancel1) ).
thf(4746,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)],[552]) ).
thf(467,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/sandbox/benchmark/theBenchmark.p',fact_list__ex__length) ).
thf(4402,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)],[467]) ).
thf(2404,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ D @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_Oequations_I1_J) ).
thf(11683,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ D @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2404]) ).
thf(2035,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/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__graph__insertE) ).
thf(10367,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)],[2035]) ).
thf(1279,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Set_OPow @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ C ) @ A ) ) @ ( hAPP @ ( c_Set_Oimage @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) ) @ ( hAPP @ ( c_Set_OPow @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__insert) ).
thf(7501,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Set_OPow @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ C ) @ A ) ) @ ( hAPP @ ( c_Set_Oimage @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) ) @ ( hAPP @ ( c_Set_OPow @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1279]) ).
thf(893,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/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).
thf(6096,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)],[893]) ).
thf(1949,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ C @ B )
= ( hAPP @ C @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_injD) ).
thf(10006,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ C @ B )
= ( hAPP @ C @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1949]) ).
thf(672,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/sandbox/benchmark/theBenchmark.p',fact_nth__drop_H) ).
thf(5201,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)],[672]) ).
thf(1304,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ B @ A ) @ ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsp_ONil) ).
thf(7591,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)],[1304]) ).
thf(2389,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/sandbox/benchmark/theBenchmark.p',fact_fold__def) ).
thf(11646,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)],[2389]) ).
thf(2398,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Fun_Obij__betw @ H @ G @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ H @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ C @ H @ B ) @ A ) ) @ E ) )
=> ( ( c_Fun_Obij__betw @ C @ H @ B @ A @ E )
<=> ( c_Fun_Obij__betw @ C @ G @ ( hAPP @ ( c_Fun_Ocomp @ H @ G @ C @ F ) @ B ) @ A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__comp__iff2) ).
thf(11670,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Fun_Obij__betw @ H @ G @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ H @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ C @ H @ B ) @ A ) ) @ E ) )
=> ( ( ( c_Fun_Obij__betw @ C @ H @ B @ A @ E )
=> ( c_Fun_Obij__betw @ C @ G @ ( hAPP @ ( c_Fun_Ocomp @ H @ G @ C @ F ) @ B ) @ A @ D ) )
& ( ( c_Fun_Obij__betw @ C @ G @ ( hAPP @ ( c_Fun_Ocomp @ H @ G @ C @ F ) @ B ) @ A @ D )
=> ( c_Fun_Obij__betw @ C @ H @ B @ A @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2398]) ).
thf(2637,axiom,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ c_fNot @ A ) )
| ~ ( hBOOL @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__1) ).
thf(12603,plain,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ c_fNot @ A ) )
| ~ ( hBOOL @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2637]) ).
thf(470,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/sandbox/benchmark/theBenchmark.p',fact_listrel__rtrancl__refl) ).
thf(4417,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)],[470]) ).
thf(917,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__is__Un) ).
thf(6168,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(2485,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/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__def) ).
thf(11948,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)],[2485]) ).
thf(348,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/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__1) ).
thf(3926,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)],[348]) ).
thf(2224,axiom,
! [A: $i,B: $i] :
~ ? [C: $i] :
( ( hAPP @ ( c_Set_Oimage @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ A )
= ( hAPP @ ( c_Set_OPow @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cantors__paradox) ).
thf(11042,plain,
! [A: $i,B: $i] :
~ ? [C: $i] :
( ( hAPP @ ( c_Set_Oimage @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ A )
= ( hAPP @ ( c_Set_OPow @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2224]) ).
thf(1757,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/sandbox/benchmark/theBenchmark.p',fact_distinct__drop) ).
thf(9291,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)],[1757]) ).
thf(1058,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Relation_OImage @ C @ C @ ( c_Relation_OId__on @ C @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__Id__on) ).
thf(6666,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Relation_OImage @ C @ C @ ( c_Relation_OId__on @ C @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(1425,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 @ ( hAPP @ ( hAPP @ ( c_COMBC @ G @ ( tc_fun @ ( tc_prod @ G @ F ) @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ ( tc_fun @ ( tc_fun @ ( tc_prod @ G @ F ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ G @ F ) @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ G ) @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ G @ F ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ ( tc_prod @ G @ F ) ) @ ( tc_fun @ F @ ( tc_fun @ ( tc_fun @ ( tc_prod @ G @ F ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ G ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ G @ F ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ G @ F ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ F ) @ ( c_member @ ( tc_prod @ G @ F ) ) ) ) @ ( c_Product__Type_OPair @ G @ F ) ) ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E ) @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ C ) ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ G @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ E ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ G @ F @ E ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__comp__rel__comp__eq) ).
thf(8031,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 @ ( hAPP @ ( hAPP @ ( c_COMBC @ G @ ( tc_fun @ ( tc_prod @ G @ F ) @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ ( tc_fun @ ( tc_fun @ ( tc_prod @ G @ F ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ G @ F ) @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ G ) @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ G @ F ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ ( tc_prod @ G @ F ) ) @ ( tc_fun @ F @ ( tc_fun @ ( tc_fun @ ( tc_prod @ G @ F ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ G ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ G @ F ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ G @ F ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ F ) @ ( c_member @ ( tc_prod @ G @ F ) ) ) ) @ ( c_Product__Type_OPair @ G @ F ) ) ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E ) @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ C ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ G @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ E ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ G @ F @ E ) @ D ) @ C ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ G @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ E ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ G @ F @ E ) @ D ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ G @ F @ E @ ( hAPP @ ( hAPP @ ( c_COMBC @ G @ ( tc_fun @ ( tc_prod @ G @ F ) @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ ( tc_fun @ ( tc_fun @ ( tc_prod @ G @ F ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ G @ F ) @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ G ) @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ G @ F ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ ( tc_prod @ G @ F ) ) @ ( tc_fun @ F @ ( tc_fun @ ( tc_fun @ ( tc_prod @ G @ F ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ G ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ G @ F ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ G @ F ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ F ) @ ( c_member @ ( tc_prod @ G @ F ) ) ) ) @ ( c_Product__Type_OPair @ G @ F ) ) ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E ) @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ C ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1425]) ).
thf(1838,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Obij__betw @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( c_Fun_Obij__betw @ D @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( c_Fun_Obij__betw @ E @ B @ ( hAPP @ ( c_Fun_Ocomp @ D @ B @ E @ A ) @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__comp) ).
thf(9613,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Obij__betw @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( c_Fun_Obij__betw @ D @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( c_Fun_Obij__betw @ E @ B @ ( hAPP @ ( c_Fun_Ocomp @ D @ B @ E @ A ) @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1838]) ).
thf(2502,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ ( hAPP @ ( c_List_Ofilter @ C @ B ) @ A ) ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__is__subset) ).
thf(12020,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ ( hAPP @ ( c_List_Ofilter @ C @ B ) @ A ) ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2502]) ).
thf(2411,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/sandbox/benchmark/theBenchmark.p',fact_acc__downwards) ).
thf(11702,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)],[2411]) ).
thf(275,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/sandbox/benchmark/theBenchmark.p',fact_le__square) ).
thf(3667,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)],[275]) ).
thf(547,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
thf(4732,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)],[547]) ).
thf(2660,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/sandbox/benchmark/theBenchmark.p',fact_removeAll__id) ).
thf(12709,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)],[2660]) ).
thf(864,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( c_List_Olist_Olist__case @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) @ D @ ( c_List_Olist_ONil @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) ) @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) ) @ ( tc_fun @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) ) @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) ) ) @ D ) @ ( c_COMBB @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_prod @ E @ D ) @ ( tc_fun @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) ) @ D ) @ ( c_List_Olist_OCons @ ( tc_prod @ E @ D ) ) ) @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) ) ) ) @ ( hAPP @ ( c_List_Ozip @ E @ D ) @ B ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__Cons1) ).
thf(5993,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( c_List_Olist_Olist__case @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) @ D @ ( c_List_Olist_ONil @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) ) @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) ) @ ( tc_fun @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) ) @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) ) ) @ D ) @ ( c_COMBB @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_prod @ E @ D ) @ ( tc_fun @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) @ ( tc_List_Olist @ ( tc_prod @ E @ D ) ) ) @ D ) @ ( c_List_Olist_OCons @ ( tc_prod @ E @ D ) ) ) @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) ) ) ) @ ( hAPP @ ( c_List_Ozip @ E @ D ) @ B ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(703,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( c_Complete__Lattice_OInf__class_OInf @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ ( c_Complete__Lattice_OInf__class_OInf @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__insert) ).
thf(5330,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( c_Complete__Lattice_OInf__class_OInf @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ ( c_Complete__Lattice_OInf__class_OInf @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(1553,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ A @ tc_HOL_Obool ) @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__Times__UNIV) ).
thf(8518,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ A @ tc_HOL_Obool ) @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1553]) ).
thf(745,axiom,
( ( c_Orderings_Obot__class_Obot @ tc_Nat_Onat )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__nat__def) ).
thf(5515,plain,
( ( c_Orderings_Obot__class_Obot @ tc_Nat_Onat )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(528,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/sandbox/benchmark/theBenchmark.p',fact_length__map) ).
thf(4668,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)],[528]) ).
thf(708,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ E ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ E ) @ B ) ) ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__finite2__eq) ).
thf(5345,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ E ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ E ) @ B ) ) ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(2429,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_Hilbert__Choice_Oinv__into @ D @ F @ B @ ( hAPP @ ( c_Fun_Ocomp @ G @ F @ D @ E ) @ C ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ G @ D @ F @ ( c_Hilbert__Choice_Oinv__into @ D @ G @ B @ C ) ) @ ( c_Hilbert__Choice_Oinv__into @ G @ F @ ( hAPP @ ( c_Set_Oimage @ D @ G @ C ) @ B ) @ E ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__comp) ).
thf(11762,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_Hilbert__Choice_Oinv__into @ D @ F @ B @ ( hAPP @ ( c_Fun_Ocomp @ G @ F @ D @ E ) @ C ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ G @ D @ F @ ( c_Hilbert__Choice_Oinv__into @ D @ G @ B @ C ) ) @ ( c_Hilbert__Choice_Oinv__into @ G @ F @ ( hAPP @ ( c_Set_Oimage @ D @ G @ C ) @ B ) @ E ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2429]) ).
thf(2330,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
=> ( ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
| ( B
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__singletonD) ).
thf(11435,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
=> ( ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
| ( B
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2330]) ).
thf(1765,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ C @ B ) )
=> ( ( hAPP @ ( c_Set_OCollect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ A ) @ c_fconj ) @ ( hAPP @ c_fequal @ B ) ) ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ C @ B ) )
=> ( ( hAPP @ ( c_Set_OCollect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ A ) @ c_fconj ) @ ( hAPP @ c_fequal @ B ) ) ) @ C ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__conv__if2) ).
thf(9333,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ C @ B ) )
=> ( ( hAPP @ ( c_Set_OCollect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ A ) @ c_fconj ) @ ( hAPP @ c_fequal @ B ) ) ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ C @ B ) )
=> ( ( hAPP @ ( c_Set_OCollect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ A ) @ c_fconj ) @ ( hAPP @ c_fequal @ B ) ) ) @ C ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1765]) ).
thf(2297,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/sandbox/benchmark/theBenchmark.p',fact_insert__fold1SetE) ).
thf(11304,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)],[2297]) ).
thf(1483,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( c_Relation_OImage @ B @ B @ A ) @ C ) ) )
=> ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( c_Wellfounded_Owf @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfI__pf) ).
thf(8238,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( c_Relation_OImage @ B @ B @ A ) @ C ) ) )
=> ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( c_Wellfounded_Owf @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1483]) ).
thf(931,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ A @ B ) )
=> ( ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ A @ E ) )
=> ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__empty__induct) ).
thf(6215,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ A @ B ) )
=> ( ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ A @ E ) )
=> ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(295,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ D )
=> ( ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ D ) @ B ) @ A )
= ( c_Complete__Lattice_OInf__class_OInf @ D @ ( hAPP @ ( c_Set_OCollect @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool @ D ) @ ( c_HOL_OEx @ ( tc_fun @ C @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_COMBS @ ( tc_fun @ C @ D ) @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_fun @ C @ D ) ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ C @ D ) @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ ( tc_fun @ C @ D ) ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_fun @ C @ D ) @ D ) @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_fun @ C @ D ) @ D ) @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBB @ D @ tc_HOL_Obool @ ( tc_fun @ C @ D ) ) ) @ c_fequal ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ C @ D ) @ C @ D ) @ ( c_COMBI @ ( tc_fun @ C @ D ) ) ) @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__apply) ).
thf(3731,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ D )
=> ( ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ D ) @ B ) @ A )
= ( c_Complete__Lattice_OInf__class_OInf @ D @ ( hAPP @ ( c_Set_OCollect @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool @ D ) @ ( c_HOL_OEx @ ( tc_fun @ C @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_COMBS @ ( tc_fun @ C @ D ) @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_fun @ C @ D ) ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ C @ D ) @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ ( tc_fun @ C @ D ) ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_fun @ C @ D ) @ D ) @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_fun @ C @ D ) @ D ) @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBB @ D @ tc_HOL_Obool @ ( tc_fun @ C @ D ) ) ) @ c_fequal ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ C @ D ) @ C @ D ) @ ( c_COMBI @ ( tc_fun @ C @ D ) ) ) @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(567,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/sandbox/benchmark/theBenchmark.p',fact_take__all) ).
thf(4808,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)],[567]) ).
thf(1508,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/sandbox/benchmark/theBenchmark.p',fact_map_Osimps_I1_J) ).
thf(8354,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)],[1508]) ).
thf(1350,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ ( hAPP @ ( c_Set_OCollect @ D ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Set_OCollect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool @ B ) @ ( c_HOL_OEx @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( c_COMBS @ D @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ D @ B ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ B ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( c_COMBB @ B @ tc_HOL_Obool @ D ) ) @ c_fequal ) ) @ A ) ) ) ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__image__set) ).
thf(7750,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ ( hAPP @ ( c_Set_OCollect @ D ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Set_OCollect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool @ B ) @ ( c_HOL_OEx @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( c_COMBS @ D @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ D @ B ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ B ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( c_COMBB @ B @ tc_HOL_Obool @ D ) ) @ c_fequal ) ) @ A ) ) ) ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1350]) ).
thf(830,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/sandbox/benchmark/theBenchmark.p',fact_rtrancl__idemp__self__comp) ).
thf(5854,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)],[830]) ).
thf(393,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBS @ ( tc_prod @ F @ E ) @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ E @ D ) @ ( tc_prod @ F @ E ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ C @ ( tc_prod @ F @ E ) ) @ A ) @ ( c_Product__Type_Ofst @ F @ E ) ) ) ) @ ( c_Product__Type_Osnd @ F @ E ) )
= ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ F @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ E @ D ) @ F ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__comp__eq) ).
thf(4123,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBS @ ( tc_prod @ F @ E ) @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ E @ D ) @ ( tc_prod @ F @ E ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ C @ ( tc_prod @ F @ E ) ) @ A ) @ ( c_Product__Type_Ofst @ F @ E ) ) ) ) @ ( c_Product__Type_Osnd @ F @ E ) )
= ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ F @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ E @ D ) @ F ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(2674,axiom,
hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_HOL_Obool ) ) @ v_ts ) @ v_G ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(12760,plain,
hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_HOL_Obool ) ) @ v_ts ) @ v_G ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2674]) ).
thf(224,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_List_Oset @ B ) @ ( hAPP @ ( c_List_Orev @ B ) @ A ) )
= ( hAPP @ ( c_List_Oset @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__rev) ).
thf(3467,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_List_Oset @ B ) @ ( hAPP @ ( c_List_Orev @ B ) @ A ) )
= ( hAPP @ ( c_List_Oset @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(286,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( c_List_Olist_ONil @ B ) )
=> ( ( c_List_Olast @ B @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ A ) @ C ) )
= ( c_List_Olast @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__appendL) ).
thf(3699,plain,
! [A: $i,B: $i,C: $i] :
( ( C
= ( c_List_Olist_ONil @ B ) )
=> ( ( c_List_Olast @ B @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ A ) @ C ) )
= ( c_List_Olast @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(2419,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ F @ E @ D ) @ B ) ) @ ( hAPP @ ( c_Relation_OImage @ F @ E @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__mono) ).
thf(11736,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ F @ E @ D ) @ B ) ) @ ( hAPP @ ( c_Relation_OImage @ F @ E @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2419]) ).
thf(1557,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( c_Set_Ovimage @ A @ D @ ( hAPP @ ( c_COMBK @ D @ A ) @ C ) ) @ B )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( c_Set_Ovimage @ A @ D @ ( hAPP @ ( c_COMBK @ D @ A ) @ C ) ) @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__const) ).
thf(8530,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( c_Set_Ovimage @ A @ D @ ( hAPP @ ( c_COMBK @ D @ A ) @ C ) ) @ B )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( c_Set_Ovimage @ A @ D @ ( hAPP @ ( c_COMBK @ D @ A ) @ C ) ) @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1557]) ).
thf(1079,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__insert) ).
thf(6748,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).
thf(1536,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/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
thf(8471,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)],[1536]) ).
thf(2583,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/sandbox/benchmark/theBenchmark.p',fact_in__set__butlastD) ).
thf(12353,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)],[2583]) ).
thf(310,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ D @ B ) @ D ) @ ( c_Product__Type_Ofst @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ D @ B ) @ C ) @ A ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__fst__zip) ).
thf(3782,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ D @ B ) @ D ) @ ( c_Product__Type_Ofst @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ D @ B ) @ C ) @ A ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(845,axiom,
! [A: $i] :
( ( c_List_Olistset @ A @ ( c_List_Olist_ONil @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_List_Olist @ A ) ) @ ( c_List_Olist_ONil @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_List_Olist @ A ) @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listset_Osimps_I1_J) ).
thf(5904,plain,
! [A: $i] :
( ( c_List_Olistset @ A @ ( c_List_Olist_ONil @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_List_Olist @ A ) ) @ ( c_List_Olist_ONil @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_List_Olist @ A ) @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(1433,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding__image__simple @ F @ E @ D @ C @ B @ A )
=> ( ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Oempty) ).
thf(8068,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding__image__simple @ F @ E @ D @ C @ B @ A )
=> ( ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1433]) ).
thf(1060,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( c_Wellfounded_OwfP @ C @ ( hAPP @ B @ D ) )
=> ( ! [D: $i,E: $i] :
( ( ( hAPP @ B @ D )
!= ( hAPP @ B @ E ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Predicate_ODomainP @ C @ C @ ( hAPP @ B @ D ) ) ) @ ( c_Predicate_ORangeP @ C @ C @ ( hAPP @ B @ E ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( c_Wellfounded_OwfP @ C @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ C @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__SUP) ).
thf(6677,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( c_Wellfounded_OwfP @ C @ ( hAPP @ B @ D ) )
=> ( ! [D: $i,E: $i] :
( ( ( hAPP @ B @ D )
!= ( hAPP @ B @ E ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Predicate_ODomainP @ C @ C @ ( hAPP @ B @ D ) ) ) @ ( c_Predicate_ORangeP @ C @ C @ ( hAPP @ B @ E ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( c_Wellfounded_OwfP @ C @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ C @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).
thf(322,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__assoc) ).
thf(3831,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(2251,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/sandbox/benchmark/theBenchmark.p',fact_drop__Suc__Cons) ).
thf(11133,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)],[2251]) ).
thf(636,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ tc_Nat_Onat ) @ A ) @ B )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
<=> ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
& ( ( hAPP @ A @ D )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( D != E )
=> ( ( hAPP @ A @ E )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__eq__1__iff) ).
thf(5053,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ tc_Nat_Onat ) @ A ) @ B )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
& ( ( hAPP @ A @ D )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( D != E )
=> ( ( hAPP @ A @ E )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) )
& ( ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
& ( ( hAPP @ A @ D )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( D != E )
=> ( ( hAPP @ A @ E )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ tc_Nat_Onat ) @ A ) @ B )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(894,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ G ) @ C ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ F ) @ ( hAPP @ ( c_Set_OCollect @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ F @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ F ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ F @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ F ) ) @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ D @ tc_HOL_Obool ) @ B ) @ G ) ) ) )
= ( hAPP @ A @ G ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ F @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_Nat_Onat @ F ) @ ( c_Finite__Set_Ocard @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ F ) @ ( c_Set_OCollect @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( c_COMBS @ D @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ C ) ) ) ) @ B ) ) ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__multicount__gen) ).
thf(6101,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ G ) @ C ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ F ) @ ( hAPP @ ( c_Set_OCollect @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ F @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ F ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ F @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ F ) ) @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ D @ tc_HOL_Obool ) @ B ) @ G ) ) ) )
= ( hAPP @ A @ G ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ F @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_Nat_Onat @ F ) @ ( c_Finite__Set_Ocard @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ F ) @ ( c_Set_OCollect @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( c_COMBS @ D @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ C ) ) ) ) @ B ) ) ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(2594,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/sandbox/benchmark/theBenchmark.p',fact_fold__graph_OinsertI) ).
thf(12404,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)],[2594]) ).
thf(124,axiom,
class_Rings_Osemiring__0 @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).
thf(3122,plain,
class_Rings_Osemiring__0 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( hAPP @ ( c_List_Oset @ C ) @ B ) ) )
=> ( ( c_List_OtakeWhile @ C @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ C ) @ c_fNot ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ C @ tc_HOL_Obool ) @ c_fequal ) @ A ) ) @ ( hAPP @ ( c_List_Orev @ C ) @ B ) )
= ( hAPP @ ( c_List_Orev @ C ) @ ( hAPP @ ( c_List_Otl @ C ) @ ( c_List_OdropWhile @ C @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ C ) @ c_fNot ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ C @ tc_HOL_Obool ) @ c_fequal ) @ A ) ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile__neq__rev) ).
thf(2946,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( hAPP @ ( c_List_Oset @ C ) @ B ) ) )
=> ( ( c_List_OtakeWhile @ C @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ C ) @ c_fNot ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ C @ tc_HOL_Obool ) @ c_fequal ) @ A ) ) @ ( hAPP @ ( c_List_Orev @ C ) @ B ) )
= ( hAPP @ ( c_List_Orev @ C ) @ ( hAPP @ ( c_List_Otl @ C ) @ ( c_List_OdropWhile @ C @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ C ) @ c_fNot ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ C @ tc_HOL_Obool ) @ c_fequal ) @ A ) ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(1204,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/sandbox/benchmark/theBenchmark.p',fact_zip__Nil) ).
thf(7205,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)],[1204]) ).
thf(969,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__Diff) ).
thf(6335,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(1159,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/sandbox/benchmark/theBenchmark.p',fact_Suc__mono) ).
thf(7065,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)],[1159]) ).
thf(333,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_List_Orev @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ D ) @ B ) @ ( hAPP @ ( c_List_Orev @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__map) ).
thf(3862,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_List_Orev @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ D ) @ B ) @ ( hAPP @ ( c_List_Orev @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(1978,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/sandbox/benchmark/theBenchmark.p',fact_map__butlast) ).
thf(10126,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)],[1978]) ).
thf(2050,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ! [G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ G ) @ H ) ) @ E ) )
=> ! [I: $i,J: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ I ) @ J ) ) @ C ) )
=> ( ( hAPP @ ( hAPP @ B @ G ) @ I )
= ( hAPP @ ( hAPP @ B @ H ) @ J ) ) ) )
=> ( c_Equiv__Relations_Ocongruent2 @ F @ D @ A @ E @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_congruent2I_H) ).
thf(10413,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ! [G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ G ) @ H ) ) @ E ) )
=> ! [I: $i,J: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ I ) @ J ) ) @ C ) )
=> ( ( hAPP @ ( hAPP @ B @ G ) @ I )
= ( hAPP @ ( hAPP @ B @ H ) @ J ) ) ) )
=> ( c_Equiv__Relations_Ocongruent2 @ F @ D @ A @ E @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2050]) ).
thf(1983,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ F ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ E @ H ) @ D ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ G @ ( tc_fun @ B @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) @ F ) @ E ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF2__I) ).
thf(10154,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ F ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ E @ H ) @ D ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ G @ ( tc_fun @ B @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) @ F ) @ E ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1983]) ).
thf(2151,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ B @ A ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Prod__UNIV) ).
thf(10791,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ B @ A ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2151]) ).
thf(1489,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Relation_ODomain @ C @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( c_Relation_ODomain @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Union) ).
thf(8282,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Relation_ODomain @ C @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( c_Relation_ODomain @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1489]) ).
thf(1313,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/sandbox/benchmark/theBenchmark.p',fact_rtrancl__listrel1__if__listrel) ).
thf(7623,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)],[1313]) ).
thf(1194,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/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofun__left__comm) ).
thf(7173,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)],[1194]) ).
thf(1763,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__idemp) ).
thf(9328,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1763]) ).
thf(200,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).
thf(3381,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(1247,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ E @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ E @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ E @ D ) ) ) ) @ ( c_Product__Type_OPair @ E @ D ) ) ) ) ) @ C ) ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP__UN__eq2) ).
thf(7389,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ E @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ E @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ E @ D ) ) ) ) @ ( c_Product__Type_OPair @ E @ D ) ) ) ) ) @ C ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ C ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ E @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ E @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ E @ D ) ) ) ) @ ( c_Product__Type_OPair @ E @ D ) ) ) ) ) @ C ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1247]) ).
thf(742,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ tc_Nat_Onat ) @ A ) @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( ( hAPP @ A @ D )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__eq__0__iff) ).
thf(5502,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ tc_Nat_Onat ) @ A ) @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( ( hAPP @ A @ D )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( ( hAPP @ A @ D )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ tc_Nat_Onat ) @ A ) @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(1836,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Set_Oimage @ F @ ( tc_prod @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ F @ D @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ D @ ( tc_prod @ E @ D ) ) @ F ) @ ( c_Product__Type_OPair @ E @ D ) ) @ C ) ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ ( c_Set_Oimage @ F @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) @ E ) @ ( c_Set_Ovimage @ F @ E @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ E ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__split__eq__Sigma) ).
thf(9608,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Set_Oimage @ F @ ( tc_prod @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ F @ D @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ D @ ( tc_prod @ E @ D ) ) @ F ) @ ( c_Product__Type_OPair @ E @ D ) ) @ C ) ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ ( c_Set_Oimage @ F @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) @ E ) @ ( c_Set_Ovimage @ F @ E @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ E ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1836]) ).
thf(2091,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/sandbox/benchmark/theBenchmark.p',fact_Range__iff) ).
thf(10566,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)],[2091]) ).
thf(502,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 ) ) )
=> ( ( c_List_Olast @ B @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ B ) @ C ) @ A ) )
= ( c_List_Olast @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__drop) ).
thf(4544,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 ) ) )
=> ( ( c_List_Olast @ B @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ B ) @ C ) @ A ) )
= ( c_List_Olast @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(2212,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2E) ).
thf(11007,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2212]) ).
thf(2274,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/sandbox/benchmark/theBenchmark.p',fact_le__Suc__eq) ).
thf(11221,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)],[2274]) ).
thf(2008,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ C @ C @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Otrancl @ C @ B ) ) @ A ) ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Otrancl @ C @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__Int__subset) ).
thf(10266,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ C @ C @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Otrancl @ C @ B ) ) @ A ) ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Otrancl @ C @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2008]) ).
thf(1431,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ ( c_Set_Ovimage @ D @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Union) ).
thf(8063,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ ( c_Set_Ovimage @ D @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1431]) ).
thf(5,axiom,
! [A: $i] :
( ! [B: $i] : ( hBOOL @ ( hAPP @ A @ B ) )
<=> ! [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 @ A @ ( hAPP @ c_Int_Onat @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__nat) ).
thf(2692,plain,
! [A: $i] :
( ( ! [B: $i] : ( hBOOL @ ( hAPP @ A @ B ) )
=> ! [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 @ A @ ( hAPP @ c_Int_Onat @ B ) ) ) ) )
& ( ! [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 @ A @ ( hAPP @ c_Int_Onat @ B ) ) ) )
=> ! [B: $i] : ( hBOOL @ ( hAPP @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1658,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/sandbox/benchmark/theBenchmark.p',fact_trans__lex__prod) ).
thf(8931,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)],[1658]) ).
thf(499,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/sandbox/benchmark/theBenchmark.p',fact_add__gr__0) ).
thf(4525,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)],[499]) ).
thf(536,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ A ) @ ( c_Complete__Lattice_OSup__class_OSup @ C @ B ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ C @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__Sup__fold__sup) ).
thf(4693,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ A ) @ ( c_Complete__Lattice_OSup__class_OSup @ C @ B ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ C @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(720,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/sandbox/benchmark/theBenchmark.p',fact_diff__mult__distrib) ).
thf(5428,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)],[720]) ).
thf(1932,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Obij__betw @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__vimage__iff) ).
thf(9936,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Obij__betw @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ ( hAPP @ ( c_Set_Ovimage @ D @ 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 @ D ) @ ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1932]) ).
thf(1305,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Obij__betw @ D @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__empty1) ).
thf(7593,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Obij__betw @ D @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1305]) ).
thf(601,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( class_Orderings_Oorder @ E )
& ( class_Orderings_Oorder @ D ) )
=> ( ( c_Orderings_Oorder__class_Omono @ D @ E @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_monoD) ).
thf(4930,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( class_Orderings_Oorder @ E )
& ( class_Orderings_Oorder @ D ) )
=> ( ( c_Orderings_Oorder__class_Omono @ D @ E @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(2023,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( ( ( hAPP @ ( c_Set_Oimage @ B @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( c_Fun_Oinj__on @ B @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__surj__inj) ).
thf(10318,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( ( ( hAPP @ ( c_Set_Oimage @ B @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( c_Fun_Oinj__on @ B @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2023]) ).
thf(2249,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/sandbox/benchmark/theBenchmark.p',fact_trancl_Or__into__trancl) ).
thf(11128,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)],[2249]) ).
thf(848,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_List_Osublist @ D @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ ( c_List_Osublist @ D @ C @ A ) ) @ ( c_List_Osublist @ D @ B @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( c_member @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__append) ).
thf(5919,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_List_Osublist @ D @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ ( c_List_Osublist @ D @ C @ A ) ) @ ( c_List_Osublist @ D @ B @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( c_member @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(264,axiom,
! [A: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ A )
=> ( ( c_Complete__Lattice_OSup__class_OSup @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__UNIV) ).
thf(3632,plain,
! [A: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ A )
=> ( ( c_Complete__Lattice_OSup__class_OSup @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(123,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
thf(3119,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(2046,axiom,
! [A: $i,B: $i] :
( ? [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) )
<=> ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__in__conv) ).
thf(10398,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) )
=> ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ? [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2046]) ).
thf(115,axiom,
! [A: $i,B: $i] :
( ( hAPP @ c_Int_Onat @ ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat) ).
thf(3078,plain,
! [A: $i,B: $i] :
( ( hAPP @ c_Int_Onat @ ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(584,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/sandbox/benchmark/theBenchmark.p',fact_length__drop) ).
thf(4883,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)],[584]) ).
thf(2146,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Fun_Othe__inv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__f__f) ).
thf(10771,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Fun_Othe__inv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2146]) ).
thf(639,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Osemilattice__inf @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ B ) @ A ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__idem) ).
thf(5081,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Osemilattice__inf @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ B ) @ A ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(2264,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__right) ).
thf(11189,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2264]) ).
thf(365,axiom,
class_Lattices_Osemilattice__inf @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Osemilattice__inf) ).
thf(4012,plain,
class_Lattices_Osemilattice__inf @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(902,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__left__commute) ).
thf(6128,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(1207,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/sandbox/benchmark/theBenchmark.p',fact_card_Oinsert) ).
thf(7222,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)],[1207]) ).
thf(388,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/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__upt) ).
thf(4109,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)],[388]) ).
thf(679,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Finite__Set_Ofolding__idem @ G @ F @ E @ D )
=> ( ( hAPP @ ( c_Fun_Ocomp @ F @ F @ C @ ( hAPP @ E @ B ) ) @ ( hAPP @ ( c_Fun_Ocomp @ F @ F @ C @ ( hAPP @ E @ B ) ) @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ F @ F @ C @ ( hAPP @ E @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__idem_Oidem__left__comp) ).
thf(5233,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Finite__Set_Ofolding__idem @ G @ F @ E @ D )
=> ( ( hAPP @ ( c_Fun_Ocomp @ F @ F @ C @ ( hAPP @ E @ B ) ) @ ( hAPP @ ( c_Fun_Ocomp @ F @ F @ C @ ( hAPP @ E @ B ) ) @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ F @ F @ C @ ( hAPP @ E @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(1454,axiom,
! [A: $i] :
( ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__empty) ).
thf(8138,plain,
! [A: $i] :
( ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1454]) ).
thf(2287,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/sandbox/benchmark/theBenchmark.p',fact_eq__card__imp__inj__on) ).
thf(11278,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)],[2287]) ).
thf(740,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Nat_Onat @ 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 ) ) @ D ) @ B ) ) @ c_FunDef_Opair__less ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ c_FunDef_Omin__strict ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ B ) @ A ) ) ) @ c_FunDef_Omin__strict ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smin__insertI) ).
thf(5497,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Nat_Onat @ 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 ) ) @ D ) @ B ) ) @ c_FunDef_Opair__less ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ c_FunDef_Omin__strict ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ B ) @ A ) ) ) @ c_FunDef_Omin__strict ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(734,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_FunDef_Oreduction__pair @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Product__Type_Ofst @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Product__Type_Osnd @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) @ C ) ) )
=> ( ( c_Wellfounded_Owf @ D @ A )
=> ( c_Wellfounded_Owf @ D @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reduction__pair__lemma) ).
thf(5475,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_FunDef_Oreduction__pair @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Product__Type_Ofst @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Product__Type_Osnd @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) @ C ) ) )
=> ( ( c_Wellfounded_Owf @ D @ A )
=> ( c_Wellfounded_Owf @ D @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(90,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/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
thf(3001,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)],[90]) ).
thf(109,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/sandbox/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib2) ).
thf(3060,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)],[109]) ).
thf(1882,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/sandbox/benchmark/theBenchmark.p',fact_filter__map) ).
thf(9772,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)],[1882]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ E @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ E @ ( tc_fun @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ E @ ( tc_fun @ E @ E ) ) @ D ) @ ( c_If @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ A ) ) ) @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ E ) ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__restrict__set) ).
thf(3018,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ E @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ E @ ( tc_fun @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ E @ ( tc_fun @ E @ E ) ) @ D ) @ ( c_If @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ A ) ) ) @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ E ) ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(2216,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( c_Fun_Oinj__on @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__diff) ).
thf(11019,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( c_Fun_Oinj__on @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2216]) ).
thf(2478,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/sandbox/benchmark/theBenchmark.p',fact_RangeE) ).
thf(11923,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)],[2478]) ).
thf(569,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/sandbox/benchmark/theBenchmark.p',fact_impossible__Cons) ).
thf(4817,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)],[569]) ).
thf(432,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( c_Wellfounded_Owf @ ( tc_List_Olist @ C ) @ ( hAPP @ ( c_List_Olexn @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__lexn) ).
thf(4263,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( c_Wellfounded_Owf @ ( tc_List_Olist @ C ) @ ( hAPP @ ( c_List_Olexn @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(822,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ ( tc_prod @ D @ B ) ) @ ( c_Enum_Oproduct @ D @ B @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__product) ).
thf(5830,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ ( tc_prod @ D @ B ) ) @ ( c_Enum_Oproduct @ D @ B @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(435,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__idem @ E @ D @ C @ B )
=> ( ( hAPP @ ( c_Fun_Ocomp @ D @ D @ D @ ( hAPP @ C @ A ) ) @ ( hAPP @ C @ A ) )
= ( hAPP @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__idem_Oidem__comp) ).
thf(4276,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__idem @ E @ D @ C @ B )
=> ( ( hAPP @ ( c_Fun_Ocomp @ D @ D @ D @ ( hAPP @ C @ A ) ) @ ( hAPP @ C @ A ) )
= ( hAPP @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(1640,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E ) @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E ) @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ C ) ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__Int__eq2) ).
thf(8864,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E ) @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E ) @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ C ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ D ) @ C ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ D ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E ) @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E ) @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ C ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1640]) ).
thf(442,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oord @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_SetInterval_Oord__class_OgreaterThan @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThan__iff) ).
thf(4315,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oord @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_SetInterval_Oord__class_OgreaterThan @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_SetInterval_Oord__class_OgreaterThan @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(1803,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/sandbox/benchmark/theBenchmark.p',fact_removeAll__append) ).
thf(9477,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)],[1803]) ).
thf(982,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/sandbox/benchmark/theBenchmark.p',fact_Suc__leI) ).
thf(6395,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)],[982]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Groups_Ocomm__monoid__add @ F )
=> ( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ F ) @ A ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ E @ F ) @ ( hAPP @ ( c_Fun_Ocomp @ D @ F @ E @ A ) @ C ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__reindex) ).
thf(2781,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Groups_Ocomm__monoid__add @ F )
=> ( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ F ) @ A ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ E @ F ) @ ( hAPP @ ( c_Fun_Ocomp @ D @ F @ E @ A ) @ C ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(530,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Enum_Oproduct @ C @ B @ ( c_List_Olist_ONil @ C ) @ A )
= ( c_List_Olist_ONil @ ( tc_prod @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_product_Osimps_I1_J) ).
thf(4676,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Enum_Oproduct @ C @ B @ ( c_List_Olist_ONil @ C ) @ A )
= ( c_List_Olist_ONil @ ( tc_prod @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(2441,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/sandbox/benchmark/theBenchmark.p',fact_refl__onD2) ).
thf(11801,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)],[2441]) ).
thf(960,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_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ ( tc_prod @ G @ F ) @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ ( tc_prod @ G @ E ) @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ G @ E ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ G @ F ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ G @ E ) @ tc_HOL_Obool ) ) @ D ) @ ( c_Relation_Orel__comp @ G @ F @ E ) ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__UNION__distrib2) ).
thf(6299,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_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ ( tc_prod @ G @ F ) @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ ( tc_prod @ G @ E ) @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ G @ E ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ G @ F ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ G @ E ) @ tc_HOL_Obool ) ) @ D ) @ ( c_Relation_Orel__comp @ G @ F @ E ) ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(1465,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Set_Oimage @ F @ E @ ( hAPP @ ( hAPP @ ( c_COMBS @ F @ E @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ F @ E @ ( tc_fun @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ E @ ( tc_fun @ E @ E ) ) @ F ) @ ( c_If @ E ) ) @ D ) ) @ C ) ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Set_OCollect @ F ) @ D ) ) ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Set_OCollect @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ F ) @ c_fNot ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_if__image__distrib) ).
thf(8176,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Set_Oimage @ F @ E @ ( hAPP @ ( hAPP @ ( c_COMBS @ F @ E @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ F @ E @ ( tc_fun @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ E @ ( tc_fun @ E @ E ) ) @ F ) @ ( c_If @ E ) ) @ D ) ) @ C ) ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Set_OCollect @ F ) @ D ) ) ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Set_OCollect @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ F ) @ c_fNot ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1465]) ).
thf(1172,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ D @ E ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ C @ ( hAPP @ B @ E ) ) ) @ ( hAPP @ C @ E ) ) ) )
=> ( c_Wellfounded_Owf @ A @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ A @ A ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ A @ A @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( tc_fun @ A @ tc_HOL_Obool ) @ A ) @ ( hAPP @ ( c_COMBS @ A @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ A ) @ c_fconj ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ A ) @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ A @ A ) @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ A ) @ ( c_COMBB @ A @ tc_HOL_Obool @ A ) ) @ c_fequal ) ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__if__measure) ).
thf(7101,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ D @ E ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ C @ ( hAPP @ B @ E ) ) ) @ ( hAPP @ C @ E ) ) ) )
=> ( c_Wellfounded_Owf @ A @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ A @ A ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ A @ A @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( tc_fun @ A @ tc_HOL_Obool ) @ A ) @ ( hAPP @ ( c_COMBS @ A @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ A ) @ c_fconj ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ A ) @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ A @ A ) @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ A ) @ ( c_COMBB @ A @ tc_HOL_Obool @ A ) ) @ c_fequal ) ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).
thf(1910,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) )
<=> ? [D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__power) ).
thf(9872,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) )
=> ? [D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ D ) @ A ) ) ) )
& ( ? [D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ D ) @ 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)],[1910]) ).
thf(1560,axiom,
! [A: $i,B: $i] : ( c_Relation_Osym @ B @ ( c_Relation_OId__on @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sym__Id__on) ).
thf(8544,plain,
! [A: $i,B: $i] : ( c_Relation_Osym @ B @ ( c_Relation_OId__on @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1560]) ).
thf(179,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( ( hAPP @ A @ F )
= ( c_Groups_Ozero__class_Ozero @ E ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__Un__zero) ).
thf(3311,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( ( hAPP @ A @ F )
= ( c_Groups_Ozero__class_Ozero @ E ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(1974,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_List_Olist__ex1 @ D @ C @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ A ) )
<=> ( ( ( hBOOL @ ( hAPP @ C @ B ) )
=> ( c_List_Olist__all @ D @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fdisj ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ D ) @ c_fNot ) @ C ) ) ) @ ( hAPP @ c_fequal @ B ) ) @ A ) )
& ( ~ ( hBOOL @ ( hAPP @ C @ B ) )
=> ( c_List_Olist__ex1 @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__ex1__simps_I2_J) ).
thf(10107,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_List_Olist__ex1 @ D @ C @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ C @ B ) )
=> ( c_List_Olist__all @ D @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fdisj ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ D ) @ c_fNot ) @ C ) ) ) @ ( hAPP @ c_fequal @ B ) ) @ A ) )
& ( ~ ( hBOOL @ ( hAPP @ C @ B ) )
=> ( c_List_Olist__ex1 @ D @ C @ A ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP @ C @ B ) )
=> ( c_List_Olist__all @ D @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fdisj ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ D ) @ c_fNot ) @ C ) ) ) @ ( hAPP @ c_fequal @ B ) ) @ A ) )
& ( ~ ( hBOOL @ ( hAPP @ C @ B ) )
=> ( c_List_Olist__ex1 @ D @ C @ A ) ) )
=> ( c_List_Olist__ex1 @ D @ C @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1974]) ).
thf(55,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 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ B ) ) @ ( hAPP @ c_Int_Onat @ A ) )
= ( hAPP @ c_Int_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J) ).
thf(2877,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 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ B ) ) @ ( hAPP @ c_Int_Onat @ A ) )
= ( hAPP @ c_Int_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(441,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ ( c_List_Olist_ONil @ D ) ) )
= A )
<=> ( ( A
!= ( c_List_Olist_ONil @ D ) )
& ( ( c_List_Obutlast @ D @ A )
= C )
& ( ( c_List_Olast @ D @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snoc__eq__iff__butlast) ).
thf(4301,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ ( c_List_Olist_ONil @ D ) ) )
= A )
=> ( ( A
!= ( c_List_Olist_ONil @ D ) )
& ( ( c_List_Obutlast @ D @ A )
= C )
& ( ( c_List_Olast @ D @ A )
= B ) ) )
& ( ( ( A
!= ( c_List_Olist_ONil @ D ) )
& ( ( c_List_Obutlast @ D @ A )
= C )
& ( ( c_List_Olast @ D @ A )
= B ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ ( c_List_Olist_ONil @ D ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(183,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Otl @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tl_Osimps_I2_J) ).
thf(3326,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Otl @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(130,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ E ) @ D ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ 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_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ E @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) ) @ B ) ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__shift__bounds__nat__ivl) ).
thf(3143,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ E ) @ D ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ 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_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ E @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) ) @ B ) ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(2677,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hAPP @ B @ C )
= ( hAPP @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ext) ).
thf(12768,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hAPP @ B @ C )
= ( hAPP @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2677]) ).
thf(1445,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/sandbox/benchmark/theBenchmark.p',fact_transp__def) ).
thf(8105,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)],[1445]) ).
thf(1846,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/sandbox/benchmark/theBenchmark.p',fact_append__self__conv2) ).
thf(9640,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)],[1846]) ).
thf(2162,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ~ ! [G: $i,H: $i] :
( ( A
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ G ) @ H ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( hAPP @ ( hAPP @ B @ G ) @ H ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__splitE) ).
thf(10830,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ~ ! [G: $i,H: $i] :
( ( A
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ G ) @ H ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( hAPP @ ( hAPP @ B @ G ) @ H ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2162]) ).
thf(1991,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/sandbox/benchmark/theBenchmark.p',fact_transD) ).
thf(10185,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)],[1991]) ).
thf(1810,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ A @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__insert) ).
thf(9508,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ A @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1810]) ).
thf(1675,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Ozip @ H @ G ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ F @ H ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ G ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ F @ C ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ F @ C @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ C @ G ) @ ( tc_fun @ C @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ G @ ( tc_prod @ H @ G ) ) @ ( tc_fun @ ( tc_fun @ C @ G ) @ ( tc_fun @ C @ ( tc_prod @ H @ G ) ) ) @ F ) @ ( c_COMBB @ G @ ( tc_prod @ H @ G ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ H @ ( tc_fun @ G @ ( tc_prod @ H @ G ) ) @ F ) @ ( c_Product__Type_OPair @ H @ G ) ) @ E ) ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ F @ C ) @ D ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__map__map) ).
thf(8985,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Ozip @ H @ G ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ F @ H ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ G ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ F @ C ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ F @ C @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ C @ G ) @ ( tc_fun @ C @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ G @ ( tc_prod @ H @ G ) ) @ ( tc_fun @ ( tc_fun @ C @ G ) @ ( tc_fun @ C @ ( tc_prod @ H @ G ) ) ) @ F ) @ ( c_COMBB @ G @ ( tc_prod @ H @ G ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ H @ ( tc_fun @ G @ ( tc_prod @ H @ G ) ) @ F ) @ ( c_Product__Type_OPair @ H @ G ) ) @ E ) ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ F @ C ) @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1675]) ).
thf(1156,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Ozip @ F @ E ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ D @ F ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ D @ E ) @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ E @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ D ) @ ( c_Product__Type_OPair @ F @ E ) ) @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ D @ E ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__map1) ).
thf(7054,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Ozip @ F @ E ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ D @ F ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ D @ E ) @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ E @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ D ) @ ( c_Product__Type_OPair @ F @ E ) ) @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ D @ E ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).
thf(2314,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ E @ C ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ E @ C ) @ A ) ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__diff__subset) ).
thf(11364,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ E @ C ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ E @ C ) @ A ) ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2314]) ).
thf(1263,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Obij__betw @ E @ D @ C @ B @ A )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ E ) @ B )
= ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__same__card) ).
thf(7453,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Obij__betw @ E @ D @ C @ B @ A )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ E ) @ B )
= ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1263]) ).
thf(262,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
!= ( c_List_Olist_ONil @ C ) )
=> ( ( c_List_Olast @ B @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ B ) @ A ) @ D ) )
= ( hAPP @ A @ ( c_List_Olast @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__map) ).
thf(3622,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
!= ( c_List_Olist_ONil @ C ) )
=> ( ( c_List_Olast @ B @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ B ) @ A ) @ D ) )
= ( hAPP @ A @ ( c_List_Olast @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(1852,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( c_Set_Oimage @ F @ E @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__UN) ).
thf(9662,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( c_Set_Oimage @ F @ E @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1852]) ).
thf(792,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/sandbox/benchmark/theBenchmark.p',fact_nat__diff__add__eq1) ).
thf(5705,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)],[792]) ).
thf(1339,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/sandbox/benchmark/theBenchmark.p',fact_add__diff__inverse) ).
thf(7717,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)],[1339]) ).
thf(780,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ G @ F @ E ) @ ( hAPP @ ( c_Fun_Ocomp @ D @ ( tc_fun @ F @ E ) @ G @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ C @ ( hAPP @ B @ ( hAPP @ ( c_Product__Type_Ofst @ G @ F ) @ A ) ) ) @ ( hAPP @ ( c_Product__Type_Osnd @ G @ F ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__comp) ).
thf(5651,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ G @ F @ E ) @ ( hAPP @ ( c_Fun_Ocomp @ D @ ( tc_fun @ F @ E ) @ G @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ C @ ( hAPP @ B @ ( hAPP @ ( c_Product__Type_Ofst @ G @ F ) @ A ) ) ) @ ( hAPP @ ( c_Product__Type_Osnd @ G @ F ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(559,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) @ ( c_List_Olists @ C @ B ) ) @ ( c_List_Olists @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists__mono) ).
thf(4772,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) @ ( c_List_Olists @ C @ B ) ) @ ( c_List_Olists @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(898,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/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
thf(6116,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)],[898]) ).
thf(1952,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_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__finite__subset) ).
thf(10015,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_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1952]) ).
thf(1378,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_List_Olistsp @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ C ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ ( tc_List_Olist @ C ) ) ) @ ( c_List_Olists @ C @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ C ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ ( tc_List_Olist @ C ) ) ) @ ( c_List_Olists @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists__Int__eq) ).
thf(7846,plain,
! [A: $i,B: $i,C: $i] :
( ( c_List_Olistsp @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ C ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ ( tc_List_Olist @ C ) ) ) @ ( c_List_Olists @ C @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ C ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ ( tc_List_Olist @ C ) ) ) @ ( c_List_Olists @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1378]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Groups_Ocomm__monoid__mult @ F )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ D ) )
=> ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ G ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ B @ G ) ) ) )
=> ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ G ) @ D ) )
=> ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ H ) @ D ) )
=> ( ( G != H )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ B @ G ) ) @ ( hAPP @ B @ H ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ F @ C @ ( c_Groups_Otimes__class_Otimes @ F ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ F @ E @ ( c_Groups_Otimes__class_Otimes @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ F @ E ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ F @ C @ ( c_Groups_Otimes__class_Otimes @ F ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ F ) ) ) @ B ) ) @ ( c_Groups_Oone__class_Oone @ F ) ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__UN__disjoint) ).
thf(3094,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Groups_Ocomm__monoid__mult @ F )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ D ) )
=> ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ G ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ B @ G ) ) ) )
=> ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ G ) @ D ) )
=> ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ H ) @ D ) )
=> ( ( G != H )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ B @ G ) ) @ ( hAPP @ B @ H ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ F @ C @ ( c_Groups_Otimes__class_Otimes @ F ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ F @ E @ ( c_Groups_Otimes__class_Otimes @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ F @ E ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ F @ C @ ( c_Groups_Otimes__class_Otimes @ F ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ F ) ) ) @ B ) ) @ ( c_Groups_Oone__class_Oone @ F ) ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(1411,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofolding__one @ D @ C @ B )
=> ( ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Osingleton) ).
thf(7981,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofolding__one @ D @ C @ B )
=> ( ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1411]) ).
thf(473,axiom,
! [A: $i,B: $i] :
( ( c_Product__Type_Omap__pair @ B @ B @ A @ A @ ( c_COMBI @ B ) @ ( c_COMBI @ A ) )
= ( c_Fun_Oid @ ( tc_prod @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair_Oidentity) ).
thf(4425,plain,
! [A: $i,B: $i] :
( ( c_Product__Type_Omap__pair @ B @ B @ A @ A @ ( c_COMBI @ B ) @ ( c_COMBI @ A ) )
= ( c_Fun_Oid @ ( tc_prod @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(2143,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__subset__eq2) ).
thf(10761,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2143]) ).
thf(2082,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/sandbox/benchmark/theBenchmark.p',fact_wf__not__sym) ).
thf(10528,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)],[2082]) ).
thf(291,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/sandbox/benchmark/theBenchmark.p',fact_map__eq__imp__length__eq) ).
thf(3714,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)],[291]) ).
thf(1056,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_List_Olist @ B ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_List_Oset @ B ) ) @ ( c_Enum_Osublists @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__set__sublists) ).
thf(6661,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_List_Olist @ B ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_List_Oset @ B ) ) @ ( c_Enum_Osublists @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).
thf(2041,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__iff) ).
thf(10381,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2041]) ).
thf(51,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/sandbox/benchmark/theBenchmark.p',fact_le__imp__0__less) ).
thf(2868,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)],[51]) ).
thf(463,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/sandbox/benchmark/theBenchmark.p',fact_less__Suc0) ).
thf(4389,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)],[463]) ).
thf(1416,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ D ) ) @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__fun__def) ).
thf(7998,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ D ) ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) ) @ A ) @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) ) @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ D ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1416]) ).
thf(1419,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I9_J) ).
thf(8008,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1419]) ).
thf(1787,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ B ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ B @ C ) @ A ) ) @ ( c_Product__Type_OPair @ D @ C ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__eta) ).
thf(9419,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ B ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ B @ C ) @ A ) ) @ ( c_Product__Type_OPair @ D @ C ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1787]) ).
thf(1938,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/sandbox/benchmark/theBenchmark.p',fact_fold1Set_Oequations) ).
thf(9957,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)],[1938]) ).
thf(684,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( c_List_Orev @ C ) @ B )
= A )
<=> ( B
= ( hAPP @ ( c_List_Orev @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__swap) ).
thf(5253,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ C ) @ B )
= A )
=> ( B
= ( hAPP @ ( c_List_Orev @ C ) @ A ) ) )
& ( ( B
= ( hAPP @ ( c_List_Orev @ C ) @ A ) )
=> ( ( hAPP @ ( c_List_Orev @ C ) @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(2117,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/sandbox/benchmark/theBenchmark.p',fact_Id__on__eqI) ).
thf(10671,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)],[2117]) ).
thf(604,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I12_J) ).
thf(4938,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(2106,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/sandbox/benchmark/theBenchmark.p',fact_trancl__into__trancl2) ).
thf(10620,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)],[2106]) ).
thf(686,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__commute) ).
thf(5263,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(755,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
<=> ( ( ( hAPP @ ( c_Product__Type_Ofst @ B @ A ) @ D )
= ( hAPP @ ( c_Product__Type_Ofst @ B @ A ) @ C ) )
& ( ( hAPP @ ( c_Product__Type_Osnd @ B @ A ) @ D )
= ( hAPP @ ( c_Product__Type_Osnd @ B @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pair__fst__snd__eq) ).
thf(5547,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D = C )
=> ( ( ( hAPP @ ( c_Product__Type_Ofst @ B @ A ) @ D )
= ( hAPP @ ( c_Product__Type_Ofst @ B @ A ) @ C ) )
& ( ( hAPP @ ( c_Product__Type_Osnd @ B @ A ) @ D )
= ( hAPP @ ( c_Product__Type_Osnd @ B @ A ) @ C ) ) ) )
& ( ( ( ( hAPP @ ( c_Product__Type_Ofst @ B @ A ) @ D )
= ( hAPP @ ( c_Product__Type_Ofst @ B @ A ) @ C ) )
& ( ( hAPP @ ( c_Product__Type_Osnd @ B @ A ) @ D )
= ( hAPP @ ( c_Product__Type_Osnd @ B @ A ) @ C ) ) )
=> ( D = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(551,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/sandbox/benchmark/theBenchmark.p',fact_nth__mem) ).
thf(4744,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)],[551]) ).
thf(2225,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Un__subset) ).
thf(11046,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2225]) ).
thf(850,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A ) ) )
=> ( ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__subset) ).
thf(5932,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A ) ) )
=> ( ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(944,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/sandbox/benchmark/theBenchmark.p',fact_distinct__sublistI) ).
thf(6256,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)],[944]) ).
thf(1995,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ F ) ) )
<=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ C ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ G ) @ ( hAPP @ B @ F ) ) )
=> ( hBOOL @ ( hAPP @ A @ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ball__UN) ).
thf(10195,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ F ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ C ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ G ) @ ( hAPP @ B @ F ) ) )
=> ( hBOOL @ ( hAPP @ A @ G ) ) ) ) )
& ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ C ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ G ) @ ( hAPP @ B @ F ) ) )
=> ( hBOOL @ ( hAPP @ A @ G ) ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1995]) ).
thf(2396,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/sandbox/benchmark/theBenchmark.p',fact_fold1Set_Ointros) ).
thf(11666,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)],[2396]) ).
thf(1756,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Relation_OImage @ B @ B @ ( c_Relation_OId @ B ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__Id) ).
thf(9288,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)],[1756]) ).
thf(784,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/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__cancel1) ).
thf(5662,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)],[784]) ).
thf(1105,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B )
= ( hAPP @ c_Nat_OSuc @ A ) )
<=> ? [D: $i,E: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ E ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ E ) )
& ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ E )
= A )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Suc__eq) ).
thf(6837,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B )
= ( hAPP @ c_Nat_OSuc @ A ) )
=> ? [D: $i,E: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ E ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ E ) )
& ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ E )
= A )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) )
& ( ? [D: $i,E: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ E ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ E ) )
& ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ E )
= A )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B )
= ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
thf(2333,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1D1) ).
thf(11442,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2333]) ).
thf(1272,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/sandbox/benchmark/theBenchmark.p',fact_diff__le__mono) ).
thf(7480,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)],[1272]) ).
thf(1254,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/sandbox/benchmark/theBenchmark.p',fact_distinct__zipI2) ).
thf(7417,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)],[1254]) ).
thf(1023,axiom,
! [A: $i,B: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) )
= ( hAPP @ ( c_List_Oset @ B ) @ A ) )
<=> ( A
= ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__empty2) ).
thf(6539,plain,
! [A: $i,B: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) )
= ( hAPP @ ( c_List_Oset @ B ) @ A ) )
=> ( A
= ( c_List_Olist_ONil @ B ) ) )
& ( ( A
= ( c_List_Olist_ONil @ B ) )
=> ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) )
= ( hAPP @ ( c_List_Oset @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(1516,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ tc_HOL_Obool ) ) @ ( c_List_Olistrel @ B @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_List_Olist @ B ) @ ( c_List_Olistrel1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__subset__rtrancl__listrel1) ).
thf(8390,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ tc_HOL_Obool ) ) @ ( c_List_Olistrel @ B @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_List_Olist @ B ) @ ( c_List_Olistrel1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1516]) ).
thf(268,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/sandbox/benchmark/theBenchmark.p',fact_less__zeroE) ).
thf(3643,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)],[268]) ).
thf(1127,axiom,
! [A: $i] :
( ( hAPP @ ( c_Relation_ORange @ A @ A ) @ ( c_Relation_OId @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Id) ).
thf(6946,plain,
! [A: $i] :
( ( hAPP @ ( c_Relation_ORange @ A @ A ) @ ( c_Relation_OId @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).
thf(1250,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/sandbox/benchmark/theBenchmark.p',fact_comp__cong) ).
thf(7404,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)],[1250]) ).
thf(477,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/sandbox/benchmark/theBenchmark.p',fact_nat__mult__less__cancel1) ).
thf(4444,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)],[477]) ).
thf(479,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ A ) @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
thf(4457,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ A ) @ B ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(2665,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/sandbox/benchmark/theBenchmark.p',fact_vimage__eq) ).
thf(12724,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)],[2665]) ).
thf(2140,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/sandbox/benchmark/theBenchmark.p',fact_takeWhile__append1) ).
thf(10752,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)],[2140]) ).
thf(2391,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__I) ).
thf(11651,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2391]) ).
thf(1386,axiom,
! [A: $i,B: $i] : ( c_List_Olistrelp @ B @ A @ ( c_List_Olist_ONil @ B ) @ ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrelp_Oequations_I1_J) ).
thf(7895,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)],[1386]) ).
thf(950,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__UN__flatten) ).
thf(6271,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(1326,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/sandbox/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).
thf(7682,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)],[1326]) ).
thf(1372,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 @ ( c_Finite__Set_Ofinite @ G ) @ A ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Ounion__disjoint) ).
thf(7821,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 @ ( c_Finite__Set_Ofinite @ G ) @ A ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1372]) ).
thf(1460,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/sandbox/benchmark/theBenchmark.p',fact_equiv__comp__eq) ).
thf(8159,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)],[1460]) ).
thf(2466,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__psubset__trans) ).
thf(11892,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2466]) ).
thf(252,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ D )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ C ) @ D ) @ B )
= A )
<=> ( ( ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ E @ C ) @ E ) @ ( c_Product__Type_Ofst @ E @ C ) ) @ A )
= D )
& ( ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ E @ C ) @ C ) @ ( c_Product__Type_Osnd @ E @ C ) ) @ A )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__eq__conv) ).
thf(3573,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ D )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ C ) @ D ) @ B )
= A )
=> ( ( ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ E @ C ) @ E ) @ ( c_Product__Type_Ofst @ E @ C ) ) @ A )
= D )
& ( ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ E @ C ) @ C ) @ ( c_Product__Type_Osnd @ E @ C ) ) @ A )
= B ) ) )
& ( ( ( ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ E @ C ) @ E ) @ ( c_Product__Type_Ofst @ E @ C ) ) @ A )
= D )
& ( ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ E @ C ) @ C ) @ ( c_Product__Type_Osnd @ E @ C ) ) @ A )
= B ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ C ) @ D ) @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(1625,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Diff__cancel2) ).
thf(8820,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1625]) ).
thf(1321,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__Un) ).
thf(7668,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1321]) ).
thf(1684,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/sandbox/benchmark/theBenchmark.p',fact_le__add__diff__inverse2) ).
thf(9012,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)],[1684]) ).
thf(1095,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/sandbox/benchmark/theBenchmark.p',fact_less__antisym) ).
thf(6805,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)],[1095]) ).
thf(1841,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/sandbox/benchmark/theBenchmark.p',fact_butlast__append) ).
thf(9620,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)],[1841]) ).
thf(1727,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Otrans @ B @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) )
<=> ( c_Relation_Otrans @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__converse) ).
thf(9144,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)],[1727]) ).
thf(2230,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_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ C ) ) @ B ) )
=> ( ( c_Fun_Oinj__on @ E @ F @ A @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ F @ A ) @ B ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ F ) @ C )
= ( hAPP @ ( c_Finite__Set_Ocard @ E ) @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__bij__eq) ).
thf(11061,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_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ C ) ) @ B ) )
=> ( ( c_Fun_Oinj__on @ E @ F @ A @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ F @ A ) @ B ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ F ) @ C )
= ( hAPP @ ( c_Finite__Set_Ocard @ E ) @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2230]) ).
thf(2499,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ C ) )
=> ( ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__class__eq) ).
thf(12005,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ C ) )
=> ( ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2499]) ).
thf(287,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Hilbert__Choice_OEps @ ( tc_prod @ C @ B ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ C @ B @ tc_HOL_Obool ) @ A ) )
= ( c_Hilbert__Choice_OEps @ ( tc_prod @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ ( tc_prod @ C @ B ) @ B @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_prod @ C @ B ) ) @ A ) @ ( c_Product__Type_Ofst @ C @ B ) ) ) @ ( c_Product__Type_Osnd @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Eps__split) ).
thf(3703,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Hilbert__Choice_OEps @ ( tc_prod @ C @ B ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ C @ B @ tc_HOL_Obool ) @ A ) )
= ( c_Hilbert__Choice_OEps @ ( tc_prod @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ ( tc_prod @ C @ B ) @ B @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_prod @ C @ B ) ) @ A ) @ ( c_Product__Type_Ofst @ C @ B ) ) ) @ ( c_Product__Type_Osnd @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(2329,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ A ) )
= ( hAPP @ ( c_Set_OCollect @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ tc_HOL_Obool @ D ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Collect__eq) ).
thf(11432,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ A ) )
= ( hAPP @ ( c_Set_OCollect @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ tc_HOL_Obool @ D ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2329]) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ocomm__monoid__add @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ B @ C ) @ ( hAPP @ ( c_COMBK @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__0) ).
thf(2968,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ocomm__monoid__add @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ B @ C ) @ ( hAPP @ ( c_COMBK @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(760,axiom,
! [A: $i,B: $i,C: $i] :
( C
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ A ) @ ( hAPP @ ( c_Product__Type_Ofst @ B @ A ) @ C ) ) @ ( hAPP @ ( c_Product__Type_Osnd @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surjective__pairing) ).
thf(5576,plain,
! [A: $i,B: $i,C: $i] :
( C
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ A ) @ ( hAPP @ ( c_Product__Type_Ofst @ B @ A ) @ C ) ) @ ( hAPP @ ( c_Product__Type_Osnd @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(1574,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ C @ B @ ( hAPP @ ( c_COMBK @ B @ C ) @ A ) ) @ D )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( D
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ C @ B @ ( hAPP @ ( c_COMBK @ B @ C ) @ A ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__constant__conv) ).
thf(8599,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ C @ B @ ( hAPP @ ( c_COMBK @ B @ C ) @ A ) ) @ D )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( D
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ C @ B @ ( hAPP @ ( c_COMBK @ B @ C ) @ A ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1574]) ).
thf(1534,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) )
<=> ( ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__empty) ).
thf(8458,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) )
=> ( ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
& ( ( ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1534]) ).
thf(2597,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/sandbox/benchmark/theBenchmark.p',fact_conversepD) ).
thf(12418,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)],[2597]) ).
thf(904,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_ORange @ C @ D ) @ B ) ) @ ( hAPP @ ( c_Relation_ORange @ C @ D ) @ A ) ) ) @ ( hAPP @ ( c_Relation_ORange @ C @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Diff__subset) ).
thf(6134,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_ORange @ C @ D ) @ B ) ) @ ( hAPP @ ( c_Relation_ORange @ C @ D ) @ A ) ) ) @ ( hAPP @ ( c_Relation_ORange @ C @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(2380,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
<=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ A @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__iff) ).
thf(11608,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ A @ F ) ) ) ) )
& ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2380]) ).
thf(2218,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ C @ C @ C ) @ B ) @ A ) ) @ B ) )
=> ( c_FunDef_Oreduction__pair @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reduction__pairI) ).
thf(11023,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ C @ C @ C ) @ B ) @ A ) ) @ B ) )
=> ( c_FunDef_Oreduction__pair @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2218]) ).
thf(1773,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Osym @ B @ A )
=> ( c_Relation_Osym @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sym__trancl) ).
thf(9365,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)],[1773]) ).
thf(1310,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I1_J) ).
thf(7609,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1310]) ).
thf(271,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ ( tc_prod @ F @ E ) @ E @ ( tc_prod @ D @ C ) @ ( c_Product__Type_Osnd @ F @ E ) ) @ ( c_Product__Type_Omap__pair @ D @ F @ C @ E @ B @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ C @ E @ ( tc_prod @ D @ C ) @ A ) @ ( c_Product__Type_Osnd @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__comp__map__pair) ).
thf(3654,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ ( tc_prod @ F @ E ) @ E @ ( tc_prod @ D @ C ) @ ( c_Product__Type_Osnd @ F @ E ) ) @ ( c_Product__Type_Omap__pair @ D @ F @ C @ E @ B @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ C @ E @ ( tc_prod @ D @ C ) @ A ) @ ( c_Product__Type_Osnd @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(2053,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/sandbox/benchmark/theBenchmark.p',fact_Suc__le__mono) ).
thf(10423,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)],[2053]) ).
thf(461,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/sandbox/benchmark/theBenchmark.p',fact_length__takeWhile__less__P__nth) ).
thf(4384,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)],[461]) ).
thf(2610,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/sandbox/benchmark/theBenchmark.p',fact_insertI1) ).
thf(12481,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)],[2610]) ).
thf(1434,axiom,
! [A: $i,B: $i] :
( ( c_List_OtakeWhile @ B @ A @ ( c_List_Olist_ONil @ B ) )
= ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile_Osimps_I1_J) ).
thf(8072,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)],[1434]) ).
thf(1586,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/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__graph__fold) ).
thf(8658,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)],[1586]) ).
thf(2591,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/sandbox/benchmark/theBenchmark.p',fact_CollectD) ).
thf(12393,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)],[2591]) ).
thf(2490,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Obij__betw @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__subset__eq) ).
thf(11965,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Obij__betw @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2490]) ).
thf(2163,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/sandbox/benchmark/theBenchmark.p',fact_rtrancl__into__trancl1) ).
thf(10834,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)],[2163]) ).
thf(1501,axiom,
! [A: $i,B: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty) ).
thf(8326,plain,
! [A: $i,B: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1501]) ).
thf(2089,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Obij__betw @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( c_Fun_Obij__betw @ B @ C @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__imp__bij__inv) ).
thf(10560,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Obij__betw @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( c_Fun_Obij__betw @ B @ C @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2089]) ).
thf(1728,axiom,
! [A: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__empty) ).
thf(9149,plain,
! [A: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1728]) ).
thf(2228,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/sandbox/benchmark/theBenchmark.p',fact_Suc__leD) ).
thf(11052,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)],[2228]) ).
thf(2551,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/sandbox/benchmark/theBenchmark.p',fact_transpE) ).
thf(12218,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)],[2551]) ).
thf(1182,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/sandbox/benchmark/theBenchmark.p',fact_take__Nil) ).
thf(7138,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)],[1182]) ).
thf(1407,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) @ c_FunDef_Omin__weak ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wmin__emptyI) ).
thf(7966,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) @ c_FunDef_Omin__weak ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1407]) ).
thf(655,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Product__Type_Omap__pair @ C @ C @ B @ B @ ( c_COMBI @ C ) @ ( c_COMBI @ B ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair__ident) ).
thf(5134,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Product__Type_Omap__pair @ C @ C @ B @ B @ ( c_COMBI @ C ) @ ( c_COMBI @ B ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(1089,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__refl) ).
thf(6788,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)],[1089]) ).
thf(1426,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 ) ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) @ B ) @ A ) ) )
=> ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( D != C ) )
=> ~ ! [F: $i,G: $i] :
( ( B
= ( hAPP @ c_Nat_OSuc @ G ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) @ G ) @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ F ) @ C ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__E) ).
thf(8036,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 ) ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) @ B ) @ A ) ) )
=> ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( D != C ) )
=> ~ ! [F: $i,G: $i] :
( ( B
= ( hAPP @ c_Nat_OSuc @ G ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) @ G ) @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ F ) @ C ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1426]) ).
thf(1916,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) )
=> ( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ B @ tc_HOL_Obool ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Union) ).
thf(9893,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) )
=> ( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ B @ tc_HOL_Obool ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1916]) ).
thf(928,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( c_List_Opartition @ E @ D @ C )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ E ) @ B ) ) @ ( hAPP @ ( c_List_Oset @ E ) @ A ) )
= ( hAPP @ ( c_List_Oset @ E ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partition__set) ).
thf(6207,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( c_List_Opartition @ E @ D @ C )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ E ) @ B ) ) @ ( hAPP @ ( c_List_Oset @ E ) @ A ) )
= ( hAPP @ ( c_List_Oset @ E ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(2101,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/sandbox/benchmark/theBenchmark.p',fact_wf__same__fst) ).
thf(10603,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)],[2101]) ).
thf(1006,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ A ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThanSuc) ).
thf(6475,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ A ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(858,axiom,
! [A: $i] :
( ( hAPP @ ( c_List_Oset @ A ) @ ( c_List_Olist_ONil @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_List_Oset_Osimps_I1_J) ).
thf(5973,plain,
! [A: $i] :
( ( hAPP @ ( c_List_Oset @ A ) @ ( c_List_Olist_ONil @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(1871,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/sandbox/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__refl) ).
thf(9739,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)],[1871]) ).
thf(1274,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/sandbox/benchmark/theBenchmark.p',fact_O__assoc) ).
thf(7485,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)],[1274]) ).
thf(1110,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/sandbox/benchmark/theBenchmark.p',fact_takeWhile__dropWhile__id) ).
thf(6876,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)],[1110]) ).
thf(427,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/sandbox/benchmark/theBenchmark.p',fact_diff__is__0__eq) ).
thf(4244,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)],[427]) ).
thf(1346,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Int2) ).
thf(7738,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1346]) ).
thf(1832,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Nitpick_Ofold__graph_H @ G @ F @ E @ D @ C @ ( hAPP @ ( hAPP @ E @ B ) @ A ) )
<=> ( ( ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) )
& ( ( hAPP @ ( hAPP @ E @ B ) @ A )
= D ) )
| ? [H: $i,I: $i] :
( ( ( hAPP @ ( hAPP @ E @ B ) @ A )
= ( hAPP @ ( hAPP @ E @ H ) @ I ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ C ) )
& ( c_Nitpick_Ofold__graph_H @ G @ F @ E @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ H ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) @ I ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_H_Oequations_I2_J) ).
thf(9581,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( c_Nitpick_Ofold__graph_H @ G @ F @ E @ D @ C @ ( hAPP @ ( hAPP @ E @ B ) @ A ) )
=> ( ( ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) )
& ( ( hAPP @ ( hAPP @ E @ B ) @ A )
= D ) )
| ? [H: $i,I: $i] :
( ( ( hAPP @ ( hAPP @ E @ B ) @ A )
= ( hAPP @ ( hAPP @ E @ H ) @ I ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ C ) )
& ( c_Nitpick_Ofold__graph_H @ G @ F @ E @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ H ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) @ I ) ) ) )
& ( ( ( ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) )
& ( ( hAPP @ ( hAPP @ E @ B ) @ A )
= D ) )
| ? [H: $i,I: $i] :
( ( ( hAPP @ ( hAPP @ E @ B ) @ A )
= ( hAPP @ ( hAPP @ E @ H ) @ I ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ C ) )
& ( c_Nitpick_Ofold__graph_H @ G @ F @ E @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ H ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) @ I ) ) )
=> ( c_Nitpick_Ofold__graph_H @ G @ F @ E @ D @ C @ ( hAPP @ ( hAPP @ E @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1832]) ).
thf(2015,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ ( c_Wellfounded_Ofinite__psubset @ C ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__finite__psubset) ).
thf(10285,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ ( c_Wellfounded_Ofinite__psubset @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ ( c_Wellfounded_Ofinite__psubset @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2015]) ).
thf(203,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__0) ).
thf(3390,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)],[203]) ).
thf(1981,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_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ A ) @ C ) )
=> ( ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__image__set__diff) ).
thf(10148,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_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ A ) @ C ) )
=> ( ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1981]) ).
thf(603,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/sandbox/benchmark/theBenchmark.p',fact_ex__least__nat__less) ).
thf(4934,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)],[603]) ).
thf(501,axiom,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).
thf(4540,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(2199,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) @ ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ A ) @ B ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__equiv__class) ).
thf(10961,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) @ ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ A ) @ B ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2199]) ).
thf(1997,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/sandbox/benchmark/theBenchmark.p',fact_list_Oinject) ).
thf(10207,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)],[1997]) ).
thf(350,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/sandbox/benchmark/theBenchmark.p',fact_takeWhile__nth) ).
thf(3937,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)],[350]) ).
thf(1364,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ F @ E @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ F @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ F @ E @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ F @ E @ D ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__distrib) ).
thf(7789,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ F @ E @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ F @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ F @ E @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ F @ E @ D ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1364]) ).
thf(1306,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/sandbox/benchmark/theBenchmark.p',fact_drop__Nil) ).
thf(7597,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)],[1306]) ).
thf(810,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Orev @ C ) @ ( hAPP @ ( c_List_Ofilter @ C @ B ) @ A ) )
= ( hAPP @ ( c_List_Ofilter @ C @ B ) @ ( hAPP @ ( c_List_Orev @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__filter) ).
thf(5776,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Orev @ C ) @ ( hAPP @ ( c_List_Ofilter @ C @ B ) @ A ) )
= ( hAPP @ ( c_List_Ofilter @ C @ B ) @ ( hAPP @ ( c_List_Orev @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(1602,axiom,
! [A: $i,B: $i] : ( c_Fun_Oinj__on @ tc_Nat_Onat @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) ) @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__add__nat) ).
thf(8732,plain,
! [A: $i,B: $i] : ( c_Fun_Oinj__on @ tc_Nat_Onat @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) ) @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1602]) ).
thf(788,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/sandbox/benchmark/theBenchmark.p',fact_lexord__linear) ).
thf(5683,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)],[788]) ).
thf(2084,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
<=> ( ( ( D = B )
& ( C = A ) )
| ( ( D = A )
& ( C = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_doubleton__eq__iff) ).
thf(10533,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
=> ( ( ( D = B )
& ( C = A ) )
| ( ( D = A )
& ( C = B ) ) ) )
& ( ( ( ( D = B )
& ( C = A ) )
| ( ( D = A )
& ( C = B ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2084]) ).
thf(1572,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ E @ D @ C @ B ) @ A )
= ( c_Hilbert__Choice_OEps @ E @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ E ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ E @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ E ) ) @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ D @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ c_fequal ) @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__def) ).
thf(8587,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ E @ D @ C @ B ) @ A )
= ( c_Hilbert__Choice_OEps @ E @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ E ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ E @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ E ) ) @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ D @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ c_fequal ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1572]) ).
thf(1533,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_fun @ C @ tc_HOL_Obool ) ) @ A ) @ 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 ) @ A ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__seteq) ).
thf(8455,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_fun @ C @ tc_HOL_Obool ) ) @ A ) @ 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 ) @ A ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1533]) ).
thf(356,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ C ) ) @ B ) @ ( c_List_Olists @ C @ A ) ) )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__lists__conv__set) ).
thf(3967,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ C ) ) @ B ) @ ( c_List_Olists @ C @ A ) ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ A ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ C ) ) @ B ) @ ( c_List_Olists @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(2018,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B )
= ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__eq__iff) ).
thf(10302,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B )
= ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B )
= ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2018]) ).
thf(2449,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ComplD) ).
thf(11833,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2449]) ).
thf(590,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ B ) @ A ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeast @ C ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I8_J) ).
thf(4902,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ B ) @ A ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeast @ C ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(186,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ A @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Oremove) ).
thf(3333,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ A @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(2284,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DiffD1) ).
thf(11261,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2284]) ).
thf(609,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_Olist__update @ D @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ B ) ) @ E ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ D @ C ) @ E ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__append1) ).
thf(4953,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_Olist__update @ D @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ B ) ) @ E ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ D @ C ) @ E ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(1496,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__Times__UNIV1) ).
thf(8307,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1496]) ).
thf(911,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_fun @ D @ C ) @ ( tc_fun @ D @ C ) ) @ B ) @ ( c_Fun_Ocomp @ C @ C @ D @ A ) )
= ( c_Fun_Ocomp @ C @ C @ D @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ C @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comp__funpow) ).
thf(6152,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_fun @ D @ C ) @ ( tc_fun @ D @ C ) ) @ B ) @ ( c_Fun_Ocomp @ C @ C @ D @ A ) )
= ( c_Fun_Ocomp @ C @ C @ D @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ C @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(628,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ B @ A ) )
=> ( ~ ( hBOOL @ ( hAPP @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( c_Orderings_Oord__class_OLeast @ tc_Nat_Onat @ B )
= ( hAPP @ c_Nat_OSuc @ ( c_Orderings_Oord__class_OLeast @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ tc_HOL_Obool @ tc_Nat_Onat ) @ B ) @ c_Nat_OSuc ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Least__Suc) ).
thf(5026,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ B @ A ) )
=> ( ~ ( hBOOL @ ( hAPP @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( c_Orderings_Oord__class_OLeast @ tc_Nat_Onat @ B )
= ( hAPP @ c_Nat_OSuc @ ( c_Orderings_Oord__class_OLeast @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ tc_HOL_Obool @ tc_Nat_Onat ) @ B ) @ c_Nat_OSuc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(346,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofolding @ D @ C @ B @ A )
=> ( ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= ( c_Fun_Oid @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Oempty) ).
thf(3920,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofolding @ D @ C @ B @ A )
=> ( ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= ( c_Fun_Oid @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(923,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding__idem @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ A ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__idem_Ounion__idem) ).
thf(6186,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding__idem @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ A ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(2475,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oord @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funD) ).
thf(11916,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oord @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2475]) ).
thf(1233,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Product__Type_Ocurry @ D @ C @ B @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ B ) @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curry__split) ).
thf(7333,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Product__Type_Ocurry @ D @ C @ B @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ B ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1233]) ).
thf(1673,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/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le__raw) ).
thf(8980,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)],[1673]) ).
thf(1934,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__left) ).
thf(9942,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1934]) ).
thf(2461,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/sandbox/benchmark/theBenchmark.p',fact_finite__Range) ).
thf(11873,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)],[2461]) ).
thf(3200,plain,
( ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint )
!= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ),
inference(polarity_switch,[status(thm)],[3199]) ).
thf(3201,plain,
( ( c_Groups_Oone__class_Oone @ tc_Int_Oint )
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(lifteq,[status(thm)],[3200]) ).
thf(918,axiom,
class_Orderings_Oord @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
thf(6171,plain,
class_Orderings_Oord @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(1551,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/sandbox/benchmark/theBenchmark.p',fact_wf__inv__image) ).
thf(8512,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)],[1551]) ).
thf(586,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Product__Type_Ofst @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ B ) @ A ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__conv) ).
thf(4889,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Product__Type_Ofst @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ B ) @ A ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(558,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( c_List_Orev @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ A ) @ ( c_List_Olist_ONil @ C ) ) )
<=> ( B
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ A ) @ ( c_List_Olist_ONil @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__singleton__conv) ).
thf(4765,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ A ) @ ( c_List_Olist_ONil @ C ) ) )
=> ( B
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ A ) @ ( c_List_Olist_ONil @ C ) ) ) )
& ( ( B
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ A ) @ ( c_List_Olist_ONil @ C ) ) )
=> ( ( hAPP @ ( c_List_Orev @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ A ) @ ( c_List_Olist_ONil @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(141,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__take) ).
thf(3190,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(2149,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/sandbox/benchmark/theBenchmark.p',fact_finite__trancl) ).
thf(10783,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)],[2149]) ).
thf(1596,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ D @ D @ D ) @ C ) @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ D @ D @ D ) @ A ) @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ D @ D @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_union__comp__emptyL) ).
thf(8708,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ D @ D @ D ) @ C ) @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ D @ D @ D ) @ A ) @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ D @ D @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1596]) ).
thf(2047,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ B @ tc_HOL_Obool ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UnionD) ).
thf(10406,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ B @ tc_HOL_Obool ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2047]) ).
thf(1963,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) @ C ) @ F ) @ E ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup2CI) ).
thf(10058,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) @ C ) @ F ) @ E ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1963]) ).
thf(3822,plain,
~ ? [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
= ( hAPP @ c_Nat_OSuc @ A ) ),
inference(miniscope,[status(thm)],[3821]) ).
thf(3823,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
inference(cnf,[status(esa)],[3822]) ).
thf(3824,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(lifteq,[status(thm)],[3823]) ).
thf(402,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/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__less__cancel1) ).
thf(4148,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)],[402]) ).
thf(2399,axiom,
! [A: $i,B: $i] :
( ( ( class_Enum_Oenum @ B )
& ( class_Enum_Oenum @ A ) )
=> ( class_Enum_Oenum @ ( tc_fun @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Enum_Oenum) ).
thf(11673,plain,
! [A: $i,B: $i] :
( ( ( class_Enum_Oenum @ B )
& ( class_Enum_Oenum @ A ) )
=> ( class_Enum_Oenum @ ( tc_fun @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2399]) ).
thf(341,axiom,
! [A: $i,B: $i] :
( ( c_Equiv__Relations_Opart__equivp @ B @ A )
=> ? [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_HOL_OEx @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBS @ B @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ B ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ B @ B @ tc_HOL_Obool ) @ A ) @ ( c_COMBI @ B ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ B @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_COMBB @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool @ B ) ) @ c_fequal ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_part__equivp__typedef) ).
thf(3903,plain,
! [A: $i,B: $i] :
( ( c_Equiv__Relations_Opart__equivp @ B @ A )
=> ? [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_HOL_OEx @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBS @ B @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ B ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ B @ B @ tc_HOL_Obool ) @ A ) @ ( c_COMBI @ B ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ B @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_COMBB @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool @ B ) ) @ c_fequal ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(1186,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Fun_Obij__betw @ G @ F @ E @ D @ C )
=> ( ( c_Fun_Obij__betw @ G @ F @ E @ B @ A )
=> ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) )
=> ( c_Fun_Obij__betw @ G @ F @ E @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__combine) ).
thf(7150,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Fun_Obij__betw @ G @ F @ E @ D @ C )
=> ( ( c_Fun_Obij__betw @ G @ F @ E @ B @ A )
=> ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) )
=> ( c_Fun_Obij__betw @ G @ F @ E @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186]) ).
thf(804,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
thf(5747,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)],[804]) ).
thf(323,axiom,
c_Orderings_Oorder__class_Omono @ tc_Nat_Onat @ tc_Nat_Onat @ c_Nat_OSuc,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mono__Suc) ).
thf(3834,plain,
c_Orderings_Oorder__class_Omono @ tc_Nat_Onat @ tc_Nat_Onat @ c_Nat_OSuc,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(2376,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/sandbox/benchmark/theBenchmark.p',fact_pos__empty__def) ).
thf(11593,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)],[2376]) ).
thf(2273,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 @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ F ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ G ) @ F ) ) @ A ) )
=> ( G = F ) ) )
=> ( 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 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Un__separator__converseE) ).
thf(11216,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 @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ F ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ G ) @ F ) ) @ A ) )
=> ( G = F ) ) )
=> ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2273]) ).
thf(700,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__infI1) ).
thf(5310,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(1556,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) @ B ) ) ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ ( hAPP @ ( c_Set_OCollect @ D ) @ B ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__split) ).
thf(8527,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) @ B ) ) ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ ( hAPP @ ( c_Set_OCollect @ D ) @ B ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1556]) ).
thf(660,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ B ) ) @ ( c_List_Olist_ONil @ B ) ) @ ( c_List_Olists @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists_ONil) ).
thf(5153,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ B ) ) @ ( c_List_Olist_ONil @ B ) ) @ ( c_List_Olists @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(1021,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__less__nat) ).
thf(6533,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(2157,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__mono) ).
thf(10815,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2157]) ).
thf(2672,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/sandbox/benchmark/theBenchmark.p',fact_list__all__iff) ).
thf(12751,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)],[2672]) ).
thf(1800,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ H @ G ) @ F ) @ E ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ H @ G ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ G ) @ B ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ H @ C ) @ F ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ H @ C @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ H @ G ) ) @ ( tc_fun @ C @ F ) @ H ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ H @ G ) @ F @ C ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ H @ ( tc_fun @ C @ G ) @ ( tc_fun @ C @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ G @ ( tc_prod @ H @ G ) ) @ ( tc_fun @ ( tc_fun @ C @ G ) @ ( tc_fun @ C @ ( tc_prod @ H @ G ) ) ) @ H ) @ ( c_COMBB @ G @ ( tc_prod @ H @ G ) @ C ) ) @ ( c_Product__Type_OPair @ H @ G ) ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ H @ C ) @ D ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__zip__map2) ).
thf(9468,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ H @ G ) @ F ) @ E ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ H @ G ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ G ) @ B ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ H @ C ) @ F ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ H @ C @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ H @ G ) ) @ ( tc_fun @ C @ F ) @ H ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ H @ G ) @ F @ C ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ H @ ( tc_fun @ C @ G ) @ ( tc_fun @ C @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ G @ ( tc_prod @ H @ G ) ) @ ( tc_fun @ ( tc_fun @ C @ G ) @ ( tc_fun @ C @ ( tc_prod @ H @ G ) ) ) @ H ) @ ( c_COMBB @ G @ ( tc_prod @ H @ G ) @ C ) ) @ ( c_Product__Type_OPair @ H @ G ) ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ H @ C ) @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1800]) ).
thf(2238,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( c_Wellfounded_Omax__ext @ D @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
& ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ E ) @ F ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ext_Osimps) ).
thf(11084,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( c_Wellfounded_Omax__ext @ D @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
& ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ E ) @ F ) ) @ A ) ) ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
& ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ E ) @ F ) ) @ A ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( c_Wellfounded_Omax__ext @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2238]) ).
thf(1632,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I9_J) ).
thf(8839,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1632]) ).
thf(1923,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ComplI) ).
thf(9913,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1923]) ).
thf(1605,axiom,
! [A: $i,B: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) )
= ( c_SetInterval_Oord_OgreaterThanAtMost @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) ) @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ tc_Nat_Onat ) @ c_fNot ) ) @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( 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/sandbox/benchmark/theBenchmark.p',fact_dvd_OgreaterThanAtMost__empty__iff2) ).
thf(8739,plain,
! [A: $i,B: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) )
= ( c_SetInterval_Oord_OgreaterThanAtMost @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) ) @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ tc_Nat_Onat ) @ c_fNot ) ) @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( 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 ) ) ) )
& ( ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) )
= ( c_SetInterval_Oord_OgreaterThanAtMost @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) ) @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ tc_Nat_Onat ) @ c_fNot ) ) @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1605]) ).
thf(2456,axiom,
! [A: $i,B: $i] :
( ( c_Hilbert__Choice_OEps @ B @ ( hAPP @ c_fequal @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_some__sym__eq__trivial) ).
thf(11856,plain,
! [A: $i,B: $i] :
( ( c_Hilbert__Choice_OEps @ B @ ( hAPP @ c_fequal @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2456]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Groups_Ocomm__monoid__add @ F )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ D ) )
=> ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ G ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ B @ G ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ E @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ C @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ F ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ F ) @ E ) @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ F ) ) @ A ) ) @ B ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ ( tc_prod @ E @ C ) @ F ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ E @ C @ F ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ C ) @ D ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__Sigma) ).
thf(2702,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Groups_Ocomm__monoid__add @ F )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ D ) )
=> ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ G ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ B @ G ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ E @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ C @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ F ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ F ) @ E ) @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ F ) ) @ A ) ) @ B ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ ( tc_prod @ E @ C ) @ F ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ E @ C @ F ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ C ) @ D ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(251,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/sandbox/benchmark/theBenchmark.p',fact_upt__eq__Nil__conv) ).
thf(3563,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)],[251]) ).
thf(23,axiom,
! [A: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ tc_Int_Oint ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
= ( hAPP @ c_Int_Onat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__atLeastZeroLessThan__int) ).
thf(2761,plain,
! [A: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ tc_Int_Oint ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
= ( hAPP @ c_Int_Onat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(2568,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/sandbox/benchmark/theBenchmark.p',fact_mem__Collect__eq) ).
thf(12282,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)],[2568]) ).
thf(415,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ A ) )
=> ( ( B != A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).
thf(4195,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ A ) )
=> ( ( B != A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(2573,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/sandbox/benchmark/theBenchmark.p',fact_list__ex__iff__raw) ).
thf(12305,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)],[2573]) ).
thf(715,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ C ) @ B ) ) @ A )
= ( c_Nat_Onat_Onat__case @ D @ C @ ( hAPP @ ( c_List_Onth @ D ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth_Osimps) ).
thf(5402,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ C ) @ B ) ) @ A )
= ( c_Nat_Onat_Onat__case @ D @ C @ ( hAPP @ ( c_List_Onth @ D ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(642,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/sandbox/benchmark/theBenchmark.p',fact_length__0__conv) ).
thf(5090,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)],[642]) ).
thf(1251,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ D @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ D @ D ) ) ) ) @ ( c_Product__Type_OPair @ D @ D ) ) ) ) @ C ) ) @ c_fequal ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) @ C ) @ ( c_Relation_OId @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reflcl__set__eq) ).
thf(7407,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ D @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ D @ D ) ) ) ) @ ( c_Product__Type_OPair @ D @ D ) ) ) ) @ C ) ) @ c_fequal ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) @ C ) @ ( c_Relation_OId @ D ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) @ C ) @ ( c_Relation_OId @ D ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ D @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ D @ D ) ) ) ) @ ( c_Product__Type_OPair @ D @ D ) ) ) ) @ C ) ) @ c_fequal ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1251]) ).
thf(57,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/sandbox/benchmark/theBenchmark.p',fact_odd__less__0) ).
thf(2883,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)],[57]) ).
thf(2123,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ E @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ E @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( c_Set_Oimage @ D @ E @ C ) ) @ ( hAPP @ ( c_Set_OPow @ D ) @ B ) ) ) @ ( hAPP @ ( c_Set_OPow @ E ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Pow__mono) ).
thf(10689,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ E @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ E @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( c_Set_Oimage @ D @ E @ C ) ) @ ( hAPP @ ( c_Set_OPow @ D ) @ B ) ) ) @ ( hAPP @ ( c_Set_OPow @ E ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2123]) ).
thf(2039,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ E @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Ocurry @ D @ C @ tc_HOL_Obool @ E ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curryI) ).
thf(10377,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ E @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Ocurry @ D @ C @ tc_HOL_Obool @ E ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2039]) ).
thf(2362,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Ocurry @ E @ D @ tc_HOL_Obool @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curryD) ).
thf(11546,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Ocurry @ E @ D @ tc_HOL_Obool @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2362]) ).
thf(331,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ D )
=> ( ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ D ) @ B ) @ A )
= ( c_Complete__Lattice_OInf__class_OInf @ D @ ( hAPP @ ( c_Set_OCollect @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool @ D ) @ ( c_HOL_OEx @ ( tc_fun @ C @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_COMBS @ ( tc_fun @ C @ D ) @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_fun @ C @ D ) ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ C @ D ) @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ ( tc_fun @ C @ D ) ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_fun @ C @ D ) @ D ) @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_fun @ C @ D ) @ D ) @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBB @ D @ tc_HOL_Obool @ ( tc_fun @ C @ D ) ) ) @ c_fequal ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ C @ D ) @ C @ D ) @ ( c_COMBI @ ( tc_fun @ C @ D ) ) ) @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fun__def) ).
thf(3856,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ D )
=> ( ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ D ) @ B ) @ A )
= ( c_Complete__Lattice_OInf__class_OInf @ D @ ( hAPP @ ( c_Set_OCollect @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool @ D ) @ ( c_HOL_OEx @ ( tc_fun @ C @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_COMBS @ ( tc_fun @ C @ D ) @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_fun @ C @ D ) ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ C @ D ) @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ ( tc_fun @ C @ D ) ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_fun @ C @ D ) @ D ) @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_fun @ C @ D ) @ D ) @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBB @ D @ tc_HOL_Obool @ ( tc_fun @ C @ D ) ) ) @ c_fequal ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ C @ D ) @ C @ D ) @ ( c_COMBI @ ( tc_fun @ C @ D ) ) ) @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(1525,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ C ) @ B ) ) @ ( hAPP @ ( c_Set_OPow @ C ) @ A ) ) ) @ ( hAPP @ ( c_Set_OPow @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Pow__subset) ).
thf(8422,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ C ) @ B ) ) @ ( hAPP @ ( c_Set_OPow @ C ) @ A ) ) ) @ ( hAPP @ ( c_Set_OPow @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1525]) ).
thf(1427,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ A @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__absorb) ).
thf(8049,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ A @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1427]) ).
thf(1488,axiom,
! [A: $i] :
( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) @ c_FunDef_Omin__strict ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smin__emptyI) ).
thf(8279,plain,
! [A: $i] :
( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) @ c_FunDef_Omin__strict ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1488]) ).
thf(2361,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/sandbox/benchmark/theBenchmark.p',fact_finite_OinsertI) ).
thf(11544,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)],[2361]) ).
thf(256,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/sandbox/benchmark/theBenchmark.p',fact_all__nat__less__eq) ).
thf(3592,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)],[256]) ).
thf(2159,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_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ D ) @ C ) )
=> ( ! [I: $i,J: $i,K: $i,L: $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 ) @ I ) @ J ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ K ) @ L ) ) ) @ B ) )
=> ( ( 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 ) @ K ) @ L ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ D ) @ C ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ K ) @ L ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ I ) @ J ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ F ) @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rtrancl__induct2) ).
thf(10819,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_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ D ) @ C ) )
=> ( ! [I: $i,J: $i,K: $i,L: $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 ) @ I ) @ J ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ K ) @ L ) ) ) @ B ) )
=> ( ( 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 ) @ K ) @ L ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ D ) @ C ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ K ) @ L ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ I ) @ J ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ F ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2159]) ).
thf(19,axiom,
( ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint )
= ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__int__def) ).
thf(2748,plain,
( ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint )
= ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(856,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_OwfP @ B @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ B ) @ ( c_COMBC @ B @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_prod @ B @ B ) ) @ ( tc_fun @ B @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ B @ B ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ B ) @ ( c_member @ ( tc_prod @ B @ B ) ) ) ) @ ( c_Product__Type_OPair @ B @ B ) ) ) ) @ A ) )
<=> ( c_Wellfounded_Owf @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__wf__eq) ).
thf(5964,plain,
! [A: $i,B: $i] :
( ( ( c_Wellfounded_OwfP @ B @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ B ) @ ( c_COMBC @ B @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_prod @ B @ B ) ) @ ( tc_fun @ B @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ B @ B ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ B ) @ ( c_member @ ( tc_prod @ B @ B ) ) ) ) @ ( c_Product__Type_OPair @ B @ B ) ) ) ) @ A ) )
=> ( c_Wellfounded_Owf @ B @ A ) )
& ( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_OwfP @ B @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ B ) @ ( c_COMBC @ B @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_prod @ B @ B ) ) @ ( tc_fun @ B @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ B @ B ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ B ) @ ( c_member @ ( tc_prod @ B @ B ) ) ) ) @ ( c_Product__Type_OPair @ B @ B ) ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(946,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_OCollect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ B ) @ c_fNot ) @ A ) )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OCollect @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__neg__eq) ).
thf(6260,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_OCollect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ B ) @ c_fNot ) @ A ) )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OCollect @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(883,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ D @ C @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ B ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__empty2) ).
thf(6070,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ D @ C @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ B ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(1052,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( c_Relation_Orefl__on @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ tc_HOL_Obool ) ) @ ( c_List_Olistrel1 @ C @ B ) ) @ ( c_List_Olistrel @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1__subset__listrel) ).
thf(6647,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( c_Relation_Orefl__on @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ tc_HOL_Obool ) ) @ ( c_List_Olistrel1 @ C @ B ) ) @ ( c_List_Olistrel @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).
thf(725,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( c_List_Opartition @ E @ D @ C )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ B ) @ A ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ ( hAPP @ ( c_List_Oset @ E ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ D @ F ) ) )
& ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ ( hAPP @ ( c_List_Oset @ E ) @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ D @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partition__P) ).
thf(5447,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( c_List_Opartition @ E @ D @ C )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) ) @ B ) @ A ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ ( hAPP @ ( c_List_Oset @ E ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ D @ F ) ) )
& ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ ( hAPP @ ( c_List_Oset @ E ) @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ D @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(2612,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/sandbox/benchmark/theBenchmark.p',fact_set__ConsD) ).
thf(12486,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)],[2612]) ).
thf(2562,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/sandbox/benchmark/theBenchmark.p',fact_List_Omember__def) ).
thf(12255,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)],[2562]) ).
thf(2624,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 ) )
=> ( ( ( hAPP @ D @ B )
= A )
=> ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ F @ E @ C @ D ) @ A )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__f__eq) ).
thf(12553,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 ) )
=> ( ( ( hAPP @ D @ B )
= A )
=> ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ F @ E @ C @ D ) @ A )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2624]) ).
thf(1737,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) )
<=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insert__iff) ).
thf(9171,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1737]) ).
thf(2265,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( hAPP @ B @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__E) ).
thf(11196,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( hAPP @ B @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2265]) ).
thf(2580,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/sandbox/benchmark/theBenchmark.p',fact_pair__box_Osimps_I2_J) ).
thf(12346,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)],[2580]) ).
thf(2305,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/sandbox/benchmark/theBenchmark.p',fact_in__inv__image) ).
thf(11328,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)],[2305]) ).
thf(1401,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ B ) @ A ) )
=> ( ( c_List_Oremdups @ B @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__remdups__id) ).
thf(7941,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)],[1401]) ).
thf(1928,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ ( c_List_Oremove1 @ C @ B @ A ) ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__remove1__subset) ).
thf(9925,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ ( c_List_Oremove1 @ C @ B @ A ) ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1928]) ).
thf(2585,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fimplies__2) ).
thf(12361,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2585]) ).
thf(2529,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/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff) ).
thf(12123,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)],[2529]) ).
thf(1736,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Ozip @ F @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ F @ C ) @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ F @ C @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ C @ E ) @ ( tc_fun @ C @ ( tc_prod @ F @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ ( tc_fun @ C @ E ) @ ( tc_fun @ C @ ( tc_prod @ F @ E ) ) ) @ F ) @ ( c_COMBB @ E @ ( tc_prod @ F @ E ) @ C ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ F @ C ) @ D ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__map2) ).
thf(9168,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Ozip @ F @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ F @ C ) @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ F @ C @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ C @ E ) @ ( tc_fun @ C @ ( tc_prod @ F @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ ( tc_fun @ C @ E ) @ ( tc_fun @ C @ ( tc_prod @ F @ E ) ) ) @ F ) @ ( c_COMBB @ E @ ( tc_prod @ F @ E ) @ C ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ F @ C ) @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1736]) ).
thf(876,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/sandbox/benchmark/theBenchmark.p',fact_o__eq__dest__lhs) ).
thf(6038,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)],[876]) ).
thf(1124,axiom,
( c_Int_OInteg
= ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ c_Int_Ointrel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Integ__def) ).
thf(6931,plain,
( c_Int_OInteg
= ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ c_Int_Ointrel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).
thf(984,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ C ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ F @ E @ D ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__subset) ).
thf(6400,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ C ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ F @ E @ D ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(88,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zminus__inverse2) ).
thf(2995,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(326,axiom,
! [A: $i] :
( ( c_Relation_OId @ A )
= ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ A @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool @ ( tc_prod @ A @ A ) ) @ ( c_HOL_OEx @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_prod @ A @ A ) @ ( tc_fun @ A @ ( tc_prod @ A @ A ) ) @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ A @ ( tc_prod @ A @ A ) ) @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( tc_prod @ A @ A ) ) @ ( c_COMBB @ ( tc_prod @ A @ A ) @ tc_HOL_Obool @ A ) ) @ c_fequal ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ A @ ( tc_prod @ A @ A ) ) @ ( c_Product__Type_OPair @ A @ A ) ) @ ( c_COMBI @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__def) ).
thf(3841,plain,
! [A: $i] :
( ( c_Relation_OId @ A )
= ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ A @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool @ ( tc_prod @ A @ A ) ) @ ( c_HOL_OEx @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_prod @ A @ A ) @ ( tc_fun @ A @ ( tc_prod @ A @ A ) ) @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ A @ ( tc_prod @ A @ A ) ) @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( tc_prod @ A @ A ) ) @ ( c_COMBB @ ( tc_prod @ A @ A ) @ tc_HOL_Obool @ A ) ) @ c_fequal ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ A @ ( tc_prod @ A @ A ) ) @ ( c_Product__Type_OPair @ A @ A ) ) @ ( c_COMBI @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(1367,axiom,
! [A: $i,B: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ B @ tc_HOL_Obool ) @ A )
= ( hAPP @ ( c_Set_OCollect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ tc_HOL_Obool @ B ) @ ( c_HOL_OEx @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ B ) @ ( hAPP @ ( c_COMBS @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A ) ) ) ) @ ( c_member @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__eq) ).
thf(7802,plain,
! [A: $i,B: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ B @ tc_HOL_Obool ) @ A )
= ( hAPP @ ( c_Set_OCollect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ tc_HOL_Obool @ B ) @ ( c_HOL_OEx @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ B ) @ ( hAPP @ ( c_COMBS @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A ) ) ) ) @ ( c_member @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1367]) ).
thf(1287,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Inter) ).
thf(7527,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1287]) ).
thf(1813,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/sandbox/benchmark/theBenchmark.p',fact_o__eq__elim) ).
thf(9517,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)],[1813]) ).
thf(316,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( c_List_Olist_ONil @ B ) )
=> ( ( c_List_Olast @ B @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ A ) @ C ) )
= A ) )
& ( ( C
!= ( c_List_Olist_ONil @ B ) )
=> ( ( c_List_Olast @ B @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ A ) @ C ) )
= ( c_List_Olast @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last_Osimps) ).
thf(3807,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( c_List_Olist_ONil @ B ) )
=> ( ( c_List_Olast @ B @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ A ) @ C ) )
= A ) )
& ( ( C
!= ( c_List_Olist_ONil @ B ) )
=> ( ( c_List_Olast @ B @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ A ) @ C ) )
= ( c_List_Olast @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(2540,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/sandbox/benchmark/theBenchmark.p',fact_r__into__rtrancl) ).
thf(12173,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)],[2540]) ).
thf(2535,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/sandbox/benchmark/theBenchmark.p',fact_Powp__def) ).
thf(12155,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)],[2535]) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__commute) ).
thf(2936,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)],[69]) ).
thf(273,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ! [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ ( hAPP @ C @ E ) ) @ ( hAPP @ C @ ( hAPP @ c_Nat_OSuc @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lift__Suc__mono__le) ).
thf(3660,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ! [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ ( hAPP @ C @ E ) ) @ ( hAPP @ C @ ( hAPP @ c_Nat_OSuc @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(795,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_List_Olexn @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexn_Osimps_I1_J) ).
thf(5722,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_List_Olexn @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(1179,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ E ) @ D ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ E ) @ D ) @ C ) ) )
=> ( ( B = A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__disj) ).
thf(7128,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ E ) @ D ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ E ) @ D ) @ C ) ) )
=> ( ( B = A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).
thf(888,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool @ C ) @ ( c_HOL_OAll @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_COMBS @ D @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fimplies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool @ D ) ) @ ( c_member @ C ) ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INTER__def) ).
thf(6084,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool @ C ) @ ( c_HOL_OAll @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_COMBS @ D @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fimplies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool @ D ) ) @ ( c_member @ C ) ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(1848,axiom,
! [A: $i] :
( ( c_SetInterval_Oord_OatLeastAtMost @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A @ A )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeastAtMost__singleton) ).
thf(9650,plain,
! [A: $i] :
( ( c_SetInterval_Oord_OatLeastAtMost @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A @ A )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1848]) ).
thf(2370,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__subset__rtrancl) ).
thf(11578,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2370]) ).
thf(1115,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ H @ G @ F ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ ( tc_prod @ H @ G ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ H @ G ) ) @ ( tc_fun @ C @ F ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ H @ G ) @ F @ C ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ H @ G @ F ) @ E ) ) ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__twice) ).
thf(6901,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ H @ G @ F ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ ( tc_prod @ H @ G ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ H @ G ) ) @ ( tc_fun @ C @ F ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ H @ G ) @ F @ C ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ H @ G @ F ) @ E ) ) ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).
thf(2097,axiom,
! [A: $i] : ( c_Wellfounded_Owf @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( c_Wellfounded_Ofinite__psubset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__finite__psubset) ).
thf(10592,plain,
! [A: $i] : ( c_Wellfounded_Owf @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( c_Wellfounded_Ofinite__psubset @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2097]) ).
thf(2121,axiom,
! [A: $i,B: $i] :
~ ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bex__empty) ).
thf(10683,plain,
! [A: $i,B: $i] :
~ ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2121]) ).
thf(2557,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_Hilbert__Choice_Oinv__into @ E @ D @ B @ C ) @ ( hAPP @ C @ A ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__f__f) ).
thf(12238,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_Hilbert__Choice_Oinv__into @ E @ D @ B @ C ) @ ( hAPP @ C @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2557]) ).
thf(865,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/sandbox/benchmark/theBenchmark.p',fact_wf__comp__self) ).
thf(5996,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)],[865]) ).
thf(2244,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__Cons__self2) ).
thf(11110,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)],[2244]) ).
thf(1786,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_HOL_Obool ) @ C ) @ ( c_Relation_Oconverse @ E @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__INTER) ).
thf(9416,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_HOL_Obool ) @ C ) @ ( c_Relation_Oconverse @ E @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1786]) ).
thf(1769,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ C @ C @ C ) @ B ) @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Wellfounded_Omin__ext @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) ) @ ( c_Wellfounded_Omin__ext @ C @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) ) ) ) ) ) @ ( c_Wellfounded_Omin__ext @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__ext__compat) ).
thf(9352,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ C @ C @ C ) @ B ) @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Wellfounded_Omin__ext @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) ) @ ( c_Wellfounded_Omin__ext @ C @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) ) ) ) ) ) @ ( c_Wellfounded_Omin__ext @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1769]) ).
thf(2092,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Finite__Set_Ofolding__image @ 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 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image_Oeq__fold) ).
thf(10571,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Finite__Set_Ofolding__image @ 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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2092]) ).
thf(2538,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/sandbox/benchmark/theBenchmark.p',fact_set__takeWhileD) ).
thf(12168,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)],[2538]) ).
thf(483,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ E @ D @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ B @ ( hAPP @ ( c_Product__Type_Ofst @ E @ D ) @ A ) ) @ ( hAPP @ ( c_Product__Type_Osnd @ E @ D ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__beta) ).
thf(4470,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ E @ D @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ B @ ( hAPP @ ( c_Product__Type_Ofst @ E @ D ) @ A ) ) @ ( hAPP @ ( c_Product__Type_Osnd @ E @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(2221,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/sandbox/benchmark/theBenchmark.p',fact_le__SucE) ).
thf(11033,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)],[2221]) ).
thf(533,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Enum_Oproduct @ E @ D @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ D @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) ) @ A ) ) @ ( c_Enum_Oproduct @ E @ D @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_product_Osimps_I2_J) ).
thf(4685,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Enum_Oproduct @ E @ D @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ D @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) ) @ A ) ) @ ( c_Enum_Oproduct @ E @ D @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(1988,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Set_Ovimage @ C @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__UNIV) ).
thf(10175,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Set_Ovimage @ C @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1988]) ).
thf(1879,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insert) ).
thf(9765,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1879]) ).
thf(874,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
<=> ( ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
& ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__empty) ).
thf(6026,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
& ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
& ( ( ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
& ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(2204,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/sandbox/benchmark/theBenchmark.p',fact_congruentD) ).
thf(10971,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)],[2204]) ).
thf(61,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ tc_Int_Oint ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Int_Oint @ B ) @ A ) )
= ( hAPP @ c_Int_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__atLeastLessThan__int) ).
thf(2904,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ tc_Int_Oint ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Int_Oint @ B ) @ A ) )
= ( hAPP @ c_Int_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(1443,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/sandbox/benchmark/theBenchmark.p',fact_self__append__conv) ).
thf(8095,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)],[1443]) ).
thf(1857,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ E ) ) )
<=> ( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
& ( hBOOL @ ( hAPP @ A @ E ) ) )
| ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bex__Un) ).
thf(9677,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ E ) ) )
=> ( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
& ( hBOOL @ ( hAPP @ A @ E ) ) )
| ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ E ) ) ) ) )
& ( ( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
& ( hBOOL @ ( hAPP @ A @ E ) ) )
| ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ E ) ) ) )
=> ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1857]) ).
thf(455,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/sandbox/benchmark/theBenchmark.p',fact_one__is__add) ).
thf(4354,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)],[455]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ D ) @ C ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) ) ) @ ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) ) )
= ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ 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 ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add) ).
thf(3042,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ D ) @ C ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) ) ) @ ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) ) )
= ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ 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 ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(1283,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_disjoint__eq__subset__Compl) ).
thf(7512,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1283]) ).
thf(857,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_OPow @ B ) @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__not__empty) ).
thf(5969,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_OPow @ B ) @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(1265,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_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ D ) @ C ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ D ) @ C ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ D ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__equiv__class) ).
thf(7459,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_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ D ) @ C ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ D ) @ C ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ D ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1265]) ).
thf(12,axiom,
class_Lattices_Osemilattice__inf @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Lattices_Osemilattice__inf) ).
thf(2717,plain,
class_Lattices_Osemilattice__inf @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1066,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/sandbox/benchmark/theBenchmark.p',fact_le__imp__diff__is__add) ).
thf(6699,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)],[1066]) ).
thf(1144,axiom,
! [A: $i,B: $i] : ( c_Relation_Otrans @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__trancl) ).
thf(7010,plain,
! [A: $i,B: $i] : ( c_Relation_Otrans @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).
thf(1933,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/sandbox/benchmark/theBenchmark.p',fact_trancl__rtrancl__absorb) ).
thf(9939,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)],[1933]) ).
thf(2375,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( ( c_Wellfounded_Owf @ C @ A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ C @ C @ C ) @ B ) @ A ) ) @ B ) )
=> ( c_Wellfounded_Owf @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__union__compatible) ).
thf(11591,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( ( c_Wellfounded_Owf @ C @ A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ C @ C @ C ) @ B ) @ A ) ) @ B ) )
=> ( c_Wellfounded_Owf @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2375]) ).
thf(1956,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 ) )
=> ( ( hAPP @ B @ E )
= ( hAPP @ B @ F ) ) )
=> ( c_Equiv__Relations_Ocongruent @ D @ A @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_congruentI) ).
thf(10030,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 ) )
=> ( ( hAPP @ B @ E )
= ( hAPP @ B @ F ) ) )
=> ( c_Equiv__Relations_Ocongruent @ D @ A @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1956]) ).
thf(1208,axiom,
! [A: $i,B: $i] :
( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__imp__le) ).
thf(7225,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)],[1208]) ).
thf(1492,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/sandbox/benchmark/theBenchmark.p',fact_add__Suc__shift) ).
thf(8290,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)],[1492]) ).
thf(2653,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/sandbox/benchmark/theBenchmark.p',fact_enum__ex) ).
thf(12660,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)],[2653]) ).
thf(360,axiom,
! [A: $i,B: $i] :
( ( B
!= ( c_List_Olist_ONil @ A ) )
=> ( ( c_List_Olast @ A @ B )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ A ) ) @ B ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__conv__nth) ).
thf(3985,plain,
! [A: $i,B: $i] :
( ( B
!= ( c_List_Olist_ONil @ A ) )
=> ( ( c_List_Olast @ A @ B )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ A ) ) @ B ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(1446,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__M__bounded__by__nat) ).
thf(8110,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1446]) ).
thf(526,axiom,
! [A: $i,B: $i] :
( ( c_FunDef_Oreduction__pair @ B @ A )
<=> ( ( c_Wellfounded_Owf @ B @ ( hAPP @ ( c_Product__Type_Ofst @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ B @ B @ B ) @ ( hAPP @ ( c_Product__Type_Ofst @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) ) @ ( hAPP @ ( c_Product__Type_Osnd @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) ) ) @ ( hAPP @ ( c_Product__Type_Ofst @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reduction__pair__def) ).
thf(4657,plain,
! [A: $i,B: $i] :
( ( ( c_FunDef_Oreduction__pair @ B @ A )
=> ( ( c_Wellfounded_Owf @ B @ ( hAPP @ ( c_Product__Type_Ofst @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ B @ B @ B ) @ ( hAPP @ ( c_Product__Type_Ofst @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) ) @ ( hAPP @ ( c_Product__Type_Osnd @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) ) ) @ ( hAPP @ ( c_Product__Type_Ofst @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) ) ) ) )
& ( ( ( c_Wellfounded_Owf @ B @ ( hAPP @ ( c_Product__Type_Ofst @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ B @ B @ B ) @ ( hAPP @ ( c_Product__Type_Ofst @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) ) @ ( hAPP @ ( c_Product__Type_Osnd @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) ) ) @ ( hAPP @ ( c_Product__Type_Ofst @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) ) ) )
=> ( c_FunDef_Oreduction__pair @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(1539,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Relation_OField @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OField @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_OField @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__Un) ).
thf(8480,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Relation_OField @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OField @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_OField @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1539]) ).
thf(1687,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/sandbox/benchmark/theBenchmark.p',fact_not__add__less2) ).
thf(9021,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)],[1687]) ).
thf(2565,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/sandbox/benchmark/theBenchmark.p',fact_THE__default__def) ).
thf(12265,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)],[2565]) ).
thf(2215,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ ( hAPP @ C @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__mem__iff) ).
thf(11016,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ ( hAPP @ C @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ ( hAPP @ C @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2215]) ).
thf(941,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
=> ( ( c_Partial__Function_Oflat__lub @ C @ A @ B )
= A ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
=> ( ( c_Partial__Function_Oflat__lub @ C @ A @ B )
= ( c_HOL_OThe @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_flat__lub__def) ).
thf(6243,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
=> ( ( c_Partial__Function_Oflat__lub @ C @ A @ B )
= A ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
=> ( ( c_Partial__Function_Oflat__lub @ C @ A @ B )
= ( c_HOL_OThe @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(1447,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
<=> ( ( hAPP @ ( c_Fun_Ocomp @ B @ C @ C @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) @ A )
= ( c_Fun_Oid @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__iff) ).
thf(8112,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ B @ C @ C @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) @ A )
= ( c_Fun_Oid @ C ) ) )
& ( ( ( hAPP @ ( c_Fun_Ocomp @ B @ C @ C @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) @ A )
= ( c_Fun_Oid @ C ) )
=> ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1447]) ).
thf(2025,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 @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ F ) @ G ) ) @ A ) )
=> ( F = G ) ) )
=> ( 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 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Un__separatorE) ).
thf(10327,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 @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ F ) @ G ) ) @ A ) )
=> ( F = G ) ) )
=> ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2025]) ).
thf(866,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/sandbox/benchmark/theBenchmark.p',fact_converse__inv__image) ).
thf(6001,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)],[866]) ).
thf(1276,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_Ocurry @ F @ E @ D @ C ) @ B ) @ A )
= ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curry__def) ).
thf(7491,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_Ocurry @ F @ E @ D @ C ) @ B ) @ A )
= ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1276]) ).
thf(2658,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/sandbox/benchmark/theBenchmark.p',fact_in__set__dropD) ).
thf(12704,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)],[2658]) ).
thf(2024,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
<=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ A @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__iff) ).
thf(10321,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ A @ F ) ) ) ) )
& ( ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2024]) ).
thf(1905,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/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oinsert__idem) ).
thf(9853,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)],[1905]) ).
thf(2342,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Un) ).
thf(11464,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2342]) ).
thf(564,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_List_Olist__all @ C @ B @ ( hAPP @ ( c_List_Orev @ C ) @ A ) )
<=> ( c_List_Olist__all @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all__rev) ).
thf(4797,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_List_Olist__all @ C @ B @ ( hAPP @ ( c_List_Orev @ C ) @ A ) )
=> ( c_List_Olist__all @ C @ B @ A ) )
& ( ( c_List_Olist__all @ C @ B @ A )
=> ( c_List_Olist__all @ C @ B @ ( hAPP @ ( c_List_Orev @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(2052,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/sandbox/benchmark/theBenchmark.p',fact_antisymD) ).
thf(10420,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)],[2052]) ).
thf(450,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/sandbox/benchmark/theBenchmark.p',fact_butlast__conv__take) ).
thf(4340,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)],[450]) ).
thf(1191,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/sandbox/benchmark/theBenchmark.p',fact_trans__inv__image) ).
thf(7165,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)],[1191]) ).
thf(239,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/sandbox/benchmark/theBenchmark.p',fact_nth__Cons__0) ).
thf(3523,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)],[239]) ).
thf(1216,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/sandbox/benchmark/theBenchmark.p',fact_add__leD2) ).
thf(7257,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)],[1216]) ).
thf(493,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__greatest) ).
thf(4503,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(1730,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ F @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ ( tc_fun @ E @ tc_HOL_Obool ) @ D ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I10_J) ).
thf(9154,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ F @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ ( tc_fun @ E @ tc_HOL_Obool ) @ D ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1730]) ).
thf(838,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oimage @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNION__eq__Union__image) ).
thf(5882,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oimage @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(1024,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I5_J) ).
thf(6546,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(120,axiom,
! [A: $i] :
( ( c_List_Otranspose @ A @ ( c_List_Olist_ONil @ ( tc_List_Olist @ A ) ) )
= ( c_List_Olist_ONil @ ( tc_List_Olist @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose_Osimps_I1_J) ).
thf(3111,plain,
! [A: $i] :
( ( c_List_Otranspose @ A @ ( c_List_Olist_ONil @ ( tc_List_Olist @ A ) ) )
= ( c_List_Olist_ONil @ ( tc_List_Olist @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(1010,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I7_J) ).
thf(6492,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(2569,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/sandbox/benchmark/theBenchmark.p',fact_insert__iff) ).
thf(12287,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)],[2569]) ).
thf(2108,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ F ) @ ( hAPP @ ( hAPP @ E @ D ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ A @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ A ) @ D ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__splitI) ).
thf(10625,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ F ) @ ( hAPP @ ( hAPP @ E @ D ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ A @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ A ) @ D ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2108]) ).
thf(2366,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ B ) @ c_Int_OInteg ) )
=> ( ! [C: $i] : ( hBOOL @ ( hAPP @ A @ ( hAPP @ c_Int_ORep__Integ @ C ) ) )
=> ( hBOOL @ ( hAPP @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Rep__Integ__induct) ).
thf(11561,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ B ) @ c_Int_OInteg ) )
=> ( ! [C: $i] : ( hBOOL @ ( hAPP @ A @ ( hAPP @ c_Int_ORep__Integ @ C ) ) )
=> ( hBOOL @ ( hAPP @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2366]) ).
thf(808,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ C ) ) @ B ) @ ( c_List_Olists @ C @ A ) ) )
<=> ( ( B
= ( c_List_Olist_ONil @ C ) )
| ? [D: $i,E: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ D ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ C ) ) @ E ) @ ( c_List_Olists @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists_Osimps) ).
thf(5758,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ C ) ) @ B ) @ ( c_List_Olists @ C @ A ) ) )
=> ( ( B
= ( c_List_Olist_ONil @ C ) )
| ? [D: $i,E: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ D ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ C ) ) @ E ) @ ( c_List_Olists @ C @ A ) ) ) ) ) )
& ( ( ( B
= ( c_List_Olist_ONil @ C ) )
| ? [D: $i,E: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ D ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ C ) ) @ E ) @ ( c_List_Olists @ C @ A ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ C ) ) @ B ) @ ( c_List_Olists @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( class_Groups_Ocomm__monoid__add @ H )
& ( class_Orderings_Oord @ G ) )
=> ( ( F = E )
=> ( ( D = C )
=> ( ! [I: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ G ) @ E ) @ I ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ G ) @ I ) @ C ) )
=> ( ( hAPP @ B @ I )
= ( hAPP @ A @ I ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ G @ H ) @ B ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ G @ F ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ G @ H ) @ A ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ G @ E ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__ivl__cong) ).
thf(2894,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( class_Groups_Ocomm__monoid__add @ H )
& ( class_Orderings_Oord @ G ) )
=> ( ( F = E )
=> ( ( D = C )
=> ( ! [I: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ G ) @ E ) @ I ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ G ) @ I ) @ C ) )
=> ( ( hAPP @ B @ I )
= ( hAPP @ A @ I ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ G @ H ) @ B ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ G @ F ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ G @ H ) @ A ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ G @ E ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(514,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/sandbox/benchmark/theBenchmark.p',fact_nat__diff__split__asm) ).
thf(4599,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)],[514]) ).
thf(1206,axiom,
! [A: $i,B: $i] :
( ( ( c_SetInterval_Oord_OatLeastLessThan @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) ) @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ tc_Nat_Onat ) @ c_fNot ) ) @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) )
<=> ~ ( ( 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/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeastLessThan__empty__iff) ).
thf(7212,plain,
! [A: $i,B: $i] :
( ( ( ( c_SetInterval_Oord_OatLeastLessThan @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) ) @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ tc_Nat_Onat ) @ c_fNot ) ) @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) )
=> ~ ( ( 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 ) ) )
=> ( ( c_SetInterval_Oord_OatLeastLessThan @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) ) @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ tc_Nat_Onat ) @ c_fNot ) ) @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1206]) ).
thf(2213,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/sandbox/benchmark/theBenchmark.p',fact_inj__on__fun__updI) ).
thf(11011,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)],[2213]) ).
thf(205,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hAPP @ c_Int_Onat @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__0) ).
thf(3396,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hAPP @ c_Int_Onat @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(1242,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/sandbox/benchmark/theBenchmark.p',fact_split__weak__cong) ).
thf(7372,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)],[1242]) ).
thf(2178,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 ) @ C ) @ A ) )
=> ( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__injective) ).
thf(10890,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 ) @ C ) @ A ) )
=> ( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2178]) ).
thf(2477,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
=> ( hBOOL @ ( hAPP @ B @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ E @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__transfer) ).
thf(11920,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
=> ( hBOOL @ ( hAPP @ B @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ E @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2477]) ).
thf(632,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) ) @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__belowI) ).
thf(5043,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) ) @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(1622,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( c_List_Osublist @ C @ B @ A ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ tc_Nat_Onat ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__sublist) ).
thf(8807,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( c_List_Osublist @ C @ B @ A ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ tc_Nat_Onat ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1622]) ).
thf(2443,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__iff) ).
thf(11805,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2443]) ).
thf(2303,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/sandbox/benchmark/theBenchmark.p',fact_r__r__into__trancl) ).
thf(11323,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)],[2303]) ).
thf(165,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__assoc) ).
thf(3266,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)],[165]) ).
thf(1151,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/sandbox/benchmark/theBenchmark.p',fact_listrel__reflcl__if__listrel1) ).
thf(7041,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)],[1151]) ).
thf(2064,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Equiv__Relations_Oequivp @ D @ C )
=> ( ( c_Quotient_OBabs @ D @ B @ ( c_Quotient_ORespects @ D @ C ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_babs__reg__eqv) ).
thf(10461,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Equiv__Relations_Oequivp @ D @ C )
=> ( ( c_Quotient_OBabs @ D @ B @ ( c_Quotient_ORespects @ D @ C ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2064]) ).
thf(1270,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 ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ B ) )
= A ) )
& ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ D @ A ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Oinsert__remove) ).
thf(7472,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 ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ B ) )
= A ) )
& ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ D @ A ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1270]) ).
thf(2646,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ B ) @ A ) )
| ~ ( hBOOL @ B )
| ( hBOOL @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fimplies__3) ).
thf(12636,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ B ) @ A ) )
| ~ ( hBOOL @ B )
| ( hBOOL @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2646]) ).
thf(244,axiom,
! [A: $i,B: $i] :
( ( c_List_Oconcat @ B @ ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olist_Olist__case @ ( tc_List_Olist @ B ) @ B @ ( c_List_Olist_ONil @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_List_Olist @ B ) @ ( tc_fun @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ B ) @ ( c_COMBK @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olist_OCons @ B ) ) @ ( c_List_Olist_ONil @ B ) ) ) ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_List_Olist @ B ) @ B ) @ ( c_List_Ohd @ B ) ) @ ( hAPP @ ( c_List_Ofilter @ ( tc_List_Olist @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ ( tc_List_Olist @ B ) ) @ c_fNot ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) @ tc_HOL_Obool ) @ c_fequal ) @ ( c_List_Olist_ONil @ B ) ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__aux__filter__head) ).
thf(3536,plain,
! [A: $i,B: $i] :
( ( c_List_Oconcat @ B @ ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olist_Olist__case @ ( tc_List_Olist @ B ) @ B @ ( c_List_Olist_ONil @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_List_Olist @ B ) @ ( tc_fun @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ B ) @ ( c_COMBK @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olist_OCons @ B ) ) @ ( c_List_Olist_ONil @ B ) ) ) ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_List_Olist @ B ) @ B ) @ ( c_List_Ohd @ B ) ) @ ( hAPP @ ( c_List_Ofilter @ ( tc_List_Olist @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ ( tc_List_Olist @ B ) ) @ c_fNot ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) @ tc_HOL_Obool ) @ c_fequal ) @ ( c_List_Olist_ONil @ B ) ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(1476,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/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq1) ).
thf(8217,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)],[1476]) ).
thf(2505,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Equiv__Relations_Oequiv @ G @ F @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ G ) @ F ) @ E ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ G ) @ F ) @ E ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ B ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ A ) @ C ) )
=> ( ( D = C )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ G @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ G ) @ B ) @ A ) ) @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__eq__iff) ).
thf(12028,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Equiv__Relations_Oequiv @ G @ F @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ G ) @ F ) @ E ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ G ) @ F ) @ E ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ B ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ A ) @ C ) )
=> ( ( ( D = C )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ G @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ G ) @ B ) @ A ) ) @ E ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ G @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ G ) @ B ) @ A ) ) @ E ) )
=> ( D = C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2505]) ).
thf(1336,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_OCollect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ B @ tc_HOL_Obool ) @ c_fequal ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__conv) ).
thf(7709,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_OCollect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ B @ tc_HOL_Obool ) @ c_fequal ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1336]) ).
thf(1190,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Set_Ovimage @ F @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ ( c_Set_Ovimage @ F @ E @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__INT) ).
thf(7162,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Set_Ovimage @ F @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ ( c_Set_Ovimage @ F @ E @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190]) ).
thf(937,axiom,
! [A: $i,B: $i] : ( c_Wellfounded_Owf @ B @ ( c_List_Omeasures @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__measures) ).
thf(6234,plain,
! [A: $i,B: $i] : ( c_Wellfounded_Owf @ B @ ( c_List_Omeasures @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(1376,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_List_Oset @ ( tc_prod @ D @ C ) ) @ ( c_Enum_Oproduct @ D @ C @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ B ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_product__list__set) ).
thf(7833,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_List_Oset @ ( tc_prod @ D @ C ) ) @ ( c_Enum_Oproduct @ D @ C @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ B ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1376]) ).
thf(202,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/sandbox/benchmark/theBenchmark.p',fact_decr__mult__lemma) ).
thf(3387,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)],[202]) ).
thf(247,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( c_List_Orev @ B ) @ A )
= ( c_List_Olist_ONil @ B ) )
<=> ( A
= ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__is__Nil__conv) ).
thf(3547,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ B ) @ A )
= ( c_List_Olist_ONil @ B ) )
=> ( A
= ( c_List_Olist_ONil @ B ) ) )
& ( ( A
= ( c_List_Olist_ONil @ B ) )
=> ( ( hAPP @ ( c_List_Orev @ B ) @ A )
= ( c_List_Olist_ONil @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(727,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofun__left__comm__idem @ E @ D @ C )
=> ( ( hAPP @ ( hAPP @ C @ B ) @ ( hAPP @ ( hAPP @ C @ B ) @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofun__left__idem) ).
thf(5456,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofun__left__comm__idem @ E @ D @ C )
=> ( ( hAPP @ ( hAPP @ C @ B ) @ ( hAPP @ ( hAPP @ C @ B ) @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(1888,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/sandbox/benchmark/theBenchmark.p',fact_single__valuedD) ).
thf(9798,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)],[1888]) ).
thf(1338,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_HOL_Obool ) @ C ) @ ( c_Relation_Oconverse @ E @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__UNION) ).
thf(7714,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_HOL_Obool ) @ C ) @ ( c_Relation_Oconverse @ E @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1338]) ).
thf(434,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/sandbox/benchmark/theBenchmark.p',fact_take__Cons_H) ).
thf(4268,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)],[434]) ).
thf(1408,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
thf(7968,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)],[1408]) ).
thf(1400,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ D @ B @ E @ ( hAPP @ ( c_Fun_Ocomp @ E @ B @ D @ A ) @ ( c_Hilbert__Choice_Oinv__into @ E @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) ) ) @ C )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__inv__o__cancel) ).
thf(7938,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ D @ B @ E @ ( hAPP @ ( c_Fun_Ocomp @ E @ B @ D @ A ) @ ( c_Hilbert__Choice_Oinv__into @ E @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) ) ) @ C )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1400]) ).
thf(1004,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_List_Olist_ONil @ C )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osimps_I2_J) ).
thf(6468,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)],[1004]) ).
thf(2611,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/sandbox/benchmark/theBenchmark.p',fact_vimageD) ).
thf(12483,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)],[2611]) ).
thf(1653,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__empty) ).
thf(8909,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1653]) ).
thf(2387,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/sandbox/benchmark/theBenchmark.p',fact_IdE) ).
thf(11633,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)],[2387]) ).
thf(156,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ E ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ D ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) ) @ D ) )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ D ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ E ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ D ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ D ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) ) @ B ) ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ C ) @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__obtain__same__length) ).
thf(3234,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ E ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ D ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) ) @ D ) )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ D ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ E ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ D ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ D ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) ) @ B ) ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ C ) @ D ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(1120,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( c_Nat_Ocompow @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__imp__UN__rel__pow) ).
thf(6916,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( c_Nat_Ocompow @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).
thf(2306,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/sandbox/benchmark/theBenchmark.p',fact_total__on__def) ).
thf(11333,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)],[2306]) ).
thf(1318,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/sandbox/benchmark/theBenchmark.p',fact_nat__less__cases) ).
thf(7639,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)],[1318]) ).
thf(2368,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/sandbox/benchmark/theBenchmark.p',fact_takeWhile_Osimps_I2_J) ).
thf(11566,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)],[2368]) ).
thf(235,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/sandbox/benchmark/theBenchmark.p',fact_take__append) ).
thf(3504,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)],[235]) ).
thf(2182,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ C @ B )
= A )
=> ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ E @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__f__eq) ).
thf(10906,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ C @ B )
= A )
=> ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ E @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2182]) ).
thf(437,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ A ) @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__absorb2) ).
thf(4283,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ A ) @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(737,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ E @ D @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ B @ ( hAPP @ ( c_Product__Type_Ofst @ E @ D ) @ A ) ) @ ( hAPP @ ( c_Product__Type_Osnd @ E @ D ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod__case__beta) ).
thf(5488,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ E @ D @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ B @ ( hAPP @ ( c_Product__Type_Ofst @ E @ D ) @ A ) ) @ ( hAPP @ ( c_Product__Type_Osnd @ E @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(1278,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E
= ( c_Inductive_Ocomplete__lattice__class_Ogfp @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) )
=> ( ( c_Orderings_Oorder__class_Omono @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ E ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__coinduct__set) ).
thf(7497,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E
= ( c_Inductive_Ocomplete__lattice__class_Ogfp @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) )
=> ( ( c_Orderings_Oorder__class_Omono @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ E ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1278]) ).
thf(1649,axiom,
! [A: $i,B: $i] : ( c_Relation_Ototal__on @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_total__on__empty) ).
thf(8900,plain,
! [A: $i,B: $i] : ( c_Relation_Ototal__on @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1649]) ).
thf(158,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) ) )
= ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ A ) @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus) ).
thf(3240,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) ) )
= ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ A ) @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(1128,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image @ H @ G @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ C ) )
=> ( ( hAPP @ ( hAPP @ D @ ( hAPP @ ( hAPP @ ( c_COMBS @ G @ H @ H ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ H @ ( tc_fun @ H @ H ) @ G ) @ F ) @ B ) ) @ A ) ) @ C )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ ( hAPP @ D @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ D @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image_Odistrib) ).
thf(6949,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image @ H @ G @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ C ) )
=> ( ( hAPP @ ( hAPP @ D @ ( hAPP @ ( hAPP @ ( c_COMBS @ G @ H @ H ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ H @ ( tc_fun @ H @ H ) @ G ) @ F ) @ B ) ) @ A ) ) @ C )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ ( hAPP @ D @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ D @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Groups_Ocomm__monoid__add @ F )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ E @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ F @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ F @ ( tc_fun @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ F @ ( tc_fun @ F @ F ) ) @ E ) @ ( c_If @ F ) ) @ C ) ) @ B ) ) @ A ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ E @ F ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_Set_OCollect @ E ) @ C ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ E @ F ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OCollect @ E ) @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__cases) ).
thf(2789,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Groups_Ocomm__monoid__add @ F )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ E @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ F @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ F @ ( tc_fun @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ F @ ( tc_fun @ F @ F ) ) @ E ) @ ( c_If @ F ) ) @ C ) ) @ B ) ) @ A ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ F ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ E @ F ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_Set_OCollect @ E ) @ C ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ E @ F ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OCollect @ E ) @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(260,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( hBOOL @ ( hAPP @ B @ A ) )
=> ( ~ ( hBOOL @ ( hAPP @ D @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ D @ ( hAPP @ c_Nat_OSuc @ E ) ) )
<=> ( hBOOL @ ( hAPP @ B @ E ) ) )
=> ( ( c_Orderings_Oord__class_OLeast @ tc_Nat_Onat @ D )
= ( hAPP @ c_Nat_OSuc @ ( c_Orderings_Oord__class_OLeast @ tc_Nat_Onat @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Least__Suc2) ).
thf(3609,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( hBOOL @ ( hAPP @ B @ A ) )
=> ( ~ ( hBOOL @ ( hAPP @ D @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ! [E: $i] :
( ( ( hBOOL @ ( hAPP @ D @ ( hAPP @ c_Nat_OSuc @ E ) ) )
=> ( hBOOL @ ( hAPP @ B @ E ) ) )
& ( ( hBOOL @ ( hAPP @ B @ E ) )
=> ( hBOOL @ ( hAPP @ D @ ( hAPP @ c_Nat_OSuc @ E ) ) ) ) )
=> ( ( c_Orderings_Oord__class_OLeast @ tc_Nat_Onat @ D )
= ( hAPP @ c_Nat_OSuc @ ( c_Orderings_Oord__class_OLeast @ tc_Nat_Onat @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(405,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Ofilter @ C @ B ) @ ( c_List_Oconcat @ C @ A ) )
= ( c_List_Oconcat @ C @ ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Ofilter @ C @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__concat) ).
thf(4159,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Ofilter @ C @ B ) @ ( c_List_Oconcat @ C @ A ) )
= ( c_List_Oconcat @ C @ ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Ofilter @ C @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(2381,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/sandbox/benchmark/theBenchmark.p',fact_folding__one_Oeq__fold) ).
thf(11615,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)],[2381]) ).
thf(1869,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ C ) )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__diff) ).
thf(9733,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ C ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1869]) ).
thf(2027,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite_OemptyI) ).
thf(10334,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2027]) ).
thf(2200,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_OwfP @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A ) @ B ) )
=> ( c_Wellfounded_OwfP @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__subset) ).
thf(10963,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_OwfP @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A ) @ B ) )
=> ( c_Wellfounded_OwfP @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2200]) ).
thf(1570,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/sandbox/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
thf(8580,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)],[1570]) ).
thf(2572,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/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oin__idem) ).
thf(12301,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)],[2572]) ).
thf(1162,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A )
= ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ C @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ C ) @ c_fdisj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ C @ tc_HOL_Obool ) @ c_fequal ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__compr__raw) ).
thf(7073,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A )
= ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ C @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ C ) @ c_fdisj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ C @ tc_HOL_Obool ) @ c_fequal ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).
thf(226,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding @ H @ G @ F @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ H ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ H ) @ C ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ G @ G @ B @ ( hAPP @ E @ C ) ) @ ( hAPP @ ( c_Fun_Ocomp @ G @ G @ B @ ( hAPP @ E @ D ) ) @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ G @ G @ B @ ( hAPP @ E @ D ) ) @ ( hAPP @ ( c_Fun_Ocomp @ G @ G @ B @ ( hAPP @ E @ C ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__left__comp_H_H) ).
thf(3472,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding @ H @ G @ F @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ H ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ H ) @ C ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ G @ G @ B @ ( hAPP @ E @ C ) ) @ ( hAPP @ ( c_Fun_Ocomp @ G @ G @ B @ ( hAPP @ E @ D ) ) @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ G @ G @ B @ ( hAPP @ E @ D ) ) @ ( hAPP @ ( c_Fun_Ocomp @ G @ G @ B @ ( hAPP @ E @ C ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(1822,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__singleton) ).
thf(9543,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1822]) ).
thf(117,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Osemiring__0 @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ E @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ E @ E ) @ D ) @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ C ) ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__left__distrib) ).
thf(3086,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Osemiring__0 @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ E @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ E @ E ) @ D ) @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ C ) ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(1731,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/sandbox/benchmark/theBenchmark.p',fact_inj__on__imageI) ).
thf(9157,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)],[1731]) ).
thf(1034,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__insert2) ).
thf(6581,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(1597,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) @ ( c_Relation_OId @ B ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reflcl__trancl) ).
thf(8711,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) @ ( c_Relation_OId @ B ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1597]) ).
thf(2548,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_New__DSequence_Opos__map @ E @ D @ C @ B @ A )
= ( c_Lazy__Sequence_Omap @ E @ D @ C @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Opos__map__def) ).
thf(12210,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_New__DSequence_Opos__map @ E @ D @ C @ B @ A )
= ( c_Lazy__Sequence_Omap @ E @ D @ C @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2548]) ).
thf(1260,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) )
<=> ( 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 ) ) @ B ) @ A ) ) @ c_Int_Ointrel ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__intrel__iff) ).
thf(7440,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) )
=> ( 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 ) ) @ B ) @ A ) ) @ c_Int_Ointrel ) ) )
& ( ( 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 ) ) @ B ) @ A ) ) @ c_Int_Ointrel ) )
=> ( ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1260]) ).
thf(116,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/sandbox/benchmark/theBenchmark.p',fact_less__bin__lemma) ).
thf(3081,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)],[116]) ).
thf(304,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_member @ ( tc_prod @ D @ D ) ) @ E ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ D @ D ) @ C ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ D @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ D @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ D @ D ) ) ) ) @ ( c_Product__Type_OPair @ D @ D ) ) ) ) @ A ) ) @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__iff__zip) ).
thf(3758,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_member @ ( tc_prod @ D @ D ) ) @ E ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ D @ D ) @ C ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ D @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ D @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ D @ D ) ) ) ) @ ( c_Product__Type_OPair @ D @ D ) ) ) ) @ A ) ) @ E ) ) ) ) )
& ( ( ( ( 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_member @ ( tc_prod @ D @ D ) ) @ E ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ D @ D ) @ C ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ D @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ D @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ D @ D ) ) ) ) @ ( c_Product__Type_OPair @ D @ D ) ) ) ) @ A ) ) @ E ) ) ) )
=> ( 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)],[304]) ).
thf(852,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/sandbox/benchmark/theBenchmark.p',fact_total__on__converse) ).
thf(5940,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)],[852]) ).
thf(1801,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_HOL_OThe @ ( tc_prod @ C @ B ) @ A )
= ( c_HOL_OThe @ ( tc_prod @ C @ B ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ C @ B @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_prod @ C @ B ) ) @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ C @ B ) @ tc_HOL_Obool @ B ) @ A ) ) @ ( c_Product__Type_OPair @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__paired__The) ).
thf(9471,plain,
! [A: $i,B: $i,C: $i] :
( ( c_HOL_OThe @ ( tc_prod @ C @ B ) @ A )
= ( c_HOL_OThe @ ( tc_prod @ C @ B ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ C @ B @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_prod @ C @ B ) ) @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ C @ B ) @ tc_HOL_Obool @ B ) @ A ) ) @ ( c_Product__Type_OPair @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1801]) ).
thf(167,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__mult @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ E @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ E @ E ) @ D ) @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ B ) ) @ A ) ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ B ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__distrib) ).
thf(3272,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__mult @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ E @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ E @ E ) @ D ) @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ B ) ) @ A ) ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ B ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(2130,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 ) )
=> ( ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ D @ A ) @ ( hAPP @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Oinsert) ).
thf(10709,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 ) )
=> ( ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ D @ A ) @ ( hAPP @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2130]) ).
thf(1478,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/sandbox/benchmark/theBenchmark.p',fact_add__Suc) ).
thf(8222,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)],[1478]) ).
thf(2458,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__upper) ).
thf(11861,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2458]) ).
thf(935,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_Owf @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Wellfounded_Omax__ext @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ext__wf) ).
thf(6229,plain,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_Owf @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Wellfounded_Omax__ext @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(1972,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B )
= A )
=> ( ( hAPP @ ( c_Set_Oimage @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oimage @ E @ D @ C ) ) @ ( hAPP @ ( c_Set_OPow @ E ) @ B ) )
= ( hAPP @ ( c_Set_OPow @ D ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Pow__surj) ).
thf(10100,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B )
= A )
=> ( ( hAPP @ ( c_Set_Oimage @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oimage @ E @ D @ C ) ) @ ( hAPP @ ( c_Set_OPow @ E ) @ B ) )
= ( hAPP @ ( c_Set_OPow @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1972]) ).
thf(635,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1) ).
thf(5050,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)],[635]) ).
thf(1814,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/sandbox/benchmark/theBenchmark.p',fact_listrel1__converse) ).
thf(9521,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)],[1814]) ).
thf(836,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I6_J) ).
thf(5876,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(37,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/sandbox/benchmark/theBenchmark.p',fact_q__neg__lemma) ).
thf(2806,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)],[37]) ).
thf(643,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ C @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ B ) @ A ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__id) ).
thf(5097,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ C @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ B ) @ A ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(972,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ E @ D ) @ C ) @ B ) @ A )
= ( hAPP @ C @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
thf(6344,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ E @ D ) @ C ) @ B ) @ A )
= ( hAPP @ C @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(1462,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/sandbox/benchmark/theBenchmark.p',fact_dropWhile__map) ).
thf(8167,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)],[1462]) ).
thf(1114,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/sandbox/benchmark/theBenchmark.p',fact_not__listrel1__Nil) ).
thf(6898,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)],[1114]) ).
thf(1700,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) @ B ) ) ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ ( hAPP @ ( c_Set_OCollect @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( c_Set_OCollect @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SetCompr__Sigma__eq) ).
thf(9057,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) @ B ) ) ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ ( hAPP @ ( c_Set_OCollect @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( c_Set_OCollect @ C ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1700]) ).
thf(2088,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/sandbox/benchmark/theBenchmark.p',fact_removeAll__filter__not) ).
thf(10557,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)],[2088]) ).
thf(2056,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ E @ D @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ A ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__fold__graphE) ).
thf(10435,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ E @ D @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ A ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2056]) ).
thf(1196,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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff1__le) ).
thf(7180,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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1196]) ).
thf(689,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/sandbox/benchmark/theBenchmark.p',fact_upt__add__eq__append) ).
thf(5271,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)],[689]) ).
thf(1442,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ C @ A ) @ D ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I10_J) ).
thf(8092,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ C @ A ) @ D ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1442]) ).
thf(460,axiom,
! [A: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ A )
=> ( ( c_Complete__Lattice_OInf__class_OInf @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__UNIV) ).
thf(4381,plain,
! [A: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ A )
=> ( ( c_Complete__Lattice_OInf__class_OInf @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(614,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/sandbox/benchmark/theBenchmark.p',fact_set__upt) ).
thf(4975,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)],[614]) ).
thf(41,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/sandbox/benchmark/theBenchmark.p',fact_zle__add1__eq__le) ).
thf(2817,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)],[41]) ).
thf(1374,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff1__less) ).
thf(7828,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1374]) ).
thf(2681,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/sandbox/benchmark/theBenchmark.p',fact_hoare__valids__def) ).
thf(12787,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)],[2681]) ).
thf(806,axiom,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan0) ).
thf(5752,plain,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(2174,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2D2) ).
thf(10874,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2174]) ).
thf(2081,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Un) ).
thf(10525,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2081]) ).
thf(2654,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/sandbox/benchmark/theBenchmark.p',fact_in__set__remove1) ).
thf(12663,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)],[2654]) ).
thf(1370,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/sandbox/benchmark/theBenchmark.p',fact_less__SucE) ).
thf(7815,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)],[1370]) ).
thf(494,axiom,
( ( hAPP @ ( c_Nat_Osize__class_Osize @ tc_HOL_Obool ) @ c_fFalse )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bool_Osize_I4_J) ).
thf(4505,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)],[494]) ).
thf(1150,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I8_J) ).
thf(7038,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_Oimage @ tc_Int_Oint @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Int_Oint @ tc_Int_Oint @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) ) @ B ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ A ) @ B ) ) )
= ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Int_Oint @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__add__int__atLeastLessThan) ).
thf(2959,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_Oimage @ tc_Int_Oint @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Int_Oint @ tc_Int_Oint @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) ) @ B ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ A ) @ B ) ) )
= ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Int_Oint @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(1642,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/sandbox/benchmark/theBenchmark.p',fact_remdups__map__remdups) ).
thf(8872,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)],[1642]) ).
thf(355,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/sandbox/benchmark/theBenchmark.p',fact_length__remdups__card__conv) ).
thf(3964,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)],[355]) ).
thf(2628,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/sandbox/benchmark/theBenchmark.p',fact_comm__monoid__big_Oinfinite) ).
thf(12566,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)],[2628]) ).
thf(2267,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oimage @ ( tc_List_Olist @ D ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_List_Oset @ D ) ) @ A ) ) )
=> ( c_Fun_Oinj__on @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ C ) @ ( hAPP @ ( c_List_Omap @ D @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__mapI) ).
thf(11201,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oimage @ ( tc_List_Olist @ D ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_List_Oset @ D ) ) @ A ) ) )
=> ( c_Fun_Oinj__on @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ C ) @ ( hAPP @ ( c_List_Omap @ D @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2267]) ).
thf(1322,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/sandbox/benchmark/theBenchmark.p',fact_listrel1I1) ).
thf(7671,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)],[1322]) ).
thf(475,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/sandbox/benchmark/theBenchmark.p',fact_nth__Cons_H) ).
thf(4433,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)],[475]) ).
thf(1347,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Hilbert__Choice_OEps @ ( tc_prod @ C @ B ) @ A )
= ( c_Hilbert__Choice_OEps @ ( tc_prod @ C @ B ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ C @ B @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_prod @ C @ B ) ) @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ C @ B ) @ tc_HOL_Obool @ B ) @ A ) ) @ ( c_Product__Type_OPair @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__paired__Eps) ).
thf(7741,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Hilbert__Choice_OEps @ ( tc_prod @ C @ B ) @ A )
= ( c_Hilbert__Choice_OEps @ ( tc_prod @ C @ B ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ C @ B @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_prod @ C @ B ) ) @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ C @ B ) @ tc_HOL_Obool @ B ) @ A ) ) @ ( c_Product__Type_OPair @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1347]) ).
thf(1366,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__eq__Compl__iff) ).
thf(7795,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1366]) ).
thf(428,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Product__Type_Osnd @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ B ) @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__conv) ).
thf(4251,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Product__Type_Osnd @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ B ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(2581,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ~ ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fconj__1) ).
thf(12349,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ~ ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2581]) ).
thf(1612,axiom,
! [A: $i] :
( ( c_Transitive__Closure_Ortrancl @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) )
= ( c_Relation_OId @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__empty) ).
thf(8767,plain,
! [A: $i] :
( ( c_Transitive__Closure_Ortrancl @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) )
= ( c_Relation_OId @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1612]) ).
thf(2445,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/sandbox/benchmark/theBenchmark.p',fact_map__removeAll__inj__on) ).
thf(11819,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)],[2445]) ).
thf(615,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ C @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
<=> ( ( hAPP @ ( c_Fun_Ocomp @ C @ B @ B @ A ) @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) )
= ( c_Fun_Oid @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__iff) ).
thf(4978,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( c_Set_Oimage @ C @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ C @ B @ B @ A ) @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) )
= ( c_Fun_Oid @ B ) ) )
& ( ( ( hAPP @ ( c_Fun_Ocomp @ C @ B @ B @ A ) @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) )
= ( c_Fun_Oid @ B ) )
=> ( ( hAPP @ ( c_Set_Oimage @ C @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(2104,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__Diff__if) ).
thf(10611,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2104]) ).
thf(2635,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/sandbox/benchmark/theBenchmark.p',fact_list__all__iff__raw) ).
thf(12592,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)],[2635]) ).
thf(1957,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 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DiffI) ).
thf(10034,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 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1957]) ).
thf(1722,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__UNIV__left) ).
thf(9125,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1722]) ).
thf(980,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ G ) @ F ) )
=> ( c_Fun_Oinj__on @ D @ C @ B @ ( hAPP @ A @ G ) ) )
=> ( c_Fun_Oinj__on @ D @ C @ B @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ F ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__INTER) ).
thf(6385,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ G ) @ F ) )
=> ( c_Fun_Oinj__on @ D @ C @ B @ ( hAPP @ A @ G ) ) )
=> ( c_Fun_Oinj__on @ D @ C @ B @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ F ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(1562,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__insert__absorb) ).
thf(8549,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1562]) ).
thf(1851,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Int__distrib2) ).
thf(9659,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1851]) ).
thf(2454,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup2E) ).
thf(11846,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2454]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__add @ D )
=> ( ( c_Fun_Oinj__on @ C @ D @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ D ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ D ) @ ( c_Fun_Oid @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ C @ D @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__reindex__id) ).
thf(2891,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__add @ D )
=> ( ( c_Fun_Oinj__on @ C @ D @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ D ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ D ) @ ( c_Fun_Oid @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ C @ D @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(575,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/sandbox/benchmark/theBenchmark.p',fact_list__all__length) ).
thf(4837,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)],[575]) ).
thf(2044,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__strict__subset) ).
thf(10393,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2044]) ).
thf(269,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oorder__refl) ).
thf(3646,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(2512,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/sandbox/benchmark/theBenchmark.p',fact_in__set__takeD) ).
thf(12053,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)],[2512]) ).
thf(389,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Equiv__Relations_Oequiv @ C @ B @ A )
=> ( c_Equiv__Relations_Oequiv @ ( tc_List_Olist @ C ) @ ( c_List_Olists @ C @ B ) @ ( c_List_Olistrel @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__listrel) ).
thf(4112,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Equiv__Relations_Oequiv @ C @ B @ A )
=> ( c_Equiv__Relations_Oequiv @ ( tc_List_Olist @ C ) @ ( c_List_Olists @ C @ B ) @ ( c_List_Olistrel @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(2593,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/sandbox/benchmark/theBenchmark.p',fact_insertE) ).
thf(12401,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)],[2593]) ).
thf(285,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ B ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I2_J) ).
thf(3695,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ B ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(185,axiom,
! [A: $i,B: $i] :
( ( c_List_Otranspose @ B @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ ( tc_List_Olist @ B ) ) @ ( c_List_Olist_ONil @ B ) ) @ A ) )
= ( c_List_Otranspose @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose_Osimps_I2_J) ).
thf(3330,plain,
! [A: $i,B: $i] :
( ( c_List_Otranspose @ B @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ ( tc_List_Olist @ B ) ) @ ( c_List_Olist_ONil @ B ) ) @ A ) )
= ( c_List_Otranspose @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(2486,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 @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UN__I) ).
thf(11951,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 @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2486]) ).
thf(2349,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__eq__subset) ).
thf(11502,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ B ) @ C ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ B ) @ C ) ) )
=> ( C = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2349]) ).
thf(409,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/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel1) ).
thf(4171,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)],[409]) ).
thf(148,axiom,
class_Groups_Ocomm__monoid__add @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
thf(3208,plain,
class_Groups_Ocomm__monoid__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(1589,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Omax__extp @ D @ C @ B @ A )
<=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) )
& ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ F ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__extp_Oequations) ).
thf(8665,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Wellfounded_Omax__extp @ D @ C @ B @ A )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) )
& ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ F ) ) ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) )
& ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ F ) ) ) ) )
=> ( c_Wellfounded_Omax__extp @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1589]) ).
thf(420,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/sandbox/benchmark/theBenchmark.p',fact_nth__append__length__plus) ).
thf(4218,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)],[420]) ).
thf(2031,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( c_Relation_Osingle__valued @ D @ C @ A )
=> ( c_Relation_Osingle__valued @ D @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__subset) ).
thf(10348,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( c_Relation_Osingle__valued @ D @ C @ A )
=> ( c_Relation_Osingle__valued @ D @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2031]) ).
thf(1579,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
<=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNION__empty__conv_I1_J) ).
thf(8624,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
& ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) )
=> ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1579]) ).
thf(2327,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/sandbox/benchmark/theBenchmark.p',fact_distinct_Osimps_I2_J) ).
thf(11423,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)],[2327]) ).
thf(961,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/sandbox/benchmark/theBenchmark.p',fact_K__record__comp) ).
thf(6302,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)],[961]) ).
thf(1543,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Osingle__valued @ C @ C @ B )
=> ( c_Relation_Osingle__valued @ C @ C @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__rel__pow) ).
thf(8492,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Osingle__valued @ C @ C @ B )
=> ( c_Relation_Osingle__valued @ C @ C @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1543]) ).
thf(2291,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/sandbox/benchmark/theBenchmark.p',fact_SigmaD1) ).
thf(11291,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)],[2291]) ).
thf(1820,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_Nat_OSuc @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Suc__Diff1) ).
thf(9538,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_Nat_OSuc @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1820]) ).
thf(2491,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/sandbox/benchmark/theBenchmark.p',fact_listrelp_Oequations_I2_J) ).
thf(11968,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)],[2491]) ).
thf(2351,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( c_Wellfounded_Owf @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__Int2) ).
thf(11515,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( c_Wellfounded_Owf @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2351]) ).
thf(1053,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Orefl__on @ C @ B @ A )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ C ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ C ) @ B ) ) ) )
& ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ D ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__def) ).
thf(6649,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Relation_Orefl__on @ C @ B @ A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ C ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ C ) @ B ) ) ) )
& ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ D ) ) @ A ) ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ C ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ C ) @ B ) ) ) )
& ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ D ) ) @ A ) ) ) )
=> ( c_Relation_Orefl__on @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(125,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ C ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( ( hAPP @ A @ F )
= ( c_Groups_Ozero__class_Ozero @ E ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ B )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__mono__zero__left) ).
thf(3123,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ C ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( ( hAPP @ A @ F )
= ( c_Groups_Ozero__class_Ozero @ E ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ B )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(2599,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/sandbox/benchmark/theBenchmark.p',fact_eqset__imp__iff) ).
thf(12423,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)],[2599]) ).
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 ) @ ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ C ) @ F ) ) @ E ) ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ F ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) )
& ( B
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ D @ C ) @ F ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1__iff__update) ).
thf(5207,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 ) @ ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ C ) @ F ) ) @ E ) ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ F ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) )
& ( B
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ D @ C ) @ F ) @ E ) ) ) )
& ( ? [E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ C ) @ F ) ) @ E ) ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ F ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) )
& ( B
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ D @ C ) @ F ) @ E ) ) )
=> ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(214,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__left__commute) ).
thf(3436,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(1825,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__eq__Diff__UNIV) ).
thf(9555,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1825]) ).
thf(1049,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff__subset__Int) ).
thf(6638,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).
thf(1429,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/sandbox/benchmark/theBenchmark.p',fact_le__add1) ).
thf(8059,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)],[1429]) ).
thf(752,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/sandbox/benchmark/theBenchmark.p',fact_nth__upt) ).
thf(5539,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)],[752]) ).
thf(1891,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_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Diff2) ).
thf(9808,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_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ) )
=> ( 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_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1891]) ).
thf(261,axiom,
! [A: $i] :
( ( c_List_Olists @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_List_Olist @ A ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists__UNIV) ).
thf(3619,plain,
! [A: $i] :
( ( c_List_Olists @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_List_Olist @ A ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(1290,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__commute) ).
thf(7536,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)],[1290]) ).
thf(521,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ C @ B ) @ B @ ( c_Product__Type_Osnd @ C @ B ) ) @ A )
= ( hAPP @ ( c_Relation_ORange @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__eq__Range) ).
thf(4640,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ C @ B ) @ B @ ( c_Product__Type_Osnd @ C @ B ) ) @ A )
= ( hAPP @ ( c_Relation_ORange @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(900,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Otrans @ B @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ B @ B @ B ) @ A ) @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__O__subset) ).
thf(6123,plain,
! [A: $i,B: $i] :
( ( c_Relation_Otrans @ B @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ B @ B @ B ) @ A ) @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(2425,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/sandbox/benchmark/theBenchmark.p',fact_SigmaE2) ).
thf(11750,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)],[2425]) ).
thf(209,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__take) ).
thf(3416,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(2452,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__least) ).
thf(11841,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2452]) ).
thf(1555,axiom,
! [A: $i,B: $i] :
( ( c_List_Oremdups @ B @ ( c_List_Oremdups @ B @ A ) )
= ( c_List_Oremdups @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remdups__remdups) ).
thf(8524,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)],[1555]) ).
thf(2205,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( hBOOL @ ( hAPP @ B @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ D ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1I) ).
thf(10974,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( hBOOL @ ( hAPP @ B @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ D ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2205]) ).
thf(1025,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I7_J) ).
thf(6549,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(2567,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/sandbox/benchmark/theBenchmark.p',fact_LeastI__ex) ).
thf(12280,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)],[2567]) ).
thf(2099,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( class_Enum_Oenum @ C )
& ( class_Enum_Oenum @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__ex @ ( tc_prod @ B @ C ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__ex @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool @ B ) @ ( c_Enum_Oenum__class_Oenum__ex @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ B @ C ) ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ B @ C ) @ tc_HOL_Obool @ C ) @ A ) ) @ ( c_Product__Type_OPair @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_enum__ex__prod__def) ).
thf(10596,plain,
! [A: $i,B: $i,C: $i] :
( ( ( class_Enum_Oenum @ C )
& ( class_Enum_Oenum @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__ex @ ( tc_prod @ B @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__ex @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool @ B ) @ ( c_Enum_Oenum__class_Oenum__ex @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ B @ C ) ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ B @ C ) @ tc_HOL_Obool @ C ) @ A ) ) @ ( c_Product__Type_OPair @ B @ C ) ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__ex @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool @ B ) @ ( c_Enum_Oenum__class_Oenum__ex @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ B @ C ) ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ B @ C ) @ tc_HOL_Obool @ C ) @ A ) ) @ ( c_Product__Type_OPair @ B @ C ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__ex @ ( tc_prod @ B @ C ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2099]) ).
thf(177,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/sandbox/benchmark/theBenchmark.p',fact_zle__diff1__eq) ).
thf(3304,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)],[177]) ).
thf(2382,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Typedef_Otype__definition @ E @ D @ C @ B @ A )
=> ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_ORep__range) ).
thf(11618,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Typedef_Otype__definition @ E @ D @ C @ B @ A )
=> ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2382]) ).
thf(2470,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
<=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__empty) ).
thf(11900,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2470]) ).
thf(1770,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ D @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) @ C ) ) @ B ) ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ D @ C ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ D @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsp__conj__eq) ).
thf(9354,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ D @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) @ C ) ) @ B ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ D @ C ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ D @ B ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ D @ C ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ D @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ D @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) @ C ) ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1770]) ).
thf(2430,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/sandbox/benchmark/theBenchmark.p',fact_refl__onD) ).
thf(11765,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)],[2430]) ).
thf(176,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/sandbox/benchmark/theBenchmark.p',fact_zadd__left__mono) ).
thf(3302,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)],[176]) ).
thf(1248,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/sandbox/benchmark/theBenchmark.p',fact_append__listrel1I) ).
thf(7394,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)],[1248]) ).
thf(2196,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ! [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ ( hAPP @ C @ E ) ) @ ( hAPP @ B @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ D ) ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funI) ).
thf(10953,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ! [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ ( hAPP @ C @ E ) ) @ ( hAPP @ B @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ D ) ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2196]) ).
thf(1494,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_List_OremoveAll @ B @ A ) @ ( c_List_Olist_ONil @ B ) )
= ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_removeAll_Osimps_I1_J) ).
thf(8301,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)],[1494]) ).
thf(2353,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__image__vimage__eq) ).
thf(11525,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2353]) ).
thf(1805,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__subset__conv) ).
thf(9483,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1805]) ).
thf(1854,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ H @ ( tc_fun @ G @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ E ) @ D ) @ C ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ D @ A ) @ C ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ H ) @ A ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF2__E) ).
thf(9670,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ H @ ( tc_fun @ G @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ E ) @ D ) @ C ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ D @ A ) @ C ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ H ) @ A ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1854]) ).
thf(1273,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/sandbox/benchmark/theBenchmark.p',fact_Nat_Odiff__diff__eq) ).
thf(7482,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)],[1273]) ).
thf(1901,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/sandbox/benchmark/theBenchmark.p',fact_listsp_Oequations_I2_J) ).
thf(9835,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)],[1901]) ).
thf(2260,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/sandbox/benchmark/theBenchmark.p',fact_acyclicI) ).
thf(11169,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)],[2260]) ).
thf(1524,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__UNIV) ).
thf(8419,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1524]) ).
thf(873,axiom,
! [A: $i,B: $i] : ( c_Relation_Orefl__on @ B @ A @ ( c_Relation_OId__on @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__Id__on) ).
thf(6024,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)],[873]) ).
thf(1362,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/sandbox/benchmark/theBenchmark.p',fact_add__diff__assoc) ).
thf(7783,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)],[1362]) ).
thf(1861,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/sandbox/benchmark/theBenchmark.p',fact_eq__comp__r) ).
thf(9702,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)],[1861]) ).
thf(2144,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) @ F ) @ C ) @ E ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2I) ).
thf(10766,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) @ F ) @ C ) @ E ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2144]) ).
thf(2166,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/sandbox/benchmark/theBenchmark.p',fact_map_Osimps_I2_J) ).
thf(10842,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)],[2166]) ).
thf(834,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__Un__distrib) ).
thf(5870,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(1253,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/sandbox/benchmark/theBenchmark.p',fact_Cons__acc__listrel1I) ).
thf(7415,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)],[1253]) ).
thf(14,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_Olexord @ D @ A ) ) )
<=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ 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 ) ) )
& ( ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) @ B )
= C ) )
| ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ 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 ) ) ) )
& ( ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ E ) @ C )
= ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ E ) @ B ) )
& ( 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/sandbox/benchmark/theBenchmark.p',fact_lexord__take__index__conv) ).
thf(2721,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_Olexord @ D @ A ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ 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 ) ) )
& ( ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) @ B )
= C ) )
| ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ 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 ) ) ) )
& ( ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ E ) @ C )
= ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ E ) @ B ) )
& ( 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_Orderings_Oord__class_Oless @ 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 ) ) )
& ( ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) @ B )
= C ) )
| ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ 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 ) ) ) )
& ( ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ E ) @ C )
= ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ E ) @ B ) )
& ( 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_Olexord @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(1969,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ C @ B )
= ( hAPP @ C @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__eq) ).
thf(10088,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( ( ( hAPP @ C @ B )
= ( hAPP @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ C @ B )
= ( hAPP @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1969]) ).
thf(1532,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Union) ).
thf(8452,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1532]) ).
thf(449,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/sandbox/benchmark/theBenchmark.p',fact_dropWhile__nth) ).
thf(4337,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)],[449]) ).
thf(1487,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Orderings_Oorder @ D )
& ( class_Enum_Oenum @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__all @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ C @ D @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ ( c_Orderings_Oord__class_Oless__eq @ D ) ) @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__fun_I1_J) ).
thf(8276,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Orderings_Oorder @ D )
& ( class_Enum_Oenum @ C ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__all @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ C @ D @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ ( c_Orderings_Oord__class_Oless__eq @ D ) ) @ B ) ) @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__all @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ C @ D @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ ( c_Orderings_Oord__class_Oless__eq @ D ) ) @ B ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1487]) ).
thf(1788,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/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__equality) ).
thf(9422,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)],[1788]) ).
thf(1033,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/sandbox/benchmark/theBenchmark.p',fact_nat__less__le) ).
thf(6572,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)],[1033]) ).
thf(1982,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( c_Relation_OImage @ E @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( c_Relation_OImage @ E @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
=> ( ( c_Equiv__Relations_Oequiv @ E @ A @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ B ) ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__equiv__class) ).
thf(10151,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( c_Relation_OImage @ E @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( c_Relation_OImage @ E @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
=> ( ( c_Equiv__Relations_Oequiv @ E @ A @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ B ) ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1982]) ).
thf(1284,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ D @ C ) @ ( tc_prod @ C @ D ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ ( tc_prod @ C @ D ) ) @ ( hAPP @ ( c_COMBC @ C @ D @ ( tc_prod @ C @ D ) ) @ ( c_Product__Type_OPair @ C @ D ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ D ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_swap__product) ).
thf(7519,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ D @ C ) @ ( tc_prod @ C @ D ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ ( tc_prod @ C @ D ) ) @ ( hAPP @ ( c_COMBC @ C @ D @ ( tc_prod @ C @ D ) ) @ ( c_Product__Type_OPair @ C @ D ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ D ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1284]) ).
thf(1398,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/sandbox/benchmark/theBenchmark.p',fact_diff__less__mono) ).
thf(7933,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)],[1398]) ).
thf(2183,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/sandbox/benchmark/theBenchmark.p',fact_set__map) ).
thf(10910,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)],[2183]) ).
thf(162,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/sandbox/benchmark/theBenchmark.p',fact_zless__add1__eq) ).
thf(3251,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)],[162]) ).
thf(2289,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ C @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( c_Fun_Oinj__on @ B @ C @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__imp__inj__inv) ).
thf(11283,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ C @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( c_Fun_Oinj__on @ B @ C @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2289]) ).
thf(2246,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_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ D ) @ A ) ) ) @ ( hAPP @ ( c_List_Oset @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__take__subset__set__take) ).
thf(11117,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_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ D ) @ A ) ) ) @ ( hAPP @ ( c_List_Oset @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2246]) ).
thf(317,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/sandbox/benchmark/theBenchmark.p',fact_nat__le__add__iff1) ).
thf(3815,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)],[317]) ).
thf(2655,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/sandbox/benchmark/theBenchmark.p',fact_accp_Oequations) ).
thf(12668,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)],[2655]) ).
thf(1776,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Otrans @ B @ A )
=> ( c_Relation_Otrans @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) @ ( c_Relation_OId @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__reflclI) ).
thf(9375,plain,
! [A: $i,B: $i] :
( ( c_Relation_Otrans @ B @ A )
=> ( c_Relation_Otrans @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) @ ( c_Relation_OId @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1776]) ).
thf(1762,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/sandbox/benchmark/theBenchmark.p',fact_append__eq__Cons__conv) ).
thf(9312,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)],[1762]) ).
thf(1122,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ A @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__insert) ).
thf(6920,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ A @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).
thf(157,axiom,
( ( c_Lattices_Osemilattice__inf__class_Oinf @ tc_Nat_Onat )
= ( c_Orderings_Oord__class_Omin @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__nat__def) ).
thf(3238,plain,
( ( c_Lattices_Osemilattice__inf__class_Oinf @ tc_Nat_Onat )
= ( c_Orderings_Oord__class_Omin @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(681,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/sandbox/benchmark/theBenchmark.p',fact_not__less0) ).
thf(5244,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)],[681]) ).
thf(2531,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/sandbox/benchmark/theBenchmark.p',fact_inj__on__def) ).
thf(12131,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)],[2531]) ).
thf(1908,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ C ) @ B ) ) @ ( hAPP @ ( c_Set_OPow @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__mono) ).
thf(9867,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ C ) @ B ) ) @ ( hAPP @ ( c_Set_OPow @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1908]) ).
thf(645,axiom,
( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_One__nat__def) ).
thf(5103,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)],[645]) ).
thf(2480,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ E ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ A @ E ) )
=> ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ E ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__induct) ).
thf(11932,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ E ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ A @ E ) )
=> ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ E ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2480]) ).
thf(747,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/sandbox/benchmark/theBenchmark.p',fact_length__append) ).
thf(5520,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)],[747]) ).
thf(1453,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I6_J) ).
thf(8135,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1453]) ).
thf(1777,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ A ) )
=> ( D != E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_disjoint__iff__not__equal) ).
thf(9377,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ A ) )
=> ( D != E ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ A ) )
=> ( D != E ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1777]) ).
thf(1391,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ E @ F @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ ( c_Relation_OImage @ E @ F @ D ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__INT__subset) ).
thf(7907,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ E @ F @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) @ C ) @ ( c_Relation_OImage @ E @ F @ D ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1391]) ).
thf(995,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ D ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ C @ D @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ D @ D ) @ C ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) ) @ A ) ) @ ( c_Orderings_Otop__class_Otop @ D ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INFI__fold__inf) ).
thf(6443,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ D ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ C @ D @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ D @ D ) @ C ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) ) @ A ) ) @ ( c_Orderings_Otop__class_Otop @ D ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(828,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_Oimage @ B @ B @ ( c_COMBI @ B ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__ident) ).
thf(5848,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_Oimage @ B @ B @ ( c_COMBI @ B ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(517,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( c_List_Olist_ONil @ B ) )
=> ( ( c_List_Olast @ B @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ A ) @ C ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__ConsL) ).
thf(4620,plain,
! [A: $i,B: $i,C: $i] :
( ( C
= ( c_List_Olist_ONil @ B ) )
=> ( ( c_List_Olast @ B @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ A ) @ C ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(1001,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/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
thf(6461,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)],[1001]) ).
thf(1669,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/sandbox/benchmark/theBenchmark.p',fact_distinct__zipI1) ).
thf(8970,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)],[1669]) ).
thf(2013,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 ) )
=> ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ! [E: $i,F: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ ( hAPP @ ( hAPP @ C @ E ) @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ ( hAPP @ B @ A ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Oclosed) ).
thf(10279,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 ) )
=> ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ! [E: $i,F: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ ( hAPP @ ( hAPP @ C @ E ) @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ ( hAPP @ B @ A ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2013]) ).
thf(2119,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ? [E: $i] :
( ( c_Fun_Oinj__on @ D @ B @ E @ C )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ B @ E ) @ C ) ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ C ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__card__le) ).
thf(10677,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( ? [E: $i] :
( ( c_Fun_Oinj__on @ D @ B @ E @ C )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ B @ E ) @ C ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ C ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ C ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A ) ) )
=> ? [E: $i] :
( ( c_Fun_Oinj__on @ D @ B @ E @ C )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ B @ E ) @ C ) ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2119]) ).
thf(2118,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ C @ D @ B ) @ ( hAPP @ ( c_Set_Ovimage @ C @ D @ B ) @ A ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__vimage__subset) ).
thf(10675,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ C @ D @ B ) @ ( hAPP @ ( c_Set_Ovimage @ C @ D @ B ) @ A ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2118]) ).
thf(172,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__mult @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__Un__Int) ).
thf(3287,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__mult @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(2506,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subsetD) ).
thf(12034,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2506]) ).
thf(572,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_List_Oset @ B ) @ A )
= ( hAPP @ ( c_Set_OCollect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool @ B ) @ ( c_HOL_OEx @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ B ) @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ tc_Nat_Onat @ B ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ B ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ B ) @ ( c_COMBB @ B @ tc_HOL_Obool @ tc_Nat_Onat ) ) @ c_fequal ) ) @ ( hAPP @ ( c_List_Onth @ B ) @ A ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__conv__nth) ).
thf(4828,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_List_Oset @ B ) @ A )
= ( hAPP @ ( c_Set_OCollect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool @ B ) @ ( c_HOL_OEx @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ B ) @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ tc_Nat_Onat @ B ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ B ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ B ) @ ( c_COMBB @ B @ tc_HOL_Obool @ tc_Nat_Onat ) ) @ c_fequal ) ) @ ( hAPP @ ( c_List_Onth @ B ) @ A ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(309,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ F )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ F ) ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ F ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ D @ F ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUPR__apply) ).
thf(3779,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ F )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ F ) ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ F ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ D @ F ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(1244,axiom,
! [A: $i,B: $i] :
( ( B = A )
=> ( ( c_SetInterval_Oord_OatLeastAtMost @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeastAtMost__singleton_H) ).
thf(7379,plain,
! [A: $i,B: $i] :
( ( B = A )
=> ( ( c_SetInterval_Oord_OatLeastAtMost @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1244]) ).
thf(210,axiom,
! [A: $i,B: $i] :
( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Enum_On__lists @ A @ B @ ( c_List_Olist_ONil @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ ( tc_List_Olist @ A ) ) @ ( c_List_Olist_ONil @ A ) ) @ ( c_List_Olist_ONil @ ( tc_List_Olist @ A ) ) ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Enum_On__lists @ A @ B @ ( c_List_Olist_ONil @ A ) )
= ( c_List_Olist_ONil @ ( tc_List_Olist @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__lists__Nil) ).
thf(3419,plain,
! [A: $i,B: $i] :
( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Enum_On__lists @ A @ B @ ( c_List_Olist_ONil @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ ( tc_List_Olist @ A ) ) @ ( c_List_Olist_ONil @ A ) ) @ ( c_List_Olist_ONil @ ( tc_List_Olist @ A ) ) ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Enum_On__lists @ A @ B @ ( c_List_Olist_ONil @ A ) )
= ( c_List_Olist_ONil @ ( tc_List_Olist @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(595,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__assoc) ).
thf(4914,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)],[595]) ).
thf(776,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) )
<=> ( ( C = A )
| ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__cancel2) ).
thf(5631,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)],[776]) ).
thf(698,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ E ) @ B ) @ A ) ) )
<=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ D ) @ ( hAPP @ A @ F ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__INF__iff) ).
thf(5303,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ E ) @ B ) @ A ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ D ) @ ( hAPP @ A @ F ) ) ) ) )
& ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ D ) @ ( hAPP @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ E ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(1259,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/sandbox/benchmark/theBenchmark.p',fact_pigeonhole) ).
thf(7438,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)],[1259]) ).
thf(1593,axiom,
! [A: $i] :
( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__not__empty) ).
thf(8688,plain,
! [A: $i] :
( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1593]) ).
thf(738,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ A ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ A ) ) @ ( hAPP @ C @ B ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__comp_H_H) ).
thf(5491,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ A ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ A ) ) @ ( hAPP @ C @ B ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(844,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ D @ C @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__empty) ).
thf(5901,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ D @ C @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(2418,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/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oeq__fold__idem_H) ).
thf(11733,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)],[2418]) ).
thf(1719,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/sandbox/benchmark/theBenchmark.p',fact_mlex__less) ).
thf(9118,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)],[1719]) ).
thf(2310,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__subsetI) ).
thf(11355,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2310]) ).
thf(2447,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/sandbox/benchmark/theBenchmark.p',fact_wf__no__infinite__down__chainE) ).
thf(11829,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)],[2447]) ).
thf(2543,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/sandbox/benchmark/theBenchmark.p',fact_ord_OgreaterThanLessThan__iff) ).
thf(12182,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)],[2543]) ).
thf(2286,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/sandbox/benchmark/theBenchmark.p',fact_in__lex__prod) ).
thf(11268,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)],[2286]) ).
thf(566,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_Product__Type_Ofst @ D @ C ) @ B )
= ( hAPP @ ( c_Product__Type_Ofst @ D @ C ) @ A ) )
=> ( ( ( hAPP @ ( c_Product__Type_Osnd @ D @ C ) @ B )
= ( hAPP @ ( c_Product__Type_Osnd @ D @ C ) @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod__eqI) ).
thf(4805,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_Product__Type_Ofst @ D @ C ) @ B )
= ( hAPP @ ( c_Product__Type_Ofst @ D @ C ) @ A ) )
=> ( ( ( hAPP @ ( c_Product__Type_Osnd @ D @ C ) @ B )
= ( hAPP @ ( c_Product__Type_Osnd @ D @ C ) @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(1498,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/sandbox/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
thf(8313,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)],[1498]) ).
thf(1830,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/sandbox/benchmark/theBenchmark.p',fact_diff__commute) ).
thf(9570,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)],[1830]) ).
thf(770,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/sandbox/benchmark/theBenchmark.p',fact_nat__eq__add__iff2) ).
thf(5610,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)],[770]) ).
thf(2177,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/sandbox/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__into__rtrancl) ).
thf(10888,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)],[2177]) ).
thf(1685,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/sandbox/benchmark/theBenchmark.p',fact_Id__O__R) ).
thf(9015,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)],[1685]) ).
thf(140,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( c_List_Olist_ONil @ B ) )
=> ( ( hAPP @ ( c_List_Ohd @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ C ) @ A ) )
= ( hAPP @ ( c_List_Ohd @ B ) @ A ) ) )
& ( ( C
!= ( c_List_Olist_ONil @ B ) )
=> ( ( hAPP @ ( c_List_Ohd @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ C ) @ A ) )
= ( hAPP @ ( c_List_Ohd @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__append) ).
thf(3182,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( c_List_Olist_ONil @ B ) )
=> ( ( hAPP @ ( c_List_Ohd @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ C ) @ A ) )
= ( hAPP @ ( c_List_Ohd @ B ) @ A ) ) )
& ( ( C
!= ( c_List_Olist_ONil @ B ) )
=> ( ( hAPP @ ( c_List_Ohd @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ C ) @ A ) )
= ( hAPP @ ( c_List_Ohd @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(254,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 ) ) )
=> ( ( c_SetInterval_Oord_OatLeastAtMost @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeastatMost__empty) ).
thf(3586,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 ) ) )
=> ( ( c_SetInterval_Oord_OatLeastAtMost @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(201,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__0__right) ).
thf(3384,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)],[201]) ).
thf(2331,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/sandbox/benchmark/theBenchmark.p',fact_wf__asym) ).
thf(11438,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)],[2331]) ).
thf(771,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ F )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ F ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ F ) @ F @ E ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ F ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ F ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ F ) @ F @ C ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ F ) @ D ) ) @ ( hAPP @ ( c_COMBC @ E @ C @ F ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP__commute) ).
thf(5616,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ F )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ F ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ F ) @ F @ E ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ F ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ F ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ F ) @ F @ C ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ F ) @ D ) ) @ ( hAPP @ ( c_COMBC @ E @ C @ F ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(2373,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ 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_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) @ ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__class__subset) ).
thf(11586,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ 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_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) @ ( hAPP @ ( c_Relation_OImage @ E @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2373]) ).
thf(2126,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ E ) @ D ) )
=> ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ G ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ B @ G ) ) @ ( hAPP @ A @ G ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__anti__mono) ).
thf(10696,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ E ) @ D ) )
=> ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ G ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ B @ G ) ) @ ( hAPP @ A @ G ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2126]) ).
thf(2587,axiom,
~ ( hBOOL @ c_fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fFalse__1) ).
thf(12368,plain,
~ ( hBOOL @ c_fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2587]) ).
thf(12369,plain,
~ ( hBOOL @ c_fFalse ),
inference(polarity_switch,[status(thm)],[12368]) ).
thf(2324,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/sandbox/benchmark/theBenchmark.p',fact_converse__pred__comp) ).
thf(11406,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)],[2324]) ).
thf(387,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/sandbox/benchmark/theBenchmark.p',fact_lexord__transI) ).
thf(4107,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)],[387]) ).
thf(1864,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 @ ( c_Finite__Set_Ofinite @ G ) @ A ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Ounion__idem) ).
thf(9713,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 @ ( c_Finite__Set_Ofinite @ G ) @ A ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1864]) ).
thf(1212,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ C @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ C ) @ c_fimplies ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ B ) ) ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__imp__eq) ).
thf(7238,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ C @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ C ) @ c_fimplies ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ B ) ) ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1212]) ).
thf(782,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/sandbox/benchmark/theBenchmark.p',fact_list_Osize_I4_J) ).
thf(5657,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)],[782]) ).
thf(481,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ G ) @ C ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ F ) @ ( hAPP @ ( c_Set_OCollect @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ F @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ F ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ F @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ F ) ) @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ D @ tc_HOL_Obool ) @ B ) @ G ) ) ) )
= A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ F @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_Nat_Onat @ F ) @ ( c_Finite__Set_Ocard @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ F ) @ ( c_Set_OCollect @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( c_COMBS @ D @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ C ) ) ) ) @ B ) ) ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__multicount) ).
thf(4462,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ G ) @ C ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ F ) @ ( hAPP @ ( c_Set_OCollect @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ F @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ F ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ F @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ F ) ) @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ D @ tc_HOL_Obool ) @ B ) @ G ) ) ) )
= A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ F @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_Nat_Onat @ F ) @ ( c_Finite__Set_Ocard @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ F ) @ ( c_Set_OCollect @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( c_COMBS @ D @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ C ) ) ) ) @ B ) ) ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(616,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding__idem @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) )
= ( hAPP @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__idem_Osubset__comp__idem) ).
thf(4985,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding__idem @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) )
= ( hAPP @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__assoc) ).
thf(2757,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)],[21]) ).
thf(2559,axiom,
! [A: $i,B: $i] :
( ? [C: $i] : ( hBOOL @ ( hAPP @ B @ C ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Hilbert__Choice_OEps @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_someI__ex) ).
thf(12246,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)],[2559]) ).
thf(1930,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__right__if0) ).
thf(9931,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1930]) ).
thf(153,axiom,
! [A: $i,B: $i] :
( ( ( c_List_Otranspose @ B @ A )
= ( c_List_Olist_ONil @ ( tc_List_Olist @ B ) ) )
<=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ B ) ) @ C ) @ ( hAPP @ ( c_List_Oset @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ( C
= ( c_List_Olist_ONil @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__empty) ).
thf(3219,plain,
! [A: $i,B: $i] :
( ( ( ( c_List_Otranspose @ B @ A )
= ( c_List_Olist_ONil @ ( tc_List_Olist @ B ) ) )
=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ B ) ) @ C ) @ ( hAPP @ ( c_List_Oset @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ( C
= ( c_List_Olist_ONil @ B ) ) ) )
& ( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ B ) ) @ C ) @ ( hAPP @ ( c_List_Oset @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ( C
= ( c_List_Olist_ONil @ B ) ) )
=> ( ( c_List_Otranspose @ B @ A )
= ( c_List_Olist_ONil @ ( tc_List_Olist @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(757,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/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__cancel) ).
thf(5563,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)],[757]) ).
thf(1104,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/sandbox/benchmark/theBenchmark.p',fact_converse__Id__on) ).
thf(6834,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)],[1104]) ).
thf(418,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/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).
thf(4203,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)],[418]) ).
thf(649,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/sandbox/benchmark/theBenchmark.p',fact_nth__zip) ).
thf(5114,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)],[649]) ).
thf(1280,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Relation_ODomain @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_ODomain @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_ODomain @ D @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Un__eq) ).
thf(7504,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Relation_ODomain @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_ODomain @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_ODomain @ D @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1280]) ).
thf(1694,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ G @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) @ F ) @ ( c_COMBB @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ G @ tc_HOL_Obool ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ F ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) @ D ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__UN__distrib2) ).
thf(9042,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ G @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) @ F ) @ ( c_COMBB @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ G @ tc_HOL_Obool ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ G @ tc_HOL_Obool ) @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ F ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) @ D ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1694]) ).
thf(2560,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/sandbox/benchmark/theBenchmark.p',fact_conversep__iff) ).
thf(12248,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)],[2560]) ).
thf(867,axiom,
! [A: $i] :
( ( hAPP @ ( c_Relation_OField @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__empty) ).
thf(6004,plain,
! [A: $i] :
( ( hAPP @ ( c_Relation_OField @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(889,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__le__nat) ).
thf(6087,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(1578,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 ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ D @ A ) ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Oinsert__remove) ).
thf(8620,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 ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ D @ A ) ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1578]) ).
thf(1906,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ C @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
<=> ! [D: $i] :
( ( hAPP @ A @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ D ) )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__iff__all) ).
thf(9857,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( c_Set_Oimage @ C @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ! [D: $i] :
( ( hAPP @ A @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ D ) )
= D ) )
& ( ! [D: $i] :
( ( hAPP @ A @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ D ) )
= D )
=> ( ( hAPP @ ( c_Set_Oimage @ C @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1906]) ).
thf(1356,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( c_COMBC @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ C ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__fold__remove) ).
thf(7768,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( c_COMBC @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ C ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1356]) ).
thf(301,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Omap @ B @ B ) @ ( c_COMBI @ B ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__ident) ).
thf(3747,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Omap @ B @ B ) @ ( c_COMBI @ B ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(2343,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__imp__rtrancl) ).
thf(11470,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2343]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ocomm__monoid__add @ C )
=> ( ( ( hAPP @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ C ) @ B ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ C ) @ B ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__shift__lb__Suc0__0__upt) ).
thf(2742,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ocomm__monoid__add @ C )
=> ( ( ( hAPP @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ C ) @ B ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ tc_Nat_Onat @ C ) @ B ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(2038,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Obij__betw @ E @ D @ C @ B @ A )
=> ( c_Fun_Oinj__on @ E @ D @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__imp__inj__on) ).
thf(10375,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Obij__betw @ E @ D @ C @ B @ A )
=> ( c_Fun_Oinj__on @ E @ D @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2038]) ).
thf(2384,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_OPow @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__iff) ).
thf(11623,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_OPow @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_OPow @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2384]) ).
thf(386,axiom,
! [A: $i] :
~ ! [B: $i,C: $i] :
( A
!= ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ C ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__Abs__Integ) ).
thf(4103,plain,
! [A: $i] :
~ ! [B: $i,C: $i] :
( A
!= ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ C ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(2005,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/sandbox/benchmark/theBenchmark.p',fact_distinct__map) ).
thf(10253,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)],[2005]) ).
thf(798,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_List_Olast @ C @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ A ) @ ( c_List_Olist_ONil @ C ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__snoc) ).
thf(5730,plain,
! [A: $i,B: $i,C: $i] :
( ( c_List_Olast @ C @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ A ) @ ( c_List_Olist_ONil @ C ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(2601,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image @ H @ G @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ C ) )
=> ( ! [I: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ I ) @ C ) )
=> ( ( hAPP @ B @ I )
= ( hAPP @ A @ I ) ) )
=> ( ( hAPP @ ( hAPP @ D @ B ) @ C )
= ( hAPP @ ( hAPP @ D @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image_Ocong) ).
thf(12433,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image @ H @ G @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ C ) )
=> ( ! [I: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ I ) @ C ) )
=> ( ( hAPP @ B @ I )
= ( hAPP @ A @ I ) ) )
=> ( ( hAPP @ ( hAPP @ D @ B ) @ C )
= ( hAPP @ ( hAPP @ D @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2601]) ).
thf(1705,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oinsert__remove) ).
thf(9079,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1705]) ).
thf(2208,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_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) )
=> ( ! [E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ A @ F ) )
=> ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ E ) @ F ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__subset__induct) ).
thf(10995,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_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) )
=> ( ! [E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ A @ F ) )
=> ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ E ) @ F ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2208]) ).
thf(2661,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Predicate_Oreflp @ C @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reflpE) ).
thf(12712,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)],[2661]) ).
thf(665,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oord @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeast @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast__iff) ).
thf(5175,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oord @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeast @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeast @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(2269,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__subsetD) ).
thf(11205,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2269]) ).
thf(1858,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/sandbox/benchmark/theBenchmark.p',fact_filter_Osimps_I2_J) ).
thf(9691,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)],[1858]) ).
thf(1138,axiom,
! [A: $i] :
( ( hAPP @ ( c_Set_OPow @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__empty) ).
thf(6989,plain,
! [A: $i] :
( ( hAPP @ ( c_Set_OPow @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).
thf(2321,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Obij__betw @ E @ D @ C @ B @ A )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
<=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__finite) ).
thf(11392,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Obij__betw @ E @ D @ C @ B @ A )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2321]) ).
thf(1674,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/sandbox/benchmark/theBenchmark.p',fact_diff__le__mono2) ).
thf(8983,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)],[1674]) ).
thf(2630,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 ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ C @ E @ A @ B ) @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__into) ).
thf(12572,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 ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ C @ E @ A @ B ) @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2630]) ).
thf(724,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/sandbox/benchmark/theBenchmark.p',fact_length__greater__0__conv) ).
thf(5439,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)],[724]) ).
thf(1229,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I8_J) ).
thf(7302,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1229]) ).
thf(1071,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_Oacyclic @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__acyclic) ).
thf(6725,plain,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_Oacyclic @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).
thf(1134,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/sandbox/benchmark/theBenchmark.p',fact_sym__inv__image) ).
thf(6974,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)],[1134]) ).
thf(2423,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ ( hAPP @ C @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ A @ D @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rangeI) ).
thf(11746,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ ( hAPP @ C @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ A @ D @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2423]) ).
thf(1295,axiom,
! [A: $i,B: $i] :
( ( c_Predicate_Oreflp @ B @ A )
<=> ( c_Relation_Orefl__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ B @ tc_HOL_Obool ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reflp__def) ).
thf(7551,plain,
! [A: $i,B: $i] :
( ( ( c_Predicate_Oreflp @ B @ A )
=> ( c_Relation_Orefl__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ B @ tc_HOL_Obool ) @ A ) ) ) )
& ( ( c_Relation_Orefl__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ B @ B @ tc_HOL_Obool ) @ A ) ) )
=> ( c_Predicate_Oreflp @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1295]) ).
thf(2256,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/sandbox/benchmark/theBenchmark.p',fact_trancl__rtrancl__trancl) ).
thf(11158,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)],[2256]) ).
thf(1397,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Oantisym @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) @ ( c_Relation_OId @ B ) ) )
<=> ( c_Relation_Oantisym @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisym__reflcl) ).
thf(7928,plain,
! [A: $i,B: $i] :
( ( ( c_Relation_Oantisym @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) @ ( c_Relation_OId @ B ) ) )
=> ( c_Relation_Oantisym @ B @ A ) )
& ( ( c_Relation_Oantisym @ B @ A )
=> ( c_Relation_Oantisym @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) @ ( c_Relation_OId @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1397]) ).
thf(2135,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_OwfP @ B @ ( c_FunDef_Oin__rel @ B @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__in__rel) ).
thf(10732,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)],[2135]) ).
thf(1410,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/sandbox/benchmark/theBenchmark.p',fact_map__pair__compose) ).
thf(7978,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)],[1410]) ).
thf(1824,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Osym @ B @ A )
=> ( c_Relation_Osym @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sym__rtrancl) ).
thf(9553,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)],[1824]) ).
thf(1999,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ F ) @ A ) @ E ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup2I1) ).
thf(10219,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ F ) @ A ) @ E ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1999]) ).
thf(358,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) )
= ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ B ) @ A ) )
<=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__empty__iff2) ).
thf(3977,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) )
= ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) )
= ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(1360,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ E ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ D @ E @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ E @ E ) @ D ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ E ) ) @ A ) ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__INFI__fold__inf) ).
thf(7778,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ E ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ D @ E @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ E @ E ) @ D ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ E ) ) @ A ) ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1360]) ).
thf(92,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/sandbox/benchmark/theBenchmark.p',fact_add1__zle__eq) ).
thf(3006,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)],[92]) ).
thf(219,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
thf(3451,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(2141,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ! [G: $i,H: $i] :
( ( F
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ G ) @ H ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( hAPP @ A @ G ) @ H ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ E @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__splitI2) ).
thf(10755,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ! [G: $i,H: $i] :
( ( F
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ G ) @ H ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( hAPP @ A @ G ) @ H ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ E @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2141]) ).
thf(1183,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
thf(7141,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183]) ).
thf(525,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/sandbox/benchmark/theBenchmark.p',fact_card_Oneutral) ).
thf(4652,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)],[525]) ).
thf(2627,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/sandbox/benchmark/theBenchmark.p',fact_vimageI) ).
thf(12562,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)],[2627]) ).
thf(1680,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_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ C ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ C ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__quotient) ).
thf(8998,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_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ C ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ C ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1680]) ).
thf(730,axiom,
c_Equiv__Relations_Oequiv @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ c_Int_Ointrel,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__intrel) ).
thf(5466,plain,
c_Equiv__Relations_Oequiv @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ c_Int_Ointrel,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(2071,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/sandbox/benchmark/theBenchmark.p',fact_List_Oset__insert) ).
thf(10489,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)],[2071]) ).
thf(839,axiom,
! [A: $i,B: $i] :
( ( c_List_OdropWhile @ B @ A @ ( c_List_Olist_ONil @ B ) )
= ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dropWhile_Osimps_I1_J) ).
thf(5885,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)],[839]) ).
thf(2372,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 ) ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) ) )
=> ? [F: $i] :
( ( 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 @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ F ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__Suc__D2) ).
thf(11583,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 ) ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) ) )
=> ? [F: $i] :
( ( 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 @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ F ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2372]) ).
thf(253,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/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__eq__diff__pred) ).
thf(3583,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)],[253]) ).
thf(1920,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/sandbox/benchmark/theBenchmark.p',fact_drop__map) ).
thf(9905,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)],[1920]) ).
thf(1537,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord__eq__less__trans) ).
thf(8473,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1537]) ).
thf(1811,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ A ) ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__cartesian__product__singleton) ).
thf(9511,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ A ) ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1811]) ).
thf(2634,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/sandbox/benchmark/theBenchmark.p',fact_in__rel__def) ).
thf(12587,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)],[2634]) ).
thf(2431,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/sandbox/benchmark/theBenchmark.p',fact_rtranclD) ).
thf(11767,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)],[2431]) ).
thf(1262,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Relation_ORange @ B @ B ) @ ( c_Relation_OId__on @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Id__on) ).
thf(7450,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)],[1262]) ).
thf(1094,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/sandbox/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
thf(6802,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)],[1094]) ).
thf(545,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/sandbox/benchmark/theBenchmark.p',fact_Suc__pred) ).
thf(4726,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)],[545]) ).
thf(1703,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__UNIV__right) ).
thf(9074,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1703]) ).
thf(1856,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Compl) ).
thf(9674,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1856]) ).
thf(996,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/sandbox/benchmark/theBenchmark.p',fact_fun__upd__same) ).
thf(6446,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)],[996]) ).
thf(12806,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ sk2 ) @ v_ts ) )
!= ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Int_Oint ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Int_Oint @ tc_HOL_Obool ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2685,2953]) ).
thf(12807,plain,
( ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ sk2 ) @ v_ts )
!= ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Int_Oint ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Int_Oint @ tc_HOL_Obool ) ) ) ),
inference(simp,[status(thm)],[12806]) ).
thf(12810,plain,
( ( ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ sk2 )
!= ( c_Finite__Set_Ofinite @ tc_Int_Oint ) )
| ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Int_Oint @ tc_HOL_Obool ) )
!= v_ts ) ),
inference(simp,[status(thm)],[12807]) ).
thf(1713,axiom,
! [A: $i] : ( c_Relation_Osingle__valued @ A @ A @ ( c_Relation_OId @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__Id) ).
thf(9101,plain,
! [A: $i] : ( c_Relation_Osingle__valued @ A @ A @ ( c_Relation_OId @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1713]) ).
thf(1064,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 @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ B )
= A ) )
& ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ B )
= ( hAPP @ ( hAPP @ D @ A ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Oremove) ).
thf(6692,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 @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ B )
= A ) )
& ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ B )
= ( hAPP @ ( hAPP @ D @ A ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__add @ D )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ D ) @ A ) @ B )
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__infinite) ).
thf(2928,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__add @ D )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ D ) @ A ) @ B )
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(1584,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 @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ D @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__insert__remove) ).
thf(8652,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 @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ D @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1584]) ).
thf(81,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 ) )
=> ( ( ( hAPP @ c_Int_Onat @ B )
= ( hAPP @ c_Int_Onat @ A ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__relations_I1_J) ).
thf(2974,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 ) )
=> ( ( ( ( hAPP @ c_Int_Onat @ B )
= ( hAPP @ c_Int_Onat @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ c_Int_Onat @ B )
= ( hAPP @ c_Int_Onat @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(1227,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Fun_Oinj__on @ H @ G @ F @ E )
=> ( ( c_Fun_Oinj__on @ D @ C @ B @ A )
=> ( c_Fun_Oinj__on @ ( tc_prod @ H @ D ) @ ( tc_prod @ G @ C ) @ ( c_Product__Type_Omap__pair @ H @ G @ D @ C @ F @ B ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ H @ D ) @ E ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ H ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair__inj__on) ).
thf(7297,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Fun_Oinj__on @ H @ G @ F @ E )
=> ( ( c_Fun_Oinj__on @ D @ C @ B @ A )
=> ( c_Fun_Oinj__on @ ( tc_prod @ H @ D ) @ ( tc_prod @ G @ C ) @ ( c_Product__Type_Omap__pair @ H @ G @ D @ C @ F @ B ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ H @ D ) @ E ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ H ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1227]) ).
thf(1506,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 @ F ) @ C ) @ D ) )
=> ( ( hAPP @ ( c_Set_Ovimage @ B @ F @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ F @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ F @ ( tc_fun @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ F @ ( tc_fun @ F @ F ) ) @ B ) @ ( c_If @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ B ) ) @ A ) ) ) @ E ) ) @ C ) ) @ D )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ C ) @ D ) )
=> ( ( hAPP @ ( c_Set_Ovimage @ B @ F @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ F @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ F @ ( tc_fun @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ F @ ( tc_fun @ F @ F ) ) @ B ) @ ( c_If @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ B ) ) @ A ) ) ) @ E ) ) @ C ) ) @ D )
= A ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ C ) @ D ) )
=> ( ( hAPP @ ( c_Set_Ovimage @ B @ F @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ F @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ F @ ( tc_fun @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ F @ ( tc_fun @ F @ F ) ) @ B ) @ ( c_If @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ B ) ) @ A ) ) ) @ E ) ) @ C ) ) @ D )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ C ) @ D ) )
=> ( ( hAPP @ ( c_Set_Ovimage @ B @ F @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ F @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ F @ ( tc_fun @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ F @ ( tc_fun @ F @ F ) ) @ B ) @ ( c_If @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ B ) ) @ A ) ) ) @ E ) ) @ C ) ) @ D )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__if) ).
thf(8340,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 @ F ) @ C ) @ D ) )
=> ( ( hAPP @ ( c_Set_Ovimage @ B @ F @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ F @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ F @ ( tc_fun @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ F @ ( tc_fun @ F @ F ) ) @ B ) @ ( c_If @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ B ) ) @ A ) ) ) @ E ) ) @ C ) ) @ D )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ C ) @ D ) )
=> ( ( hAPP @ ( c_Set_Ovimage @ B @ F @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ F @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ F @ ( tc_fun @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ F @ ( tc_fun @ F @ F ) ) @ B ) @ ( c_If @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ B ) ) @ A ) ) ) @ E ) ) @ C ) ) @ D )
= A ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ C ) @ D ) )
=> ( ( hAPP @ ( c_Set_Ovimage @ B @ F @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ F @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ F @ ( tc_fun @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ F @ ( tc_fun @ F @ F ) ) @ B ) @ ( c_If @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ B ) ) @ A ) ) ) @ E ) ) @ C ) ) @ D )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ C ) @ D ) )
=> ( ( hAPP @ ( c_Set_Ovimage @ B @ F @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ F @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ F @ ( tc_fun @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ F @ ( tc_fun @ F @ F ) ) @ B ) @ ( c_If @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ B ) ) @ A ) ) ) @ E ) ) @ C ) ) @ D )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1506]) ).
thf(1521,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_ODomain @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_ODomain @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_ODomain @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Int__subset) ).
thf(8413,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_ODomain @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_ODomain @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_ODomain @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1521]) ).
thf(338,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/sandbox/benchmark/theBenchmark.p',fact_nat__le__add__iff2) ).
thf(3893,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)],[338]) ).
thf(9,axiom,
( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( hAPP @ c_Int_Onat @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__numerals_I2_J) ).
thf(2710,plain,
( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( hAPP @ c_Int_Onat @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(2066,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/sandbox/benchmark/theBenchmark.p',fact_finite__Field) ).
thf(10467,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)],[2066]) ).
thf(1686,axiom,
! [A: $i] :
( ( c_Relation_OId__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__empty) ).
thf(9018,plain,
! [A: $i] :
( ( c_Relation_OId__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1686]) ).
thf(977,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_Set_Oimage @ E @ B @ ( hAPP @ ( c_COMBK @ B @ E ) @ A ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__constant) ).
thf(6377,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_Set_Oimage @ E @ B @ ( hAPP @ ( c_COMBK @ B @ E ) @ A ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(1393,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I3_J) ).
thf(7911,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1393]) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ E @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ E @ ( tc_fun @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ E @ ( tc_fun @ E @ E ) ) @ D ) @ ( c_If @ E ) ) @ ( hAPP @ c_fequal @ B ) ) ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ E ) ) ) @ C )
= ( hAPP @ A @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ E @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ E @ ( tc_fun @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ E @ ( tc_fun @ E @ E ) ) @ D ) @ ( c_If @ E ) ) @ ( hAPP @ c_fequal @ B ) ) ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ E ) ) ) @ C )
= ( c_Groups_Ozero__class_Ozero @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__delta_H) ).
thf(2931,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ E @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ E @ ( tc_fun @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ E @ ( tc_fun @ E @ E ) ) @ D ) @ ( c_If @ E ) ) @ ( hAPP @ c_fequal @ B ) ) ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ E ) ) ) @ C )
= ( hAPP @ A @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ E @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ E @ ( tc_fun @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ E @ ( tc_fun @ E @ E ) ) @ D ) @ ( c_If @ E ) ) @ ( hAPP @ c_fequal @ B ) ) ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ E ) ) ) @ C )
= ( c_Groups_Ozero__class_Ozero @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(859,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/sandbox/benchmark/theBenchmark.p',fact_list__all__append) ).
thf(5976,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)],[859]) ).
thf(1240,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ C ) @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ C ) @ ( c_Relation_OImage @ C @ C @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ C ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__def) ).
thf(7366,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ C ) @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ C ) @ ( c_Relation_OImage @ C @ C @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ C ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1240]) ).
thf(1073,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Un__distrib2) ).
thf(6730,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).
thf(245,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ D ) @ C ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) ) ) @ ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less) ).
thf(3539,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ D ) @ C ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) ) ) @ ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ D ) @ C ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) ) ) @ ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(26,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 ) )
=> ( ( ( hAPP @ c_Int_Onat @ B )
= ( hAPP @ c_Int_Onat @ A ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__nat__nat__iff) ).
thf(2770,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 ) )
=> ( ( ( ( hAPP @ c_Int_Onat @ B )
= ( hAPP @ c_Int_Onat @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ c_Int_Onat @ B )
= ( hAPP @ c_Int_Onat @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(1428,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ C ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
<=> ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__is__empty) ).
thf(8052,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ C ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
=> ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ C ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1428]) ).
thf(1637,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_List_Omeasures @ C @ ( c_List_Olist_ONil @ ( tc_fun @ C @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__measures_I1_J) ).
thf(8853,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_List_Omeasures @ C @ ( c_List_Olist_ONil @ ( tc_fun @ C @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1637]) ).
thf(576,axiom,
! [A: $i,B: $i] :
( ( c_List_Oconcat @ ( tc_List_Olist @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ ( tc_List_Olist @ B ) ) ) @ ( c_List_Olist_Olist__case @ ( tc_List_Olist @ ( tc_List_Olist @ B ) ) @ B @ ( c_List_Olist_ONil @ ( tc_List_Olist @ B ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ ( tc_List_Olist @ B ) ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ ( tc_List_Olist @ B ) ) @ ( tc_List_Olist @ ( tc_List_Olist @ B ) ) ) @ ( c_List_Olist_OCons @ ( tc_List_Olist @ B ) ) ) @ ( c_List_Olist_ONil @ ( tc_List_Olist @ B ) ) ) ) ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Otl @ B ) ) @ ( hAPP @ ( c_List_Ofilter @ ( tc_List_Olist @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ ( tc_List_Olist @ B ) ) @ c_fNot ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) @ tc_HOL_Obool ) @ c_fequal ) @ ( c_List_Olist_ONil @ B ) ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__aux__filter__tail) ).
thf(4844,plain,
! [A: $i,B: $i] :
( ( c_List_Oconcat @ ( tc_List_Olist @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ ( tc_List_Olist @ B ) ) ) @ ( c_List_Olist_Olist__case @ ( tc_List_Olist @ ( tc_List_Olist @ B ) ) @ B @ ( c_List_Olist_ONil @ ( tc_List_Olist @ B ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ ( tc_List_Olist @ B ) ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ ( tc_List_Olist @ B ) ) @ ( tc_List_Olist @ ( tc_List_Olist @ B ) ) ) @ ( c_List_Olist_OCons @ ( tc_List_Olist @ B ) ) ) @ ( c_List_Olist_ONil @ ( tc_List_Olist @ B ) ) ) ) ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Otl @ B ) ) @ ( hAPP @ ( c_List_Ofilter @ ( tc_List_Olist @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ ( tc_List_Olist @ B ) ) @ c_fNot ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) @ tc_HOL_Obool ) @ c_fequal ) @ ( c_List_Olist_ONil @ B ) ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(2605,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/sandbox/benchmark/theBenchmark.p',fact_RangeP_Ointros) ).
thf(12460,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)],[2605]) ).
thf(2152,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ G @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ~ ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ D ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ C @ H ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP2__E) ).
thf(10793,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ G @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ~ ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ D ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ C @ H ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2152]) ).
thf(2115,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_OwfP @ B @ A )
<=> ! [C: $i] : ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__accp__iff) ).
thf(10660,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)],[2115]) ).
thf(1528,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/sandbox/benchmark/theBenchmark.p',fact_zip_Osimps_I1_J) ).
thf(8440,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)],[1528]) ).
thf(1308,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 ) @ C )
= ( hAPP @ ( hAPP @ D @ B ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__rec) ).
thf(7603,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 ) @ C )
= ( hAPP @ ( hAPP @ D @ B ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1308]) ).
thf(77,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 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ B ) ) @ ( hAPP @ c_Int_Onat @ A ) )
= ( hAPP @ c_Int_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J) ).
thf(2962,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 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ B ) ) @ ( hAPP @ c_Int_Onat @ A ) )
= ( hAPP @ c_Int_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(1097,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Relation_ORange @ C @ B ) @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ C @ B ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ C @ B @ tc_HOL_Obool ) @ A ) ) )
= ( hAPP @ ( c_Set_OCollect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool @ B ) @ ( c_HOL_OEx @ C ) ) @ ( hAPP @ ( c_COMBC @ C @ B @ tc_HOL_Obool ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Collect__split) ).
thf(6811,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Relation_ORange @ C @ B ) @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ C @ B ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ C @ B @ tc_HOL_Obool ) @ A ) ) )
= ( hAPP @ ( c_Set_OCollect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool @ B ) @ ( c_HOL_OEx @ C ) ) @ ( hAPP @ ( c_COMBC @ C @ B @ tc_HOL_Obool ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).
thf(424,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Set_Ovimage @ F @ ( tc_prod @ E @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ F @ E @ ( hAPP @ ( c_Fun_Ocomp @ ( tc_prod @ E @ D ) @ E @ F @ ( c_Product__Type_Ofst @ E @ D ) ) @ C ) ) @ B ) ) @ ( hAPP @ ( c_Set_Ovimage @ F @ D @ ( hAPP @ ( c_Fun_Ocomp @ ( tc_prod @ E @ D ) @ D @ F @ ( c_Product__Type_Osnd @ E @ D ) ) @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Times) ).
thf(4232,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Set_Ovimage @ F @ ( tc_prod @ E @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ F @ E @ ( hAPP @ ( c_Fun_Ocomp @ ( tc_prod @ E @ D ) @ E @ F @ ( c_Product__Type_Ofst @ E @ D ) ) @ C ) ) @ B ) ) @ ( hAPP @ ( c_Set_Ovimage @ F @ D @ ( hAPP @ ( c_Fun_Ocomp @ ( tc_prod @ E @ D ) @ D @ F @ ( c_Product__Type_Osnd @ E @ D ) ) @ C ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(2651,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/sandbox/benchmark/theBenchmark.p',fact_accp__downward) ).
thf(12655,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)],[2651]) ).
thf(2307,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ E ) @ D ) ) @ ( c_Wellfounded_Omax__ext @ F @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ ( c_Wellfounded_Omax__ext @ F @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ D ) @ A ) ) ) @ ( c_Wellfounded_Omax__ext @ F @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ext__additive) ).
thf(11348,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ E ) @ D ) ) @ ( c_Wellfounded_Omax__ext @ F @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ ( c_Wellfounded_Omax__ext @ F @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ D ) @ A ) ) ) @ ( c_Wellfounded_Omax__ext @ F @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2307]) ).
thf(2059,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Fun_Oinj__on @ H @ G @ F @ E )
=> ( ! [I: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ I ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ H @ tc_HOL_Obool ) ) @ ( hAPP @ B @ I ) ) @ E ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( ( hAPP @ ( c_Set_Oimage @ H @ G @ F ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ H @ tc_HOL_Obool ) ) @ C ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ H @ tc_HOL_Obool ) @ ( tc_fun @ G @ tc_HOL_Obool ) @ D ) @ ( c_Set_Oimage @ H @ G @ F ) ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__INT) ).
thf(10444,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Fun_Oinj__on @ H @ G @ F @ E )
=> ( ! [I: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ I ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ H @ tc_HOL_Obool ) ) @ ( hAPP @ B @ I ) ) @ E ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( ( hAPP @ ( c_Set_Oimage @ H @ G @ F ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ H @ tc_HOL_Obool ) ) @ C ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ H @ tc_HOL_Obool ) @ ( tc_fun @ G @ tc_HOL_Obool ) @ D ) @ ( c_Set_Oimage @ H @ G @ F ) ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2059]) ).
thf(2365,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_OCollect @ B ) @ ( hAPP @ c_fequal @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__conv2) ).
thf(11558,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_OCollect @ B ) @ ( hAPP @ c_fequal @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2365]) ).
thf(997,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__eq__Inter) ).
thf(6449,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(675,axiom,
! [A: $i] :
( ( c_Enum_Osublists @ A @ ( c_List_Olist_ONil @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ ( tc_List_Olist @ A ) ) @ ( c_List_Olist_ONil @ A ) ) @ ( c_List_Olist_ONil @ ( tc_List_Olist @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublists_Osimps_I1_J) ).
thf(5216,plain,
! [A: $i] :
( ( c_Enum_Osublists @ A @ ( c_List_Olist_ONil @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ ( tc_List_Olist @ A ) ) @ ( c_List_Olist_ONil @ A ) ) @ ( c_List_Olist_ONil @ ( tc_List_Olist @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(325,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_List_Olist_Olist__case @ D @ C @ B @ A ) @ ( c_List_Olist_ONil @ C ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osimps_I4_J) ).
thf(3838,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_List_Olist_Olist__case @ D @ C @ B @ A ) @ ( c_List_Olist_ONil @ C ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(47,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_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ B ) ) @ ( hAPP @ c_Int_Onat @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__eq__zless) ).
thf(2835,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_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ B ) ) @ ( hAPP @ c_Int_Onat @ 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_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ B ) ) @ ( hAPP @ c_Int_Onat @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(1117,axiom,
! [A: $i] :
( ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__UNIV) ).
thf(6907,plain,
! [A: $i] :
( ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).
thf(1568,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Osym @ B @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) )
<=> ( c_Relation_Osym @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sym__converse) ).
thf(8573,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)],[1568]) ).
thf(1245,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__compl) ).
thf(7383,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1245]) ).
thf(2011,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_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Diff) ).
thf(10275,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_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2011]) ).
thf(1599,axiom,
( c_Wellfounded_Opred__nat
= ( 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 ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ c_fequal ) ) @ c_Nat_OSuc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__nat__def) ).
thf(8719,plain,
( c_Wellfounded_Opred__nat
= ( 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 ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ c_fequal ) ) @ c_Nat_OSuc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1599]) ).
thf(1954,axiom,
! [A: $i,B: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_OCollect @ B ) @ A ) )
<=> ! [C: $i] :
~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__Collect__eq) ).
thf(10020,plain,
! [A: $i,B: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_OCollect @ B ) @ A ) )
=> ! [C: $i] :
~ ( hBOOL @ ( hAPP @ A @ C ) ) )
& ( ! [C: $i] :
~ ( hBOOL @ ( hAPP @ A @ C ) )
=> ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_OCollect @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1954]) ).
thf(2085,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/sandbox/benchmark/theBenchmark.p',fact_rev__ImageI) ).
thf(10549,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)],[2085]) ).
thf(777,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_List_Orev @ B ) @ ( hAPP @ ( c_List_Orev @ B ) @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__rev__ident) ).
thf(5641,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_List_Orev @ B ) @ ( hAPP @ ( c_List_Orev @ B ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(2168,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
<=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP1__iff) ).
thf(10852,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ A ) ) ) )
& ( ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2168]) ).
thf(2682,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ B ) @ A ) )
| ( hBOOL @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fconj__3) ).
thf(12797,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ B ) @ A ) )
| ( hBOOL @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2682]) ).
thf(1872,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/sandbox/benchmark/theBenchmark.p',fact_pred__nat__trancl__eq__le) ).
thf(9741,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)],[1872]) ).
thf(1918,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ A @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__upper) ).
thf(9899,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ A @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1918]) ).
thf(1076,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_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__diff__nat) ).
thf(6738,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_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).
thf(457,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ A ) @ C ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__infI2) ).
thf(4373,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ A ) @ C ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(2433,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ B ) ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ C @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ C ) @ c_fconj ) @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__conjI) ).
thf(11775,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ B ) ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ C @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ C ) @ c_fconj ) @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2433]) ).
thf(2607,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/sandbox/benchmark/theBenchmark.p',fact_pos__not__random__dseq__def) ).
thf(12465,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)],[2607]) ).
thf(1941,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/sandbox/benchmark/theBenchmark.p',fact_Pair__inject) ).
thf(9975,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)],[1941]) ).
thf(345,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ F )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ F ) ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ F ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ D @ F ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INFI__apply) ).
thf(3917,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ F )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ F ) ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ F ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ D @ F ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(1902,axiom,
! [A: $i] :
( ( c_Transitive__Closure_Otrancl @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__empty) ).
thf(9841,plain,
! [A: $i] :
( ( c_Transitive__Closure_Otrancl @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1902]) ).
thf(1747,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I9_J) ).
thf(9249,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1747]) ).
thf(1269,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ C @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ C ) @ c_fdisj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__def) ).
thf(7469,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ C @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ C ) @ c_fdisj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1269]) ).
thf(933,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ B ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__Times__UNIV2) ).
thf(6223,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ B ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(957,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/sandbox/benchmark/theBenchmark.p',fact_trancl__converse) ).
thf(6288,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)],[957]) ).
thf(2240,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( c_Fun_Oinj__on @ B @ D @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Set_Ovimage @ B @ D @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__vimageI) ).
thf(11102,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( c_Fun_Oinj__on @ B @ D @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Set_Ovimage @ B @ D @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2240]) ).
thf(2279,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/sandbox/benchmark/theBenchmark.p',fact_mem__Sigma__iff) ).
thf(11245,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)],[2279]) ).
thf(281,axiom,
! [A: $i,B: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ B )
=> ( ( c_Orderings_Oorder__class_Omono @ B @ B @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B ) @ ( hAPP @ A @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ B @ A ) ) ) @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gfp__lemma3) ).
thf(3687,plain,
! [A: $i,B: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ B )
=> ( ( c_Orderings_Oorder__class_Omono @ B @ B @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B ) @ ( hAPP @ A @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ B @ A ) ) ) @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(2317,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_Nat_Ocompow @ ( tc_prod @ F @ F ) @ tc_HOL_Obool ) @ C ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ D ) @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ E ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ F @ F ) @ tc_HOL_Obool ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__Suc__I) ).
thf(11380,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_Nat_Ocompow @ ( tc_prod @ F @ F ) @ tc_HOL_Obool ) @ C ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ D ) @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ E ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ F @ F ) @ tc_HOL_Obool ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2317]) ).
thf(2179,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__imp__subset) ).
thf(10893,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2179]) ).
thf(1368,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/sandbox/benchmark/theBenchmark.p',fact_trans__less__add2) ).
thf(7805,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)],[1368]) ).
thf(2616,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_Quotient_OBabs @ E @ B @ C @ A ) @ D )
= ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Babs__def) ).
thf(12497,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_Quotient_OBabs @ E @ B @ C @ A ) @ D )
= ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2616]) ).
thf(1715,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) @ ( c_Relation_OId @ B ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__reflcl__absorb) ).
thf(9106,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) @ ( c_Relation_OId @ B ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1715]) ).
thf(1859,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__mono) ).
thf(9698,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1859]) ).
thf(2676,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/sandbox/benchmark/theBenchmark.p',fact_type__definition_ORep) ).
thf(12765,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)],[2676]) ).
thf(2379,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/sandbox/benchmark/theBenchmark.p',fact_set__zip__rightD) ).
thf(11605,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)],[2379]) ).
thf(2250,axiom,
! [A: $i,B: $i] :
( ( c_HOL_OThe @ B @ ( hAPP @ c_fequal @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__sym__eq__trivial) ).
thf(11130,plain,
! [A: $i,B: $i] :
( ( c_HOL_OThe @ B @ ( hAPP @ c_fequal @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2250]) ).
thf(288,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/sandbox/benchmark/theBenchmark.p',fact_Suc__pred_H) ).
thf(3706,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)],[288]) ).
thf(1202,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Equiv__Relations_Oequiv @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ F @ F @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) ) @ ( hAPP @ ( c_Relation_OImage @ F @ F @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ B ) @ A ) ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__class__nondisjoint) ).
thf(7200,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Equiv__Relations_Oequiv @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ F @ F @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) ) @ ( hAPP @ ( c_Relation_OImage @ F @ F @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ B ) @ A ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1202]) ).
thf(796,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofun__left__comm__idem @ E @ D @ C )
=> ( c_Finite__Set_Ofun__left__comm__idem @ B @ D @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ D @ D ) @ B ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofun__left__comm__idem__apply) ).
thf(5725,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofun__left__comm__idem @ E @ D @ C )
=> ( c_Finite__Set_Ofun__left__comm__idem @ B @ D @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ D @ D ) @ B ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(540,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/sandbox/benchmark/theBenchmark.p',fact_map__nth) ).
thf(4703,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)],[540]) ).
thf(2435,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__upper1) ).
thf(11781,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2435]) ).
thf(1767,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ D @ D @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotientI) ).
thf(9345,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ D @ D @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1767]) ).
thf(1235,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/sandbox/benchmark/theBenchmark.p',fact_list__eq__iff__zip__eq) ).
thf(7339,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)],[1235]) ).
thf(2094,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Obij__betw @ E @ D @ C @ B @ A )
<=> ( ( c_Fun_Oinj__on @ E @ D @ C @ B )
& ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__def) ).
thf(10576,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( c_Fun_Obij__betw @ E @ D @ C @ B @ A )
=> ( ( c_Fun_Oinj__on @ E @ D @ C @ B )
& ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B )
= A ) ) )
& ( ( ( c_Fun_Oinj__on @ E @ D @ C @ B )
& ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B )
= A ) )
=> ( c_Fun_Obij__betw @ E @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2094]) ).
thf(922,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/sandbox/benchmark/theBenchmark.p',fact_append__in__listsp__conv) ).
thf(6180,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)],[922]) ).
thf(2553,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Equiv__Relations_Oequivp @ C @ B )
=> ( ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( c_Quotient_ORespects @ C @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ D ) ) )
<=> ? [D: $i] : ( hBOOL @ ( hAPP @ A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bex__reg__eqv) ).
thf(12224,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Equiv__Relations_Oequivp @ C @ B )
=> ( ( ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( c_Quotient_ORespects @ C @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ D ) ) )
=> ? [D: $i] : ( hBOOL @ ( hAPP @ A @ D ) ) )
& ( ? [D: $i] : ( hBOOL @ ( hAPP @ A @ D ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( c_Quotient_ORespects @ C @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2553]) ).
thf(1926,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( c_Fun_Oinj__on @ E @ D @ C @ A )
=> ( c_Fun_Oinj__on @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__Int) ).
thf(9921,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ B )
=> ( ( c_Fun_Oinj__on @ E @ D @ C @ A )
=> ( c_Fun_Oinj__on @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1926]) ).
thf(1316,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Oacyclic @ B @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) )
<=> ( c_Wellfounded_Oacyclic @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__converse) ).
thf(7630,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)],[1316]) ).
thf(1975,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_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_Oimage @ C @ C @ A ) @ B ) ) )
=> ( c_Fun_Oinj__on @ C @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__surj__inj) ).
thf(10119,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_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_Oimage @ C @ C @ A ) @ B ) ) )
=> ( c_Fun_Oinj__on @ C @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1975]) ).
thf(1781,axiom,
! [A: $i,B: $i] :
( ( c_Relation_OId__on @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_prod @ B @ B ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ B ) @ ( c_Set_Oinsert @ ( tc_prod @ B @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ B @ B @ ( tc_prod @ B @ B ) ) @ ( c_Product__Type_OPair @ B @ B ) ) @ ( c_COMBI @ B ) ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__def) ).
thf(9398,plain,
! [A: $i,B: $i] :
( ( c_Relation_OId__on @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_prod @ B @ B ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ B ) @ ( c_Set_Oinsert @ ( tc_prod @ B @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ B @ B @ ( tc_prod @ B @ B ) ) @ ( c_Product__Type_OPair @ B @ B ) ) @ ( c_COMBI @ B ) ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1781]) ).
thf(1281,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/sandbox/benchmark/theBenchmark.p',fact_trans__le__add1) ).
thf(7507,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)],[1281]) ).
thf(1237,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ B ) ) ) ) )
=> ( B
= ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__card__intvl__is__intvl) ).
thf(7356,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ B ) ) ) ) )
=> ( B
= ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1237]) ).
thf(1210,axiom,
! [A: $i,B: $i] :
( ( c_FunDef_Orp__inv__image @ B @ A )
= ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ A @ B ) @ ( tc_prod @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ A @ B ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ A @ B ) @ ( tc_prod @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ ( tc_fun @ A @ B ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ A @ B ) @ ( tc_prod @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ) ) @ ( tc_fun @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ A @ B ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ A @ B ) @ ( tc_prod @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ) ) ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ A @ B ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ A @ B ) @ ( tc_prod @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ A @ B ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) @ ( tc_prod @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ) ) @ ( tc_fun @ ( tc_fun @ ( tc_fun @ A @ B ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ A @ B ) @ ( tc_prod @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ) ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ ( c_COMBS @ ( tc_fun @ A @ B ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) @ ( tc_prod @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ A @ B ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ A @ B ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) @ ( tc_prod @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ) ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) @ ( tc_prod @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ) @ ( tc_fun @ A @ B ) ) @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ) ) @ ( c_Relation_Oinv__image @ B @ A ) ) ) ) ) @ ( c_Relation_Oinv__image @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rp__inv__image__def) ).
thf(7232,plain,
! [A: $i,B: $i] :
( ( c_FunDef_Orp__inv__image @ B @ A )
= ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ A @ B ) @ ( tc_prod @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ A @ B ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ A @ B ) @ ( tc_prod @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ ( tc_fun @ A @ B ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ A @ B ) @ ( tc_prod @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ) ) @ ( tc_fun @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ A @ B ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ A @ B ) @ ( tc_prod @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ) ) ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ A @ B ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ A @ B ) @ ( tc_prod @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ A @ B ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) @ ( tc_prod @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ) ) @ ( tc_fun @ ( tc_fun @ ( tc_fun @ A @ B ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ A @ B ) @ ( tc_prod @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ) ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ ( c_COMBS @ ( tc_fun @ A @ B ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) @ ( tc_prod @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ A @ B ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ A @ B ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) @ ( tc_prod @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ) ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) @ ( tc_prod @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ) @ ( tc_fun @ A @ B ) ) @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ) ) @ ( c_Relation_Oinv__image @ B @ A ) ) ) ) ) @ ( c_Relation_Oinv__image @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1210]) ).
thf(1008,axiom,
! [A: $i] : ( c_Relation_Orefl__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__empty) ).
thf(6485,plain,
! [A: $i] : ( c_Relation_Orefl__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(930,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/sandbox/benchmark/theBenchmark.p',fact_zip__append1) ).
thf(6212,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)],[930]) ).
thf(1565,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/sandbox/benchmark/theBenchmark.p',fact_vimage__compose) ).
thf(8560,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)],[1565]) ).
thf(2625,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/sandbox/benchmark/theBenchmark.p',fact_part__equivp__transp) ).
thf(12557,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)],[2625]) ).
thf(2312,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IntD2) ).
thf(11359,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2312]) ).
thf(2357,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 ) ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) ) )
=> ~ ! [F: $i] :
( ( 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 @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ F ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__Suc__E2) ).
thf(11535,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 ) ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) ) )
=> ~ ! [F: $i] :
( ( 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 @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ F ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2357]) ).
thf(2313,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Set_Oimage @ C @ B @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__empty) ).
thf(11361,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Set_Oimage @ C @ B @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2313]) ).
thf(487,axiom,
! [A: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A )
= ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( hAPP @ c_Int_ORep__Integ @ A ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ tc_Nat_Onat @ tc_Nat_Onat @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ tc_Nat_Onat ) @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) ) ) @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) ) ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__int__def) ).
thf(4481,plain,
! [A: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A )
= ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( hAPP @ c_Int_ORep__Integ @ A ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ tc_Nat_Onat @ tc_Nat_Onat @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ tc_Nat_Onat ) @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) ) ) @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) ) ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(1809,axiom,
! [A: $i] :
~ ! [B: $i] :
( ( A
= ( hAPP @ c_Int_OAbs__Integ @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ B ) @ c_Int_OInteg ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Abs__Integ__cases) ).
thf(9503,plain,
! [A: $i] :
~ ! [B: $i] :
( ( A
= ( hAPP @ c_Int_OAbs__Integ @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ B ) @ c_Int_OInteg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1809]) ).
thf(772,axiom,
! [A: $i,B: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ B )
=> ( ( c_Orderings_Oorder__class_Omono @ B @ B @ A )
=> ( ( c_Inductive_Ocomplete__lattice__class_Ogfp @ B @ A )
= ( hAPP @ A @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gfp__unfold) ).
thf(5619,plain,
! [A: $i,B: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ B )
=> ( ( c_Orderings_Oorder__class_Omono @ B @ B @ A )
=> ( ( c_Inductive_Ocomplete__lattice__class_Ogfp @ B @ A )
= ( hAPP @ A @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(484,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ C @ A ) ) ) ) )
=> ( ( c_Orderings_Oorder__class_Omono @ C @ C @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ C @ A ) ) ) @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ C @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_coinduct__lemma) ).
thf(4473,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ C @ A ) ) ) ) )
=> ( ( c_Orderings_Oorder__class_Omono @ C @ C @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ C @ A ) ) ) @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ C @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(335,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( ( c_Orderings_Oorder__class_Omono @ tc_Nat_Onat @ B @ A )
<=> ! [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B ) @ ( hAPP @ A @ C ) ) @ ( hAPP @ A @ ( hAPP @ c_Nat_OSuc @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mono__iff__le__Suc) ).
thf(3881,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( ( ( c_Orderings_Oorder__class_Omono @ tc_Nat_Onat @ B @ A )
=> ! [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B ) @ ( hAPP @ A @ C ) ) @ ( hAPP @ A @ ( hAPP @ c_Nat_OSuc @ C ) ) ) ) )
& ( ! [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B ) @ ( hAPP @ A @ C ) ) @ ( hAPP @ A @ ( hAPP @ c_Nat_OSuc @ C ) ) ) )
=> ( c_Orderings_Oorder__class_Omono @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(1868,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/sandbox/benchmark/theBenchmark.p',fact_Image__iff) ).
thf(9727,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)],[1868]) ).
thf(1717,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/sandbox/benchmark/theBenchmark.p',fact_equivE) ).
thf(9111,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)],[1717]) ).
thf(729,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_Oimage @ B @ B @ ( c_Fun_Oid @ B ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__id) ).
thf(5463,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_Oimage @ B @ B @ ( c_Fun_Oid @ B ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(1217,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
= ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ C ) @ B ) @ A ) )
<=> ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__is__empty2) ).
thf(7260,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
= ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ C ) @ B ) @ A ) )
=> ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
= ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1217]) ).
thf(447,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I1_J) ).
thf(4331,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(550,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__left__idem) ).
thf(4741,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(2547,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/sandbox/benchmark/theBenchmark.p',fact_equivp__transp) ).
thf(12207,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)],[2547]) ).
thf(1667,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/sandbox/benchmark/theBenchmark.p',fact_diff__diff__right) ).
thf(8954,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)],[1667]) ).
thf(1815,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/sandbox/benchmark/theBenchmark.p',fact_append__take__drop__id) ).
thf(9524,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)],[1815]) ).
thf(764,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Product__Type_Osnd @ C @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ C @ B @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ B ) @ C ) @ ( c_COMBI @ B ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__def) ).
thf(5587,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Product__Type_Osnd @ C @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ C @ B @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ B ) @ C ) @ ( c_COMBI @ B ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(964,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/sandbox/benchmark/theBenchmark.p',fact_map__pair_Ocomp) ).
thf(6320,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)],[964]) ).
thf(2020,axiom,
class_Nat_Osize @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Nat_Osize) ).
thf(10311,plain,
class_Nat_Osize @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2020]) ).
thf(2160,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/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Oinsert) ).
thf(10824,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)],[2160]) ).
thf(476,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/sandbox/benchmark/theBenchmark.p',fact_nth__take) ).
thf(4441,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)],[476]) ).
thf(1783,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Relation_OImage @ F @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( c_Relation_OImage @ F @ E @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__UN) ).
thf(9403,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Relation_OImage @ F @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( c_Relation_OImage @ F @ E @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1783]) ).
thf(142,axiom,
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_Oimage @ tc_Int_Oint @ tc_Nat_Onat @ c_Int_Onat ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Int_Oint @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J) ).
thf(3193,plain,
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_Oimage @ tc_Int_Oint @ tc_Nat_Onat @ c_Int_Onat ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Int_Oint @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(211,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_List_Otranspose @ D @ ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ D ) ) @ ( hAPP @ ( c_List_Omap @ C @ D ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ D ) ) @ ( hAPP @ ( c_List_Omap @ C @ D ) @ B ) ) @ ( c_List_Otranspose @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__map__map) ).
thf(3427,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_List_Otranspose @ D @ ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ D ) ) @ ( hAPP @ ( c_List_Omap @ C @ D ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ D ) ) @ ( hAPP @ ( c_List_Omap @ C @ D ) @ B ) ) @ ( c_List_Otranspose @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(366,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ A ) )
= ( c_Nat_Onat_Onat__case @ ( tc_List_Olist @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( c_List_Odrop @ D ) ) @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__Cons) ).
thf(4013,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ A ) )
= ( c_Nat_Onat_Onat__case @ ( tc_List_Olist @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( c_List_Odrop @ D ) ) @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(2614,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/sandbox/benchmark/theBenchmark.p',fact_insertI2) ).
thf(12492,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)],[2614]) ).
thf(1299,axiom,
! [A: $i] : ( c_Fun_Oinj__on @ tc_Nat_Onat @ tc_Nat_Onat @ c_Nat_OSuc @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__Suc) ).
thf(7578,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)],[1299]) ).
thf(585,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ D @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ D @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ D @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ C ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funpow__mult) ).
thf(4886,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ D @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ D @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ D @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ C ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(431,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/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__1) ).
thf(4260,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)],[431]) ).
thf(87,axiom,
class_Rings_Osemiring__0 @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).
thf(2994,plain,
class_Rings_Osemiring__0 @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(507,axiom,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).
thf(4580,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(1409,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OSigma @ D @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Union) ).
thf(7975,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OSigma @ D @ C ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1409]) ).
thf(2142,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/sandbox/benchmark/theBenchmark.p',fact_converseD) ).
thf(10759,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)],[2142]) ).
thf(2528,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/sandbox/benchmark/theBenchmark.p',fact_ord_OlessThan__iff) ).
thf(12118,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)],[2528]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
!= ( c_List_Olist_ONil @ C ) )
=> ( ( hAPP @ ( c_List_Ohd @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ B ) @ A ) @ D ) )
= ( hAPP @ A @ ( hAPP @ ( c_List_Ohd @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__map) ).
thf(2784,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
!= ( c_List_Olist_ONil @ C ) )
=> ( ( hAPP @ ( c_List_Ohd @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ B ) @ A ) @ D ) )
= ( hAPP @ A @ ( hAPP @ ( c_List_Ohd @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(2034,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/sandbox/benchmark/theBenchmark.p',fact_rtrancl__eq__or__trancl) ).
thf(10354,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)],[2034]) ).
thf(1749,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_List_Ofilter @ B @ A ) @ ( c_List_Olist_ONil @ B ) )
= ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter_Osimps_I1_J) ).
thf(9259,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)],[1749]) ).
thf(1812,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I4_J) ).
thf(9514,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1812]) ).
thf(1702,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/sandbox/benchmark/theBenchmark.p',fact_in__listrel1__converse) ).
thf(9069,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)],[1702]) ).
thf(174,axiom,
! [A: $i] :
( ? [B: $i] : ( hBOOL @ ( hAPP @ A @ B ) )
<=> ? [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 @ A @ ( hAPP @ c_Int_Onat @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__nat) ).
thf(3293,plain,
! [A: $i] :
( ( ? [B: $i] : ( hBOOL @ ( hAPP @ A @ B ) )
=> ? [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 @ A @ ( hAPP @ c_Int_Onat @ B ) ) ) ) )
& ( ? [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 @ A @ ( hAPP @ c_Int_Onat @ B ) ) ) )
=> ? [B: $i] : ( hBOOL @ ( hAPP @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(813,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ D )
=> ( ( C
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ D ) @ C ) @ ( hAPP @ ( c_COMBK @ D @ B ) @ A ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP__const) ).
thf(5785,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ D )
=> ( ( C
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ D ) @ C ) @ ( hAPP @ ( c_COMBK @ D @ B ) @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(2001,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/sandbox/benchmark/theBenchmark.p',fact_acc__downward) ).
thf(10223,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)],[2001]) ).
thf(1261,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/sandbox/benchmark/theBenchmark.p',fact_List_Omap_Ocompositionality) ).
thf(7447,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)],[1261]) ).
thf(1914,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/sandbox/benchmark/theBenchmark.p',fact_rtrancl__trancl__trancl) ).
thf(9884,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)],[1914]) ).
thf(1621,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/sandbox/benchmark/theBenchmark.p',fact_card__image) ).
thf(8804,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)],[1621]) ).
thf(2172,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/sandbox/benchmark/theBenchmark.p',fact_equivpI) ).
thf(10867,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)],[2172]) ).
thf(2636,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/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__f__eq) ).
thf(12599,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)],[2636]) ).
thf(277,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/sandbox/benchmark/theBenchmark.p',fact_length__remdups__eq) ).
thf(3672,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)],[277]) ).
thf(548,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Relation_OImage @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) @ ( c_List_Olistrel @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_List_Olist @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_List_Olist @ D ) @ tc_HOL_Obool ) ) ) )
= ( c_List_Oset__Cons @ D @ ( hAPP @ ( c_Relation_OImage @ D @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) @ ( hAPP @ ( c_Relation_OImage @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) @ ( c_List_Olistrel @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_List_Olist @ D ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_List_Olist @ D ) @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__Cons) ).
thf(4735,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Relation_OImage @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) @ ( c_List_Olistrel @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_List_Olist @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_List_Olist @ D ) @ tc_HOL_Obool ) ) ) )
= ( c_List_Oset__Cons @ D @ ( hAPP @ ( c_Relation_OImage @ D @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) @ ( hAPP @ ( c_Relation_OImage @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) @ ( c_List_Olistrel @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_List_Olist @ D ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_List_Olist @ D ) @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(1055,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ F ) @ E ) )
=> ( ( c_Nitpick_Ofold__graph_H @ G @ D @ C @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) @ A )
=> ( c_Nitpick_Ofold__graph_H @ G @ D @ C @ B @ E @ ( hAPP @ ( hAPP @ C @ F ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_H_Ointros_I2_J) ).
thf(6659,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ F ) @ E ) )
=> ( ( c_Nitpick_Ofold__graph_H @ G @ D @ C @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) @ A )
=> ( c_Nitpick_Ofold__graph_H @ G @ D @ C @ B @ E @ ( hAPP @ ( hAPP @ C @ F ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).
thf(1660,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( c_List_Oset @ C ) @ ( hAPP @ ( c_List_Ofilter @ C @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ C ) @ c_fNot ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ C @ tc_HOL_Obool ) @ c_fequal ) @ A ) ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__minus__filter__out) ).
thf(8936,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( c_List_Oset @ C ) @ ( hAPP @ ( c_List_Ofilter @ C @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ C ) @ c_fNot ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ C @ tc_HOL_Obool ) @ c_fequal ) @ A ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1660]) ).
thf(1899,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/sandbox/benchmark/theBenchmark.p',fact_RangeI) ).
thf(9826,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)],[1899]) ).
thf(1297,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/sandbox/benchmark/theBenchmark.p',fact_eq__diff__iff) ).
thf(7562,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)],[1297]) ).
thf(1291,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I7_J) ).
thf(7539,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1291]) ).
thf(1080,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/sandbox/benchmark/theBenchmark.p',fact_diff__cancel) ).
thf(6751,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)],[1080]) ).
thf(1130,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ H @ G ) @ F ) @ E ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ H @ G ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ D @ H ) @ C ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ D @ G ) @ F ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ G @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ G @ ( tc_prod @ H @ G ) ) @ ( tc_fun @ G @ F ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ H @ G ) @ F @ G ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ H @ ( tc_fun @ G @ ( tc_prod @ H @ G ) ) @ D ) @ ( c_Product__Type_OPair @ H @ G ) ) @ C ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ D @ G ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__zip__map) ).
thf(6962,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ H @ G ) @ F ) @ E ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ H @ G ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ D @ H ) @ C ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ D @ G ) @ F ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ G @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ G @ ( tc_prod @ H @ G ) ) @ ( tc_fun @ G @ F ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ H @ G ) @ F @ G ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ H @ ( tc_fun @ G @ ( tc_prod @ H @ G ) ) @ D ) @ ( c_Product__Type_OPair @ H @ G ) ) @ C ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ D @ G ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).
thf(2060,axiom,
! [A: $i,B: $i] :
( ( c_List_OremoveAll @ B @ A )
= ( c_List_Ofilter @ B @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ B ) @ c_fNot ) @ ( hAPP @ c_fequal @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_removeAll__filter__not__eq) ).
thf(10449,plain,
! [A: $i,B: $i] :
( ( c_List_OremoveAll @ B @ A )
= ( c_List_Ofilter @ B @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ B ) @ c_fNot ) @ ( hAPP @ c_fequal @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2060]) ).
thf(1387,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/sandbox/benchmark/theBenchmark.p',fact_distinct__filter) ).
thf(7897,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)],[1387]) ).
thf(1665,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ D ) ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ D ) @ tc_HOL_Obool ) ) ) )
=> ( ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ C @ A )
=> ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ D ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__derivs_Oinsert) ).
thf(8949,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ D ) ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ D ) @ tc_HOL_Obool ) ) ) )
=> ( ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ C @ A )
=> ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ D ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1665]) ).
thf(131,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_List_Olist_ONil @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ C ) ) )
=> ( ( hAPP @ ( c_List_Ohd @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ B ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ B ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__drop__conv__nth) ).
thf(3146,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_List_Olist_ONil @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ C ) ) )
=> ( ( hAPP @ ( c_List_Ohd @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ B ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ B ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(2220,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
=> ( ~ ( hBOOL @ ( hAPP @ C @ A ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1E) ).
thf(11030,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
=> ( ~ ( hBOOL @ ( hAPP @ C @ A ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2220]) ).
thf(880,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= B ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I4_J) ).
thf(6056,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= B ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(1980,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/sandbox/benchmark/theBenchmark.p',fact_Cons__eq__filter__iff) ).
thf(10132,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)],[1980]) ).
thf(410,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/sandbox/benchmark/theBenchmark.p',fact_ex__nat__less__eq) ).
thf(4177,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)],[410]) ).
thf(1500,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ C ) @ B ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__add__Un) ).
thf(8323,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ C ) @ B ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1500]) ).
thf(1631,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/sandbox/benchmark/theBenchmark.p',fact_map__map) ).
thf(8836,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)],[1631]) ).
thf(580,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/sandbox/benchmark/theBenchmark.p',fact_upt__rec) ).
thf(4859,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)],[580]) ).
thf(1850,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Oset @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ B ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__append) ).
thf(9656,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Oset @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ B ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1850]) ).
thf(663,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
=> ( ( c_List_Obutlast @ C @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ C @ B ) @ D ) @ A ) )
= ( c_List_Obutlast @ C @ B ) ) )
& ( ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
=> ( ( c_List_Obutlast @ C @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ C @ B ) @ D ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ C @ ( c_List_Obutlast @ C @ B ) ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_butlast__list__update) ).
thf(5165,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
=> ( ( c_List_Obutlast @ C @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ C @ B ) @ D ) @ A ) )
= ( c_List_Obutlast @ C @ B ) ) )
& ( ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
=> ( ( c_List_Obutlast @ C @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ C @ B ) @ D ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ C @ ( c_List_Obutlast @ C @ B ) ) @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(1017,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_Oimage @ ( tc_List_Olist @ B ) @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_List_Oset @ B ) ) @ ( hAPP @ ( c_List_Oset @ ( tc_List_Olist @ B ) ) @ ( c_Enum_Osublists @ B @ A ) ) )
= ( hAPP @ ( c_Set_OPow @ B ) @ ( hAPP @ ( c_List_Oset @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublists__powset) ).
thf(6517,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_Oimage @ ( tc_List_Olist @ B ) @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_List_Oset @ B ) ) @ ( hAPP @ ( c_List_Oset @ ( tc_List_Olist @ B ) ) @ ( c_Enum_Osublists @ B @ A ) ) )
= ( hAPP @ ( c_Set_OPow @ B ) @ ( hAPP @ ( c_List_Oset @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(1325,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 ) )
=> ( ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ A ) )
=> ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ D @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Ounion__disjoint) ).
thf(7679,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 ) )
=> ( ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ A ) )
=> ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ D @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1325]) ).
thf(1823,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( c_Relation_ODomain @ C @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
<=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__empty__iff) ).
thf(9546,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( c_Relation_ODomain @ C @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) ) )
& ( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Relation_ODomain @ C @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1823]) ).
thf(885,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ C ) @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__empty) ).
thf(6076,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ C ) @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(1358,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ B @ B @ B ) @ A ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) )
=> ( c_Wellfounded_Owf @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__no__loop) ).
thf(7773,plain,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ B @ B @ B ) @ A ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) )
=> ( c_Wellfounded_Owf @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1358]) ).
thf(1177,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/sandbox/benchmark/theBenchmark.p',fact_folding__one_Oeq__fold_H) ).
thf(7122,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)],[1177]) ).
thf(221,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ c_Nat_OSuc @ A ) )
=> ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ C @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__SucD) ).
thf(3455,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ c_Nat_OSuc @ A ) )
=> ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(534,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/sandbox/benchmark/theBenchmark.p',fact_gr0I) ).
thf(4688,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)],[534]) ).
thf(847,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ A ) @ ( c_List_Olist_ONil @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__Nil2) ).
thf(5916,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)],[847]) ).
thf(169,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__Suc__Suc) ).
thf(3278,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(2150,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ E ) @ D ) )
=> ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ G ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ B @ G ) ) @ ( hAPP @ A @ G ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ F @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ C ) @ E ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ C ) @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__mono) ).
thf(10788,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ E ) @ D ) )
=> ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ G ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ B @ G ) ) @ ( hAPP @ A @ G ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ F @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ C ) @ E ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ C ) @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2150]) ).
thf(1885,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/sandbox/benchmark/theBenchmark.p',fact_trans__def) ).
thf(9783,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)],[1885]) ).
thf(2518,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/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__f__f) ).
thf(12075,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)],[2518]) ).
thf(994,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ C @ C ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A )
= ( hAPP @ ( c_Fun_Ocomp @ C @ C @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ C @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funpow_Osimps_I2_J) ).
thf(6440,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ C @ C ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A )
= ( hAPP @ ( c_Fun_Ocomp @ C @ C @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ C @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(1100,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/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).
thf(6821,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)],[1100]) ).
thf(1538,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Relation_OImage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ E @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_OImage @ E @ D @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__Un) ).
thf(8477,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Relation_OImage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ E @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_OImage @ E @ D @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1538]) ).
thf(1141,axiom,
! [A: $i] : ( c_Relation_Otrans @ A @ ( c_Relation_OId @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__Id) ).
thf(6998,plain,
! [A: $i] : ( c_Relation_Otrans @ A @ ( c_Relation_OId @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).
thf(543,axiom,
! [A: $i] : ( c_Fun_Obij__betw @ A @ A @ ( c_Fun_Oid @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__id) ).
thf(4722,plain,
! [A: $i] : ( c_Fun_Obij__betw @ A @ A @ ( c_Fun_Oid @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(2509,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ C ) ) @ D ) @ B ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ C @ ( hAPP @ c_Nat_OSuc @ A ) @ D ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ C ) ) @ D ) @ B ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ C @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_triples__valid__Suc) ).
thf(12043,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ C ) ) @ D ) @ B ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ C @ ( hAPP @ c_Nat_OSuc @ A ) @ D ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ C ) ) @ D ) @ B ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ C @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2509]) ).
thf(622,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/sandbox/benchmark/theBenchmark.p',fact_length__remdups__leq) ).
thf(5003,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)],[622]) ).
thf(1741,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( c_Set_OCollect @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ ( tc_List_Olist @ C ) @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_List_Olist @ C ) ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ C ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_List_Olist @ C ) ) @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( c_List_Oset @ C ) ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ C ) @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_List_Olist @ C ) ) @ c_fequal ) @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__lists__length__eq) ).
thf(9202,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( c_Set_OCollect @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ ( tc_List_Olist @ C ) @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_List_Olist @ C ) ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ C ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_List_Olist @ C ) ) @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( c_List_Oset @ C ) ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ C ) @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_List_Olist @ C ) ) @ c_fequal ) @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1741]) ).
thf(408,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Omap @ D @ C ) @ B ) @ ( c_List_Oconcat @ D @ A ) )
= ( c_List_Oconcat @ C @ ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( c_List_Omap @ D @ C ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__concat) ).
thf(4168,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Omap @ D @ C ) @ B ) @ ( c_List_Oconcat @ D @ A ) )
= ( c_List_Oconcat @ C @ ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( c_List_Omap @ D @ C ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(2402,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ E ) @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ E ) @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ E @ D ) @ A ) @ B ) ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__update__subsetI) ).
thf(11679,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ E ) @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ E ) @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ E @ D ) @ A ) @ B ) ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2402]) ).
thf(1161,axiom,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Otrancl @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) @ ( c_Relation_OId @ B ) ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__reflcl) ).
thf(7070,plain,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Otrancl @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) @ ( c_Relation_OId @ B ) ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).
thf(1050,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ C @ A ) @ D ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I10_J) ).
thf(6641,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ C @ A ) @ D ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).
thf(948,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ C @ B )
=> ( ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ A @ C )
=> ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cut) ).
thf(6266,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ C @ B )
=> ( ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ A @ C )
=> ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(1043,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_Set_OPow @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__bottom) ).
thf(6621,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_Set_OPow @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).
thf(598,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ tc_Nat_Onat ) @ ( c_List_Oupt @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__upt) ).
thf(4922,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)],[598]) ).
thf(1189,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ A ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff__insert) ).
thf(7159,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ A ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189]) ).
thf(1651,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Relation_ODomain @ B @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__empty) ).
thf(8904,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Relation_ODomain @ B @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1651]) ).
thf(2079,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/sandbox/benchmark/theBenchmark.p',fact_converse__rtrancl__into__rtrancl) ).
thf(10521,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)],[2079]) ).
thf(2004,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityE) ).
thf(10246,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2004]) ).
thf(815,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ A ) )
& ( B != A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__le) ).
thf(5790,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ A ) )
& ( B != A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ A ) )
& ( B != A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(869,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ D ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ C ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ D @ C ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__list__update) ).
thf(6012,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ D ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ C ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ D @ C ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(2275,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Ocurry @ E @ D @ tc_HOL_Obool @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curryE) ).
thf(11230,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Ocurry @ E @ D @ tc_HOL_Obool @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2275]) ).
thf(1224,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_List_Olistrelp @ D @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ D @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ D @ D ) ) ) ) @ ( c_Product__Type_OPair @ D @ 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 ) ) @ B ) @ A ) ) @ ( c_List_Olistrel @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrelp__listrel__eq) ).
thf(7283,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_List_Olistrelp @ D @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ D @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ D @ D ) ) ) ) @ ( c_Product__Type_OPair @ D @ 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 ) ) @ B ) @ A ) ) @ ( c_List_Olistrel @ D @ 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_Olistrel @ D @ C ) ) )
=> ( c_List_Olistrelp @ D @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ D @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ D @ D ) ) ) ) @ ( c_Product__Type_OPair @ D @ D ) ) ) ) @ C ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1224]) ).
thf(361,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ B ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ D @ D @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) ) @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__le__fold__inf) ).
thf(3988,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ B ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ D @ D @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) ) @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(1843,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/sandbox/benchmark/theBenchmark.p',fact_remdups__filter) ).
thf(9631,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)],[1843]) ).
thf(2420,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ ( c_Set_Oimage @ C @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( c_Fun_Obij__betw @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bijI) ).
thf(11738,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ ( c_Set_Oimage @ C @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( c_Fun_Obij__betw @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2420]) ).
thf(2481,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Wellfounded_Oacc @ C @ A ) ) @ ( c_Wellfounded_Oacc @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__subset) ).
thf(11937,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Wellfounded_Oacc @ C @ A ) ) @ ( c_Wellfounded_Oacc @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2481]) ).
thf(1307,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__insert) ).
thf(7600,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1307]) ).
thf(634,axiom,
! [A: $i] :
( ( hAPP @ ( c_List_Omap @ A @ A ) @ ( c_Fun_Oid @ A ) )
= ( c_Fun_Oid @ ( tc_List_Olist @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_List_Omap_Oid) ).
thf(5047,plain,
! [A: $i] :
( ( hAPP @ ( c_List_Omap @ A @ A ) @ ( c_Fun_Oid @ A ) )
= ( c_Fun_Oid @ ( tc_List_Olist @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(1912,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/sandbox/benchmark/theBenchmark.p',fact_part__equivpI) ).
thf(9879,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)],[1912]) ).
thf(1148,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/sandbox/benchmark/theBenchmark.p',fact_append1__eq__conv) ).
thf(7026,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)],[1148]) ).
thf(678,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding @ H @ G @ F @ E )
=> ( ( hAPP @ ( c_Fun_Ocomp @ G @ G @ D @ ( hAPP @ F @ C ) ) @ ( hAPP @ ( c_Fun_Ocomp @ G @ G @ D @ ( hAPP @ F @ B ) ) @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ G @ G @ D @ ( hAPP @ F @ B ) ) @ ( hAPP @ ( c_Fun_Ocomp @ G @ G @ D @ ( hAPP @ F @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__left__comp) ).
thf(5229,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding @ H @ G @ F @ E )
=> ( ( hAPP @ ( c_Fun_Ocomp @ G @ G @ D @ ( hAPP @ F @ C ) ) @ ( hAPP @ ( c_Fun_Ocomp @ G @ G @ D @ ( hAPP @ F @ B ) ) @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ G @ G @ D @ ( hAPP @ F @ B ) ) @ ( hAPP @ ( c_Fun_Ocomp @ G @ G @ D @ ( hAPP @ F @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(794,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 ) ) )
=> ( ( ( E = B )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ D @ C ) @ E ) @ A ) ) @ B )
= A ) )
& ( ( E != B )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ D @ C ) @ E ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__list__update) ).
thf(5716,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 ) ) )
=> ( ( ( E = B )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ D @ C ) @ E ) @ A ) ) @ B )
= A ) )
& ( ( E != B )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ D @ C ) @ E ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(297,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/sandbox/benchmark/theBenchmark.p',fact_nth__via__drop) ).
thf(3737,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)],[297]) ).
thf(1167,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ C @ ( c_List_Olist_ONil @ C ) ) @ B ) @ A )
= ( c_List_Olist_ONil @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__code_I1_J) ).
thf(7087,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ C @ ( c_List_Olist_ONil @ C ) ) @ B ) @ A )
= ( c_List_Olist_ONil @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).
thf(1567,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 @ ( hAPP @ ( c_member @ G ) @ A ) @ C ) )
=> ? [H: $i] :
( ( B
= ( hAPP @ ( hAPP @ E @ A ) @ H ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ F @ E @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) ) @ H ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__graph__insertE__aux) ).
thf(8569,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 @ ( hAPP @ ( c_member @ G ) @ A ) @ C ) )
=> ? [H: $i] :
( ( B
= ( hAPP @ ( hAPP @ E @ A ) @ H ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ F @ E @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) ) @ H ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1567]) ).
thf(1601,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/sandbox/benchmark/theBenchmark.p',fact_self__append__conv2) ).
thf(8725,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)],[1601]) ).
thf(267,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/sandbox/benchmark/theBenchmark.p',fact_list_Osize_I3_J) ).
thf(3640,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)],[267]) ).
thf(1334,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ B @ A ) @ ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsp_Oequations_I1_J) ).
thf(7705,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)],[1334]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Ohd @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd_Osimps) ).
thf(2863,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Ohd @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(939,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 @ ( c_Finite__Set_Ofinite @ E ) @ A ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ D @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
= ( hAPP @ ( hAPP @ D @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Ounion__inter) ).
thf(6238,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 @ ( c_Finite__Set_Ofinite @ E ) @ A ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ D @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
= ( hAPP @ ( hAPP @ D @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(1317,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl2) ).
thf(7635,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)],[1317]) ).
thf(769,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_List_Osublist @ D @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_If @ ( tc_List_Olist @ D ) ) @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ C ) @ ( c_List_Olist_ONil @ D ) ) ) @ ( c_List_Olist_ONil @ D ) ) ) @ ( c_List_Osublist @ D @ B @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( c_member @ tc_Nat_Onat ) ) @ c_Nat_OSuc ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__Cons) ).
thf(5607,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_List_Osublist @ D @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_If @ ( tc_List_Olist @ D ) ) @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ C ) @ ( c_List_Olist_ONil @ D ) ) ) @ ( c_List_Olist_ONil @ D ) ) ) @ ( c_List_Osublist @ D @ B @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( c_member @ tc_Nat_Onat ) ) @ c_Nat_OSuc ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(1005,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__empty__left) ).
thf(6472,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(1904,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_OCollect @ D ) @ A ) ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Collect) ).
thf(9847,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_OCollect @ D ) @ A ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_OCollect @ D ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1904]) ).
thf(236,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/sandbox/benchmark/theBenchmark.p',fact_lexord__cons__cons) ).
thf(3507,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)],[236]) ).
thf(2340,axiom,
! [A: $i,B: $i] :
( ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ B @ tc_HOL_Obool ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Inter) ).
thf(11460,plain,
! [A: $i,B: $i] :
( ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ B @ tc_HOL_Obool ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2340]) ).
thf(2522,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__def) ).
thf(12088,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)],[2522]) ).
thf(2359,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/sandbox/benchmark/theBenchmark.p',fact_rtrancl__converseD) ).
thf(11540,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)],[2359]) ).
thf(2369,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/sandbox/benchmark/theBenchmark.p',fact_Domain__iff) ).
thf(11573,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)],[2369]) ).
thf(1456,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Otrans @ C @ B )
=> ( ( c_Relation_Otrans @ C @ A )
=> ( c_Relation_Otrans @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__Int) ).
thf(8143,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Otrans @ C @ B )
=> ( ( c_Relation_Otrans @ C @ A )
=> ( c_Relation_Otrans @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1456]) ).
thf(653,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ ( c_List_Olist_ONil @ C ) )
= ( hAPP @ ( c_List_Orev @ C ) @ A ) )
<=> ( A
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ ( c_List_Olist_ONil @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__rev__conv) ).
thf(5125,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ ( c_List_Olist_ONil @ C ) )
= ( hAPP @ ( c_List_Orev @ C ) @ A ) )
=> ( A
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ ( c_List_Olist_ONil @ C ) ) ) )
& ( ( A
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ ( c_List_Olist_ONil @ C ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ ( c_List_Olist_ONil @ C ) )
= ( hAPP @ ( c_List_Orev @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(2426,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ A )
=> ( c_Fun_Obij__betw @ D @ C @ B @ A @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__imp__bij__betw) ).
thf(11753,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ A )
=> ( c_Fun_Obij__betw @ D @ C @ B @ A @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2426]) ).
thf(2408,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/sandbox/benchmark/theBenchmark.p',fact_single__valued__confluent) ).
thf(11694,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)],[2408]) ).
thf(1558,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/sandbox/benchmark/theBenchmark.p',fact_less__trans__Suc) ).
thf(8537,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)],[1558]) ).
thf(648,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding @ H @ G @ F @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ H ) @ D ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ G @ G @ C @ ( hAPP @ F @ B ) ) @ ( hAPP @ ( c_Fun_Ocomp @ G @ G @ C @ ( hAPP @ E @ D ) ) @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ G @ G @ C @ ( hAPP @ E @ D ) ) @ ( hAPP @ ( c_Fun_Ocomp @ G @ G @ C @ ( hAPP @ F @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__left__comp_H) ).
thf(5111,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding @ H @ G @ F @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ H ) @ D ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ G @ G @ C @ ( hAPP @ F @ B ) ) @ ( hAPP @ ( c_Fun_Ocomp @ G @ G @ C @ ( hAPP @ E @ D ) ) @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ G @ G @ C @ ( hAPP @ E @ D ) ) @ ( hAPP @ ( c_Fun_Ocomp @ G @ G @ C @ ( hAPP @ F @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(151,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ B ) @ ( hAPP @ ( c_List_Otl @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__tl) ).
thf(3214,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ B ) @ ( hAPP @ ( c_List_Otl @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(1037,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/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).
thf(6597,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)],[1037]) ).
thf(163,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( class_Rings_Osemiring__0 @ G )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ G ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ F @ G ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ G ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ F @ G ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ C @ tc_HOL_Obool ) @ G ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ G ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ G ) @ F ) @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ G ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ C @ G ) @ ( tc_fun @ C @ G ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ G @ G ) @ ( tc_fun @ ( tc_fun @ C @ G ) @ ( tc_fun @ C @ G ) ) @ F ) @ ( c_COMBB @ G @ G @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ G @ ( tc_fun @ G @ G ) @ F ) @ ( c_Groups_Otimes__class_Otimes @ G ) ) @ E ) ) ) @ B ) ) ) @ A ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__product) ).
thf(3260,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( class_Rings_Osemiring__0 @ G )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ G ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ F @ G ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ G ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ F @ G ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ C @ tc_HOL_Obool ) @ G ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ G ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ G ) @ F ) @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ G ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ C @ G ) @ ( tc_fun @ C @ G ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ G @ G ) @ ( tc_fun @ ( tc_fun @ C @ G ) @ ( tc_fun @ C @ G ) ) @ F ) @ ( c_COMBB @ G @ G @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ G @ ( tc_fun @ G @ G ) @ F ) @ ( c_Groups_Otimes__class_Otimes @ G ) ) @ E ) ) ) @ B ) ) ) @ A ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(741,axiom,
! [A: $i,B: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ B @ tc_HOL_Obool ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_COMBI @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__def) ).
thf(5499,plain,
! [A: $i,B: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ B @ tc_HOL_Obool ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_COMBI @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(1863,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/sandbox/benchmark/theBenchmark.p',fact_fold1__def) ).
thf(9710,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)],[1863]) ).
thf(608,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ A ) )
=> ( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ A ) @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__empty) ).
thf(4950,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ A ) )
=> ( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ A ) @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(1819,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Set_Oimage @ E @ D @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ D @ E ) @ B ) @ A ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
= ( hAPP @ ( c_Set_Oimage @ C @ D @ B ) @ ( hAPP @ ( c_Set_Oimage @ E @ C @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__composition) ).
thf(9535,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Set_Oimage @ E @ D @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ D @ E ) @ B ) @ A ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
= ( hAPP @ ( c_Set_Oimage @ C @ D @ B ) @ ( hAPP @ ( c_Set_Oimage @ E @ C @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1819]) ).
thf(1101,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Osym @ C @ B )
=> ( ( c_Relation_Osym @ C @ A )
=> ( c_Relation_Osym @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sym__Int) ).
thf(6826,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Osym @ C @ B )
=> ( ( c_Relation_Osym @ C @ A )
=> ( c_Relation_Osym @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).
thf(2488,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ D ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1I1) ).
thf(11956,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ D ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2488]) ).
thf(638,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_List_Orev @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ A ) )
<=> ( C
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ ( hAPP @ ( c_List_Orev @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ ( c_List_Olist_ONil @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__eq__Cons__iff) ).
thf(5074,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ A ) )
=> ( C
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ ( hAPP @ ( c_List_Orev @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ ( c_List_Olist_ONil @ D ) ) ) ) )
& ( ( C
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ ( hAPP @ ( c_List_Orev @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ ( c_List_Olist_ONil @ D ) ) ) )
=> ( ( hAPP @ ( c_List_Orev @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(766,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/sandbox/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
thf(5592,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)],[766]) ).
thf(2036,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__lower1) ).
thf(10371,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2036]) ).
thf(1153,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Orefl__on @ C @ B @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ C @ C @ C ) @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ A ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__comp__subset) ).
thf(7045,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Orefl__on @ C @ B @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ C @ C @ C ) @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ A ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153]) ).
thf(748,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Oleft__idem) ).
thf(5523,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(149,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 @ ( tc_List_Olist @ B ) ) ) @ ( c_List_Otranspose @ B @ A ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ ( tc_List_Olist @ B ) ) @ ( c_List_Otranspose @ B @ A ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_List_Olist @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ B ) @ tc_Nat_Onat @ B ) @ ( c_List_Onth @ B ) ) @ C ) ) @ ( hAPP @ ( c_List_Ofilter @ ( tc_List_Olist @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ tc_HOL_Obool @ ( tc_List_Olist @ B ) ) @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) ) @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__transpose) ).
thf(3209,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 @ ( tc_List_Olist @ B ) ) ) @ ( c_List_Otranspose @ B @ A ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ ( tc_List_Olist @ B ) ) @ ( c_List_Otranspose @ B @ A ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_List_Olist @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ B ) @ tc_Nat_Onat @ B ) @ ( c_List_Onth @ B ) ) @ C ) ) @ ( hAPP @ ( c_List_Ofilter @ ( tc_List_Olist @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ tc_HOL_Obool @ ( tc_List_Olist @ B ) ) @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) ) @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(1683,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ D @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1Set__sing) ).
thf(9005,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ D @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ D @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1683]) ).
thf(520,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__is__0) ).
thf(4630,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)],[520]) ).
thf(1510,axiom,
! [A: $i] :
( ( c_Wellfounded_Ofinite__psubset @ A )
= ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_COMBS @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ c_fconj ) ) @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) ) @ ( c_Finite__Set_Ofinite @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__psubset__def) ).
thf(8364,plain,
! [A: $i] :
( ( c_Wellfounded_Ofinite__psubset @ A )
= ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_COMBS @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ c_fconj ) ) @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) ) @ ( c_Finite__Set_Ofinite @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1510]) ).
thf(512,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/sandbox/benchmark/theBenchmark.p',fact_length__butlast) ).
thf(4593,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)],[512]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zmult__distrib) ).
thf(2888,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)],[58]) ).
thf(1955,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_OCollect @ B ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__def) ).
thf(10027,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_OCollect @ B ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1955]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A )
= ( c_Nat_Onat_Onat__case @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Nat_OSuc ) @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ tc_Nat_Onat ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__Suc1) ).
thf(2831,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A )
= ( c_Nat_Onat_Onat__case @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Nat_OSuc ) @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ tc_Nat_Onat ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(909,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I7_J) ).
thf(6146,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(3,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 @ tc_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ B ) ) @ ( hAPP @ c_Int_Onat @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__relations_I2_J) ).
thf(2687,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 @ tc_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ B ) ) @ ( hAPP @ c_Int_Onat @ 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_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ B ) ) @ ( hAPP @ c_Int_Onat @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(2689,plain,
! [B: $i,A: $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 @ tc_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ B ) ) @ ( hAPP @ c_Int_Onat @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) ) ),
inference(cnf,[status(esa)],[2687]) ).
thf(954,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Un__Int) ).
thf(6280,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(110,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__add @ D )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ D ) @ A ) @ B )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D ) ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ D ) @ A ) @ B )
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_OF__eq) ).
thf(3063,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__add @ D )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ D ) @ A ) @ B )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D ) ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ D ) @ A ) @ B )
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(1985,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnE) ).
thf(10164,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1985]) ).
thf(293,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/sandbox/benchmark/theBenchmark.p',fact_diff__add__0) ).
thf(3722,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)],[293]) ).
thf(248,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ E ) @ C ) @ B ) ) @ A ) )
<=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ B @ F ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP__le__iff) ).
thf(3554,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ E ) @ C ) @ B ) ) @ A ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ B @ F ) ) @ A ) ) ) )
& ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ B @ F ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ E ) @ C ) @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(854,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 ) ) )
<=> ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__gt__0__iff) ).
thf(5948,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 ) ) )
=> ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) ) ) )
& ( ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) ) )
=> ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(391,axiom,
! [A: $i,B: $i] : ( c_Wellfounded_Owf @ B @ ( hAPP @ ( c_Wellfounded_Omeasure @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__measure) ).
thf(4117,plain,
! [A: $i,B: $i] : ( c_Wellfounded_Owf @ B @ ( hAPP @ ( c_Wellfounded_Omeasure @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(305,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/sandbox/benchmark/theBenchmark.p',fact_nat__mult__le__cancel1) ).
thf(3769,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)],[305]) ).
thf(2103,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/sandbox/benchmark/theBenchmark.p',fact_rtrancl__idemp) ).
thf(10608,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)],[2103]) ).
thf(160,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/sandbox/benchmark/theBenchmark.p',fact_zmult__zless__mono2) ).
thf(3246,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)],[160]) ).
thf(2232,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( hAPP @ ( c_Set_Oimage @ C @ D @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__surj__f__inv__f) ).
thf(11066,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( hAPP @ ( c_Set_Oimage @ C @ D @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2232]) ).
thf(2111,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_List_Omap @ E @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ E @ D ) @ C ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__map__eq__map) ).
thf(10636,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_List_Omap @ E @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ E @ D ) @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( 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)],[2111]) ).
thf(218,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( c_Complete__Lattice_OSup__class_OSup @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__binary) ).
thf(3448,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( c_Complete__Lattice_OSup__class_OSup @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(498,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( c_Nat_Onat_Onat__case @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_COMBI @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc) ).
thf(4522,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( c_Nat_Onat_Onat__case @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_COMBI @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(721,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/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__less) ).
thf(5431,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)],[721]) ).
thf(1083,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/sandbox/benchmark/theBenchmark.p',fact_comp__equivI) ).
thf(6762,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)],[1083]) ).
thf(1546,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ A @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__absorb) ).
thf(8498,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ A @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1546]) ).
thf(1744,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ A )
= ( hAPP @ ( c_Set_OCollect @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ C ) ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__def) ).
thf(9214,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ A )
= ( hAPP @ ( c_Set_OCollect @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ C ) ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1744]) ).
thf(2075,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ B ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__rtrancl__UnI) ).
thf(10504,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ B ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2075]) ).
thf(1946,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/sandbox/benchmark/theBenchmark.p',fact_DomainE) ).
thf(9991,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)],[1946]) ).
thf(2516,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/sandbox/benchmark/theBenchmark.p',fact_pred__comp_Ointros) ).
thf(12071,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)],[2516]) ).
thf(591,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Orev @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ ( hAPP @ ( c_List_Orev @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ ( c_List_Olist_ONil @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev_Osimps_I2_J) ).
thf(4905,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Orev @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ ( hAPP @ ( c_List_Orev @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ ( c_List_Olist_ONil @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(2057,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__anti__mono) ).
thf(10439,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2057]) ).
thf(351,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding @ F @ E @ D @ C )
=> ( ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ D @ B ) ) @ ( hAPP @ D @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ D @ A ) ) @ ( hAPP @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__comp) ).
thf(3940,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding @ F @ E @ D @ C )
=> ( ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ D @ B ) ) @ ( hAPP @ D @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ D @ A ) ) @ ( hAPP @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(1137,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/sandbox/benchmark/theBenchmark.p',fact_butlast_Osimps_I2_J) ).
thf(6981,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)],[1137]) ).
thf(1277,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/sandbox/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
thf(7494,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)],[1277]) ).
thf(1844,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/sandbox/benchmark/theBenchmark.p',fact_trancl__unfold__left) ).
thf(9634,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)],[1844]) ).
thf(731,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/sandbox/benchmark/theBenchmark.p',fact_nth__append__length) ).
thf(5467,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)],[731]) ).
thf(1755,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/sandbox/benchmark/theBenchmark.p',fact_fun__upd__idem__iff) ).
thf(9281,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)],[1755]) ).
thf(413,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/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__zero) ).
thf(4190,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)],[413]) ).
thf(2492,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/sandbox/benchmark/theBenchmark.p',fact_removeAll_Osimps_I2_J) ).
thf(11974,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)],[2492]) ).
thf(318,axiom,
! [A: $i,B: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ B )
=> ( ( c_Complete__Lattice_OSup__class_OSup @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__singleton) ).
thf(3818,plain,
! [A: $i,B: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ B )
=> ( ( c_Complete__Lattice_OSup__class_OSup @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(2604,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/sandbox/benchmark/theBenchmark.p',fact_irrefl__def) ).
thf(12455,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)],[2604]) ).
thf(283,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/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono) ).
thf(3691,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)],[283]) ).
thf(121,axiom,
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
= ( hAPP @ c_Int_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__numerals_I1_J) ).
thf(3114,plain,
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
= ( hAPP @ c_Int_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(2688,plain,
! [B: $i,A: $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 @ tc_Int_Oint ) @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ B ) ) @ ( hAPP @ c_Int_Onat @ A ) ) ) ),
inference(cnf,[status(esa)],[2687]) ).
thf(2328,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IntE) ).
thf(11429,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2328]) ).
thf(1298,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
<=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INTER__UNIV__conv_I1_J) ).
thf(7568,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
& ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) )
=> ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1298]) ).
thf(1697,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( c_Set_OCollect @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ ( tc_List_Olist @ C ) @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_List_Olist @ C ) ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ C ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_List_Olist @ C ) ) @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( c_List_Oset @ C ) ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ C ) @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_List_Olist @ C ) ) @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) ) @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__lists__length__le) ).
thf(9050,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( c_Set_OCollect @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ ( tc_List_Olist @ C ) @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_List_Olist @ C ) ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ C ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_List_Olist @ C ) ) @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( c_List_Oset @ C ) ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ C ) @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_List_Olist @ C ) ) @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) ) @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1697]) ).
thf(1970,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ A @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ ( tc_fun @ D @ tc_HOL_Obool ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_weak__coinduct) ).
thf(10095,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ A @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ ( tc_fun @ D @ tc_HOL_Obool ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1970]) ).
thf(188,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ D ) @ A ) @ B )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D ) ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Oeq__fold) ).
thf(3344,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ D ) @ A ) @ B )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D ) ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(1545,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ C @ C @ C ) @ B ) @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Wellfounded_Omax__ext @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) ) @ ( c_Wellfounded_Omax__ext @ C @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) ) ) ) ) ) @ ( c_Wellfounded_Omax__ext @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ext__compat) ).
thf(8496,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ C @ C @ C ) @ B ) @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Wellfounded_Omax__ext @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) ) @ ( c_Wellfounded_Omax__ext @ C @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) ) ) ) ) ) @ ( c_Wellfounded_Omax__ext @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1545]) ).
thf(2293,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/sandbox/benchmark/theBenchmark.p',fact_splitI) ).
thf(11295,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)],[2293]) ).
thf(1285,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I9_J) ).
thf(7522,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1285]) ).
thf(2294,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ? [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 @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__INT) ).
thf(11297,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ? [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 @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2294]) ).
thf(146,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/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
thf(3202,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)],[146]) ).
thf(2132,axiom,
! [A: $i] :
( A
!= ( hAPP @ c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
thf(10717,plain,
! [A: $i] :
( A
!= ( hAPP @ c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2132]) ).
thf(2134,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/sandbox/benchmark/theBenchmark.p',fact_remove1_Osimps_I2_J) ).
thf(10724,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)],[2134]) ).
thf(227,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Oleft__commute) ).
thf(3475,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(2170,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 ) ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) ) )
=> ~ ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) @ B ) @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ F ) @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__Suc__E) ).
thf(10861,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 ) ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) ) )
=> ~ ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) @ B ) @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ F ) @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2170]) ).
thf(1168,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ D ) ) @ B ) @ A ) )
=> ( ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ D ) ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ D ) @ tc_HOL_Obool ) ) ) )
& ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_derivs__insertD) ).
thf(7090,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ D ) ) @ B ) @ A ) )
=> ( ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ D ) ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ D ) @ tc_HOL_Obool ) ) ) )
& ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).
thf(1829,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_Ocurry @ F @ E @ D @ C ) @ B ) @ A )
= ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curry__conv) ).
thf(9567,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_Ocurry @ F @ E @ D @ C ) @ B ) @ A )
= ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1829]) ).
thf(1403,axiom,
! [A: $i] :
( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_OCollect @ A ) @ ( hAPP @ ( c_COMBK @ tc_HOL_Obool @ A ) @ c_fTrue ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__def) ).
thf(7947,plain,
! [A: $i] :
( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_OCollect @ A ) @ ( hAPP @ ( c_COMBK @ tc_HOL_Obool @ A ) @ c_fTrue ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1403]) ).
thf(1894,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Owf @ D @ C )
=> ( ( c_Fun_Oinj__on @ D @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( c_Wellfounded_Owf @ B @ ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ D @ D ) @ ( tc_prod @ B @ B ) @ ( c_Product__Type_Omap__pair @ D @ B @ D @ B @ A @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__map__pair__image) ).
thf(9815,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Owf @ D @ C )
=> ( ( c_Fun_Oinj__on @ D @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( c_Wellfounded_Owf @ B @ ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ D @ D ) @ ( tc_prod @ B @ B ) @ ( c_Product__Type_Omap__pair @ D @ B @ D @ B @ A @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1894]) ).
thf(1634,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/sandbox/benchmark/theBenchmark.p',fact_filter__append) ).
thf(8845,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)],[1634]) ).
thf(401,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Odrop @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__0) ).
thf(4145,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)],[401]) ).
thf(1014,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_List_Ofilter @ D @ C ) @ ( hAPP @ ( c_List_Ofilter @ D @ B ) @ A ) )
= ( hAPP @ ( c_List_Ofilter @ D @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) @ B ) ) @ C ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__filter) ).
thf(6508,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_List_Ofilter @ D @ C ) @ ( hAPP @ ( c_List_Ofilter @ D @ B ) @ A ) )
= ( hAPP @ ( c_List_Ofilter @ D @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) @ B ) ) @ C ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(1384,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I1_J) ).
thf(7879,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1384]) ).
thf(1550,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I4_J) ).
thf(8509,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1550]) ).
thf(314,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ ( tc_prod @ F @ E ) @ F @ ( tc_prod @ D @ C ) @ ( c_Product__Type_Ofst @ F @ E ) ) @ ( c_Product__Type_Omap__pair @ D @ F @ C @ E @ B @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ D @ F @ ( tc_prod @ D @ C ) @ B ) @ ( c_Product__Type_Ofst @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__comp__map__pair) ).
thf(3801,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ ( tc_prod @ F @ E ) @ F @ ( tc_prod @ D @ C ) @ ( c_Product__Type_Ofst @ F @ E ) ) @ ( c_Product__Type_Omap__pair @ D @ F @ C @ E @ B @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ D @ F @ ( tc_prod @ D @ C ) @ B ) @ ( c_Product__Type_Ofst @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(901,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ E @ D ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBC__1) ).
thf(6125,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ E @ D ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(1706,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_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__mono) ).
thf(9082,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_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1706]) ).
thf(307,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/sandbox/benchmark/theBenchmark.p',fact_le0) ).
thf(3774,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)],[307]) ).
thf(2592,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/sandbox/benchmark/theBenchmark.p',fact_wf__acc__iff) ).
thf(12396,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)],[2592]) ).
thf(454,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ D ) @ ( c_List_OtakeWhile @ E @ C @ B ) ) @ A )
= ( c_List_OtakeWhile @ ( tc_prod @ E @ D ) @ ( hAPP @ ( c_Fun_Ocomp @ E @ tc_HOL_Obool @ ( tc_prod @ E @ D ) @ C ) @ ( c_Product__Type_Ofst @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ D ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__takeWhile__fst) ).
thf(4351,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ D ) @ ( c_List_OtakeWhile @ E @ C @ B ) ) @ A )
= ( c_List_OtakeWhile @ ( tc_prod @ E @ D ) @ ( hAPP @ ( c_Fun_Ocomp @ E @ tc_HOL_Obool @ ( tc_prod @ E @ D ) @ C ) @ ( c_Product__Type_Ofst @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ D ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(974,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__Int) ).
thf(6352,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(246,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Partial__Function_Ofun__lub @ F @ E @ D @ C @ B @ A )
= ( hAPP @ C @ ( hAPP @ ( c_Set_OCollect @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ D @ F ) @ tc_HOL_Obool ) @ tc_HOL_Obool @ F ) @ ( c_HOL_OEx @ ( tc_fun @ D @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ D @ F ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ F ) @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( c_COMBS @ ( tc_fun @ D @ F ) @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_fun @ D @ F ) ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ D @ F ) @ ( tc_fun @ ( tc_fun @ D @ F ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ ( tc_fun @ D @ F ) ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_fun @ D @ F ) @ F ) @ ( tc_fun @ ( tc_fun @ D @ F ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_fun @ D @ F ) @ F ) @ ( tc_fun @ ( tc_fun @ D @ F ) @ tc_HOL_Obool ) ) @ F ) @ ( c_COMBB @ F @ tc_HOL_Obool @ ( tc_fun @ D @ F ) ) ) @ c_fequal ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ D @ F ) @ D @ F ) @ ( c_COMBI @ ( tc_fun @ D @ F ) ) ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__lub__def) ).
thf(3544,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Partial__Function_Ofun__lub @ F @ E @ D @ C @ B @ A )
= ( hAPP @ C @ ( hAPP @ ( c_Set_OCollect @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ D @ F ) @ tc_HOL_Obool ) @ tc_HOL_Obool @ F ) @ ( c_HOL_OEx @ ( tc_fun @ D @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ D @ F ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ F ) @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( c_COMBS @ ( tc_fun @ D @ F ) @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_fun @ D @ F ) ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ D @ F ) @ ( tc_fun @ ( tc_fun @ D @ F ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ ( tc_fun @ D @ F ) ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_fun @ D @ F ) @ F ) @ ( tc_fun @ ( tc_fun @ D @ F ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_fun @ D @ F ) @ F ) @ ( tc_fun @ ( tc_fun @ D @ F ) @ tc_HOL_Obool ) ) @ F ) @ ( c_COMBB @ F @ tc_HOL_Obool @ ( tc_fun @ D @ F ) ) ) @ c_fequal ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ D @ F ) @ D @ F ) @ ( c_COMBI @ ( tc_fun @ D @ F ) ) ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(920,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I6_J) ).
thf(6174,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(321,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/sandbox/benchmark/theBenchmark.p',fact_diff__0__eq__0) ).
thf(3828,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)],[321]) ).
thf(396,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/sandbox/benchmark/theBenchmark.p',fact_dvd__1__left) ).
thf(4132,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)],[396]) ).
thf(1458,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Fun_Obij__betw @ H @ G @ F @ E @ D )
=> ( ( c_Fun_Obij__betw @ G @ C @ B @ D @ A )
<=> ( c_Fun_Obij__betw @ H @ C @ ( hAPP @ ( c_Fun_Ocomp @ G @ C @ H @ B ) @ F ) @ E @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__comp__iff) ).
thf(8148,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Fun_Obij__betw @ H @ G @ F @ E @ D )
=> ( ( ( c_Fun_Obij__betw @ G @ C @ B @ D @ A )
=> ( c_Fun_Obij__betw @ H @ C @ ( hAPP @ ( c_Fun_Ocomp @ G @ C @ H @ B ) @ F ) @ E @ A ) )
& ( ( c_Fun_Obij__betw @ H @ C @ ( hAPP @ ( c_Fun_Ocomp @ G @ C @ H @ B ) @ F ) @ E @ A )
=> ( c_Fun_Obij__betw @ G @ C @ B @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1458]) ).
thf(1302,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) ) @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP__UN__eq) ).
thf(7583,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1302]) ).
thf(328,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/sandbox/benchmark/theBenchmark.p',fact_butlast__take) ).
thf(3847,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)],[328]) ).
thf(2266,axiom,
! [A: $i,B: $i] :
( ( c_HOL_OThe @ B @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ B @ tc_HOL_Obool ) @ c_fequal ) @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__eq__trivial) ).
thf(11198,plain,
! [A: $i,B: $i] :
( ( c_HOL_OThe @ B @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ B @ tc_HOL_Obool ) @ c_fequal ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2266]) ).
thf(1710,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Diff__Int) ).
thf(9093,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1710]) ).
thf(1473,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E ) @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E ) @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ C ) ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__Un__eq2) ).
thf(8206,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E ) @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E ) @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ C ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ D ) @ C ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ D ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E ) @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F ) @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E ) @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ C ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1473]) ).
thf(1951,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( 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/sandbox/benchmark/theBenchmark.p',fact_map__removeAll__inj) ).
thf(10012,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( 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)],[1951]) ).
thf(193,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Otl @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ B ) @ ( hAPP @ ( c_List_Otl @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tl__drop) ).
thf(3359,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Otl @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ B ) @ ( hAPP @ ( c_List_Otl @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(184,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/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
thf(3329,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)],[184]) ).
thf(138,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Groups_Ocomm__monoid__add @ F )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ E @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ F ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ F ) @ E ) @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ F ) ) @ C ) ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ ( tc_prod @ E @ D ) @ F ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ E @ D @ F ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__cartesian__product) ).
thf(3174,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Groups_Ocomm__monoid__add @ F )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ E @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ F ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ F ) @ E ) @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ F ) ) @ C ) ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ ( tc_prod @ E @ D ) @ F ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ E @ D @ F ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(561,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Fun_Oid @ B ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_id__apply) ).
thf(4781,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Fun_Oid @ B ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(1922,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__subsetI) ).
thf(9911,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1922]) ).
thf(2388,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
& ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__eq) ).
thf(11637,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
& ( B != A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
& ( B != A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2388]) ).
thf(330,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/sandbox/benchmark/theBenchmark.p',fact_listrel1__eq__len) ).
thf(3853,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)],[330]) ).
thf(2137,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/sandbox/benchmark/theBenchmark.p',fact_ImageE) ).
thf(10739,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)],[2137]) ).
thf(669,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/sandbox/benchmark/theBenchmark.p',fact_nth__take__lemma) ).
thf(5186,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)],[669]) ).
thf(691,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Orev @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) @ B ) ) @ ( hAPP @ ( c_List_Orev @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__take) ).
thf(5277,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Orev @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) @ B ) ) @ ( hAPP @ ( c_List_Orev @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(2438,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/sandbox/benchmark/theBenchmark.p',fact_take__Suc__Cons) ).
thf(11788,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)],[2438]) ).
thf(496,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__0) ).
thf(4510,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)],[496]) ).
thf(2623,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/sandbox/benchmark/theBenchmark.p',fact_conversep_Oequations) ).
thf(12548,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)],[2623]) ).
thf(72,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__1) ).
thf(2949,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)],[72]) ).
thf(1527,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ B ) ) @ ( hAPP @ A @ C ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__diff1__nat) ).
thf(8433,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ B ) ) @ ( hAPP @ A @ C ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1527]) ).
thf(1139,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/sandbox/benchmark/theBenchmark.p',fact_eq__Nil__appendI) ).
thf(6992,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)],[1139]) ).
thf(1883,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/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__eq__card) ).
thf(9775,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)],[1883]) ).
thf(658,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Ozip @ D @ B ) @ ( hAPP @ ( c_List_Orev @ D ) @ C ) ) @ ( hAPP @ ( c_List_Orev @ B ) @ A ) )
= ( hAPP @ ( c_List_Orev @ ( tc_prod @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ D @ B ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__rev) ).
thf(5147,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Ozip @ D @ B ) @ ( hAPP @ ( c_List_Orev @ D ) @ C ) ) @ ( hAPP @ ( c_List_Orev @ B ) @ A ) )
= ( hAPP @ ( c_List_Orev @ ( tc_prod @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ D @ B ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(1979,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot2E) ).
thf(10129,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1979]) ).
thf(1716,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Orefl__on @ E @ D @ C )
=> ( ( c_Relation_Orefl__on @ E @ B @ A )
=> ( c_Relation_Orefl__on @ E @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__Int) ).
thf(9109,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Orefl__on @ E @ D @ C )
=> ( ( c_Relation_Orefl__on @ E @ B @ A )
=> ( c_Relation_Orefl__on @ E @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1716]) ).
thf(1351,axiom,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) @ ( c_Relation_OId @ B ) ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__reflcl) ).
thf(7752,plain,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) @ ( c_Relation_OId @ B ) ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1351]) ).
thf(2649,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/sandbox/benchmark/theBenchmark.p',fact_triple__valid__Suc) ).
thf(12647,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)],[2649]) ).
thf(1383,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/sandbox/benchmark/theBenchmark.p',fact_upt__Suc__append) ).
thf(7876,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)],[1383]) ).
thf(565,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) ) @ C ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ A ) )
= ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__add__atLeastLessThan) ).
thf(4802,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) ) @ C ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ A ) )
= ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(1807,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
<=> ( c_Wellfounded_Owf @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ C @ C @ C ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ C @ C @ C ) @ A ) @ B ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__union__merge) ).
thf(9495,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Wellfounded_Owf @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( c_Wellfounded_Owf @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ C @ C @ C ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ C @ C @ C ) @ A ) @ B ) ) ) @ A ) ) )
& ( ( c_Wellfounded_Owf @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ C @ C @ C ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ C @ C @ C ) @ A ) @ B ) ) ) @ A ) )
=> ( c_Wellfounded_Owf @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1807]) ).
thf(1971,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/sandbox/benchmark/theBenchmark.p',fact_Range__insert) ).
thf(10097,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)],[1971]) ).
thf(1264,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__Diff__distrib1) ).
thf(7456,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1264]) ).
thf(2602,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/sandbox/benchmark/theBenchmark.p',fact_insert__code) ).
thf(12439,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)],[2602]) ).
thf(611,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
<=> ( ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).
thf(4959,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)],[611]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ E ) ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ F ) @ B ) )
=> ( ( E != F )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ G ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ G ) @ F ) )
=> ( ( hAPP @ A @ G )
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ D ) @ A ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ D ) @ A ) ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__UNION__zero) ).
thf(2838,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ E ) ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ F ) @ B ) )
=> ( ( E != F )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ G ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ G ) @ F ) )
=> ( ( hAPP @ A @ G )
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ D ) @ A ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ D ) @ A ) ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(884,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/sandbox/benchmark/theBenchmark.p',fact_Range__def) ).
thf(6073,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)],[884]) ).
thf(2644,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Equiv__Relations_Oequivp @ C @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equivp__reflp) ).
thf(12630,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)],[2644]) ).
thf(800,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ? [C: $i] : ( c_Fun_Obij__betw @ B @ tc_Nat_Onat @ C @ A @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__bij__betw__finite__nat) ).
thf(5736,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ? [C: $i] : ( c_Fun_Obij__betw @ B @ tc_Nat_Onat @ C @ A @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(1503,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/sandbox/benchmark/theBenchmark.p',fact_less__diff__iff) ).
thf(8331,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)],[1503]) ).
thf(2450,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__left__if0) ).
thf(11835,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2450]) ).
thf(2564,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/sandbox/benchmark/theBenchmark.p',fact_pos__union__def) ).
thf(12262,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)],[2564]) ).
thf(2678,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/sandbox/benchmark/theBenchmark.p',fact_filter__id__conv) ).
thf(12771,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)],[2678]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ ( tc_List_Olist @ C ) ) @ ( c_Enum_On__lists @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__n__lists) ).
thf(2992,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ ( tc_List_Olist @ C ) ) @ ( c_Enum_On__lists @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(1394,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( c_Equiv__Relations_Oquotient @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ D ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ C ) @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ D ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__diff1) ).
thf(7919,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( c_Equiv__Relations_Oquotient @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ D ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ C ) @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ D ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1394]) ).
thf(1300,axiom,
class_Nat_Osize @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Nat_Osize) ).
thf(7580,plain,
class_Nat_Osize @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1300]) ).
thf(2017,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/sandbox/benchmark/theBenchmark.p',fact_Pair__eq) ).
thf(10293,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)],[2017]) ).
thf(1808,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ B ) )
=> ( ( hAPP @ C @ B )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) ) ) @ ( hAPP @ D @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Oremove) ).
thf(9500,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ B ) )
=> ( ( hAPP @ C @ B )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) ) ) @ ( hAPP @ D @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1808]) ).
thf(518,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Orev @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) @ B ) ) @ ( hAPP @ ( c_List_Orev @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__drop) ).
thf(4624,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Orev @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) @ B ) ) @ ( hAPP @ ( c_List_Orev @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(963,axiom,
! [A: $i,B: $i] : ( c_List_Olist__all @ B @ A @ ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all__simps_I2_J) ).
thf(6318,plain,
! [A: $i,B: $i] : ( c_List_Olist__all @ B @ A @ ( c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(1266,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__empty) ).
thf(7461,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1266]) ).
thf(1086,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ A ) @ ( c_List_Olist_ONil @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct_Osimps_I1_J) ).
thf(6775,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ A ) @ ( c_List_Olist_ONil @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).
thf(192,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_Oappend @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ ( hAPP @ ( c_List_Ohd @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ B ) @ C ) @ A ) ) ) @ ( c_List_Olist_ONil @ B ) ) )
= ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__hd__drop) ).
thf(3356,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_Oappend @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ B ) @ ( hAPP @ ( c_List_Ohd @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ B ) @ C ) @ A ) ) ) @ ( c_List_Olist_ONil @ B ) ) )
= ( hAPP @ ( hAPP @ ( c_List_Otake @ B ) @ ( hAPP @ c_Nat_OSuc @ C ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(2319,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/sandbox/benchmark/theBenchmark.p',fact_Domain__insert) ).
thf(11386,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)],[2319]) ).
thf(1160,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/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__le) ).
thf(7067,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)],[1160]) ).
thf(2229,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/sandbox/benchmark/theBenchmark.p',fact_List_Oinsert__def) ).
thf(11054,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)],[2229]) ).
thf(2464,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/sandbox/benchmark/theBenchmark.p',fact_in__set__conv__decomp__first) ).
thf(11882,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)],[2464]) ).
thf(1772,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_ODomain @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_ODomain @ D @ C ) @ A ) ) ) @ ( hAPP @ ( c_Relation_ODomain @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Diff__subset) ).
thf(9363,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_ODomain @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_ODomain @ D @ C ) @ A ) ) ) @ ( hAPP @ ( c_Relation_ODomain @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1772]) ).
thf(618,axiom,
class_Orderings_Oorder @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
thf(4991,plain,
class_Orderings_Oorder @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(1430,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ D @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ D @ E @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_OImage @ D @ E @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__Int__subset) ).
thf(8061,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ D @ E @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ D @ E @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_OImage @ D @ E @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1430]) ).
thf(726,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ A ) @ ( c_Complete__Lattice_OInf__class_OInf @ C @ B ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ C @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__Inf__fold__inf) ).
thf(5453,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ A ) @ ( c_Complete__Lattice_OInf__class_OInf @ C @ B ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ C @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(400,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ D ) ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__finite__subset) ).
thf(4143,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ D ) ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(602,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ C ) ) @ B ) @ ( c_Wellfounded_Oacc @ ( tc_List_Olist @ C ) @ ( c_List_Olistrel1 @ C @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ C ) ) @ B ) @ ( c_List_Olists @ C @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists__accI) ).
thf(4932,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ C ) ) @ B ) @ ( c_Wellfounded_Oacc @ ( tc_List_Olist @ C ) @ ( c_List_Olistrel1 @ C @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ C ) ) @ B ) @ ( c_List_Olists @ C @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(1468,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Oinj__on @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ B ) @ ( hAPP @ ( c_List_Omap @ C @ B ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) )
<=> ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__map) ).
thf(8185,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Fun_Oinj__on @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ B ) @ ( hAPP @ ( c_List_Omap @ C @ B ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) )
=> ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( c_Fun_Oinj__on @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ B ) @ ( hAPP @ ( c_List_Omap @ C @ B ) @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1468]) ).
thf(2211,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( hAPP @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__D) ).
thf(11005,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( hAPP @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2211]) ).
thf(1943,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equals0D) ).
thf(9983,plain,
! [A: $i,B: $i,C: $i] :
( ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1943]) ).
thf(425,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/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel2) ).
thf(4235,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)],[425]) ).
thf(1603,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/sandbox/benchmark/theBenchmark.p',fact_mlex__leq) ).
thf(8734,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)],[1603]) ).
thf(98,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( ( hAPP @ A @ F )
= ( c_Groups_Ozero__class_Ozero @ E ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Ounion__inter__neutral) ).
thf(3024,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( ( hAPP @ A @ F )
= ( c_Groups_Ozero__class_Ozero @ E ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(1784,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Un__distrib) ).
thf(9406,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1784]) ).
thf(1203,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Obij__betw @ D @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__empty2) ).
thf(7202,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Obij__betw @ D @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1203]) ).
thf(1845,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__INT) ).
thf(9637,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1845]) ).
thf(1257,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ B ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord__less__eq__trans) ).
thf(7426,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ B ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1257]) ).
thf(423,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/sandbox/benchmark/theBenchmark.p',fact_card__def) ).
thf(4225,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)],[423]) ).
thf(70,axiom,
! [A: $i] :
( ( ( hAPP @ c_Int_Onat @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__0__iff) ).
thf(2939,plain,
! [A: $i] :
( ( ( ( hAPP @ c_Int_Onat @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( 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 ) ) )
=> ( ( hAPP @ c_Int_Onat @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(2558,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/sandbox/benchmark/theBenchmark.p',fact_insertCI) ).
thf(12241,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)],[2558]) ).
thf(1563,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/sandbox/benchmark/theBenchmark.p',fact_listrel1E) ).
thf(8552,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)],[1563]) ).
thf(1199,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ D @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( c_Fun_Ocomp @ D @ D @ D @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ D @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ D @ D ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funpow__add) ).
thf(7192,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ D @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( c_Fun_Ocomp @ D @ D @ D @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ D @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ D @ D ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1199]) ).
thf(1754,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
thf(9274,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)],[1754]) ).
thf(1440,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Fun_Obij__betw @ H @ G @ F @ E @ D )
=> ( ( c_Fun_Obij__betw @ G @ C @ B @ D @ A )
=> ( c_Fun_Obij__betw @ H @ C @ ( hAPP @ ( c_Fun_Ocomp @ G @ C @ H @ B ) @ F ) @ E @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__trans) ).
thf(8087,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Fun_Obij__betw @ H @ G @ F @ E @ D )
=> ( ( c_Fun_Obij__betw @ G @ C @ B @ D @ A )
=> ( c_Fun_Obij__betw @ H @ C @ ( hAPP @ ( c_Fun_Ocomp @ G @ C @ H @ B ) @ F ) @ E @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1440]) ).
thf(1015,axiom,
class_Orderings_Owellorder @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Owellorder) ).
thf(6511,plain,
class_Orderings_Owellorder @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).
thf(914,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oorder__class_Omono @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_coinduct__set) ).
thf(6161,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oorder__class_Omono @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(644,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/sandbox/benchmark/theBenchmark.p',fact_image__Suc__atLeastLessThan) ).
thf(5100,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)],[644]) ).
thf(2243,axiom,
! [A: $i,B: $i] :
( ( c_Equiv__Relations_Oequivp @ B @ A )
=> ( c_Equiv__Relations_Opart__equivp @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equivp__implies__part__equivp) ).
thf(11108,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)],[2243]) ).
thf(1619,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__Diff__eq) ).
thf(8798,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1619]) ).
thf(563,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/sandbox/benchmark/theBenchmark.p',fact_diff__less) ).
thf(4795,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)],[563]) ).
thf(238,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ D @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ C ) @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__code_I2_J) ).
thf(3520,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ D @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ C ) @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(1459,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ B @ C ) @ B @ ( c_Product__Type_Ofst @ B @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ B @ C ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) @ D ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( D
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ B @ C ) @ B @ ( c_Product__Type_Ofst @ B @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ B @ C ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) @ D ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__image__times) ).
thf(8151,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ B @ C ) @ B @ ( c_Product__Type_Ofst @ B @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ B @ C ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) @ D ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( D
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ B @ C ) @ B @ ( c_Product__Type_Ofst @ B @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ B @ C ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) @ D ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1459]) ).
thf(1989,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityD2) ).
thf(10178,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1989]) ).
thf(1639,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/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__diff) ).
thf(8861,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)],[1639]) ).
thf(1340,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( c_member @ tc_Nat_Onat ) ) @ c_Nat_OSuc ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ A ) ) ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ tc_Nat_Onat ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__less__Suc2) ).
thf(7720,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( c_member @ tc_Nat_Onat ) ) @ c_Nat_OSuc ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ A ) ) ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ tc_Nat_Onat ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1340]) ).
thf(1328,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ ( c_Relation_OId__on @ B @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ B @ B ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__subset__Times) ).
thf(7690,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ ( c_Relation_OId__on @ B @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ B @ B ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1328]) ).
thf(842,axiom,
class_Orderings_Oord @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
thf(5895,plain,
class_Orderings_Oord @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(1275,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Un) ).
thf(7488,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1275]) ).
thf(430,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/sandbox/benchmark/theBenchmark.p',fact_listrel__Nil2) ).
thf(4257,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)],[430]) ).
thf(2508,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/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oidem) ).
thf(12039,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)],[2508]) ).
thf(529,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ D ) @ C ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) ) ) @ ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le) ).
thf(4671,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ D ) @ C ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) ) ) @ ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ D ) @ C ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) ) ) @ ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(280,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Fun_Oid @ B ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_id__def) ).
thf(3684,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Fun_Oid @ B ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(932,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/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__insert) ).
thf(6220,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)],[932]) ).
thf(988,axiom,
! [A: $i,B: $i] :
( ( ( c_List_Olist_ONil @ B )
= ( c_List_Oremdups @ B @ A ) )
<=> ( A
= ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remdups__eq__nil__right__iff) ).
thf(6420,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)],[988]) ).
thf(2296,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_List_Oset @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__set) ).
thf(11302,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)],[2296]) ).
thf(1881,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/sandbox/benchmark/theBenchmark.p',fact_trancl__trans) ).
thf(9770,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)],[1881]) ).
thf(1091,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__absorb) ).
thf(6793,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).
thf(2566,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ F @ E @ D @ C ) @ B )
= ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ F @ E @ D @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ C ) @ D ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ C ) @ D ) ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__injective) ).
thf(12277,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ F @ E @ D @ C ) @ B )
= ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ F @ E @ D @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ C ) @ D ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ C ) @ D ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2566]) ).
thf(1994,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ B ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__subset__Cons) ).
thf(10193,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ B ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1994]) ).
thf(1490,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A )
= ( hAPP @ ( c_Set_OCollect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ B ) @ c_fNot ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__eq) ).
thf(8285,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A )
= ( hAPP @ ( c_Set_OCollect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ B ) @ c_fNot ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1490]) ).
thf(823,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/sandbox/benchmark/theBenchmark.p',fact_listrel__trans) ).
thf(5832,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)],[823]) ).
thf(54,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/sandbox/benchmark/theBenchmark.p',fact_unique__quotient__lemma) ).
thf(2875,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)],[54]) ).
thf(2026,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top1I) ).
thf(10332,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2026]) ).
thf(2532,axiom,
! [A: $i] :
( ~ ~ ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ c_fNot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__2) ).
thf(12145,plain,
! [A: $i] :
( ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ c_fNot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2532]) ).
thf(1629,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 @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) )
=> ( C = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__0__E) ).
thf(8830,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 @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) )
=> ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1629]) ).
thf(171,axiom,
! [A: $i] :
( ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ A )
= ( hAPP @ ( c_Set_Oimage @ tc_Int_Oint @ tc_Nat_Onat @ c_Int_Onat ) @ ( hAPP @ ( c_Set_OCollect @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Int_Oint @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Int_Oint ) @ c_fconj ) @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ tc_HOL_Obool @ tc_Int_Oint ) @ A ) @ c_Int_Onat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J) ).
thf(3284,plain,
! [A: $i] :
( ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ A )
= ( hAPP @ ( c_Set_Oimage @ tc_Int_Oint @ tc_Nat_Onat @ c_Int_Onat ) @ ( hAPP @ ( c_Set_OCollect @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Int_Oint @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Int_Oint ) @ c_fconj ) @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ tc_HOL_Obool @ tc_Int_Oint ) @ A ) @ c_Int_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(1067,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oimage @ C @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__image__eq) ).
thf(6706,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oimage @ C @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).
thf(2131,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 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ E ) @ A ) @ D ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__singleton__iff) ).
thf(10712,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 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ E ) @ A ) @ D ) ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ E ) @ A ) @ D ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Relation_OImage @ C @ E @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2131]) ).
thf(22,axiom,
c_Typedef_Otype__definition @ tc_Int_Oint @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ c_Int_ORep__Integ @ c_Int_OAbs__Integ @ c_Int_OInteg,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition__Integ) ).
thf(2760,plain,
c_Typedef_Otype__definition @ tc_Int_Oint @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ c_Int_ORep__Integ @ c_Int_OAbs__Integ @ c_Int_OInteg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(2007,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/sandbox/benchmark/theBenchmark.p',fact_acyclic__def) ).
thf(10261,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)],[2007]) ).
thf(1171,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/sandbox/benchmark/theBenchmark.p',fact_wf) ).
thf(7099,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)],[1171]) ).
thf(1818,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Relation_ORange @ B @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__empty) ).
thf(9532,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Relation_ORange @ B @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1818]) ).
thf(228,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hAPP @ ( hAPP @ C @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Oeq__fold) ).
thf(3478,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hAPP @ ( hAPP @ C @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ F @ E @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(213,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/sandbox/benchmark/theBenchmark.p',fact_drop__append) ).
thf(3433,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)],[213]) ).
thf(353,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ G @ F @ E @ D ) @ C )
= ( hAPP @ ( c_Fun_Ocomp @ F @ F @ E @ ( c_Fun_Oid @ F ) ) @ B ) )
=> ( ( hAPP @ D @ ( hAPP @ C @ A ) )
= ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__eq__id__dest) ).
thf(3946,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ G @ F @ E @ D ) @ C )
= ( hAPP @ ( c_Fun_Ocomp @ F @ F @ E @ ( c_Fun_Oid @ F ) ) @ B ) )
=> ( ( hAPP @ D @ ( hAPP @ C @ A ) )
= ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(129,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A ) ) @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__nonzero) ).
thf(3139,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)],[129]) ).
thf(835,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Un__disjoint) ).
thf(5873,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(1664,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Int__distrib) ).
thf(8946,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1664]) ).
thf(1701,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_SetInterval_Oord_OatLeastAtMost @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) )
<=> ( ( C = B )
& ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeastAtMost__singleton__iff) ).
thf(9060,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( c_SetInterval_Oord_OatLeastAtMost @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) )
=> ( ( C = B )
& ( B = A ) ) )
& ( ( ( C = B )
& ( B = A ) )
=> ( ( c_SetInterval_Oord_OatLeastAtMost @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1701]) ).
thf(2579,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/sandbox/benchmark/theBenchmark.p',fact_part__equivp__symp) ).
thf(12343,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)],[2579]) ).
thf(538,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/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono2) ).
thf(4698,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)],[538]) ).
thf(1324,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_List_Opartition @ C @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( c_List_Ofilter @ C @ B ) @ A ) ) @ ( hAPP @ ( c_List_Ofilter @ C @ ( hAPP @ ( c_Fun_Ocomp @ tc_HOL_Obool @ tc_HOL_Obool @ C @ c_fNot ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partition__filter__conv) ).
thf(7676,plain,
! [A: $i,B: $i,C: $i] :
( ( c_List_Opartition @ C @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( c_List_Ofilter @ C @ B ) @ A ) ) @ ( hAPP @ ( c_List_Ofilter @ C @ ( hAPP @ ( c_Fun_Ocomp @ tc_HOL_Obool @ tc_HOL_Obool @ C @ c_fNot ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1324]) ).
thf(1131,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_List_Olist @ A ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_List_Olist @ A ) @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_infinite__UNIV__listI) ).
thf(6965,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_List_Olist @ A ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_List_Olist @ A ) @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).
thf(1968,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/sandbox/benchmark/theBenchmark.p',fact_Not__Domain__rtrancl) ).
thf(10082,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)],[1968]) ).
thf(255,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_List_Olast @ tc_Nat_Onat @ ( c_List_Oupt @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__upt) ).
thf(3589,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_List_Olast @ tc_Nat_Onat @ ( c_List_Oupt @ B @ A ) )
= ( 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)],[255]) ).
thf(667,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__inf__iff) ).
thf(5179,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(1424,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Relation_OImage @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) @ ( c_List_Olistrel @ B @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_List_Olist @ B ) ) @ ( c_List_Olist_ONil @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_List_Olist @ B ) @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_List_Olist @ B ) ) @ ( c_List_Olist_ONil @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_List_Olist @ B ) @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__Nil) ).
thf(8028,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Relation_OImage @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) @ ( c_List_Olistrel @ B @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_List_Olist @ B ) ) @ ( c_List_Olist_ONil @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_List_Olist @ B ) @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_List_Olist @ B ) ) @ ( c_List_Olist_ONil @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_List_Olist @ B ) @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1424]) ).
thf(509,axiom,
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ ( c_SetInterval_Oord__class_OatLeast @ tc_Nat_Onat ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__atLeast__UNIV) ).
thf(4587,plain,
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ ( c_SetInterval_Oord__class_OatLeast @ tc_Nat_Onat ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(606,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/sandbox/benchmark/theBenchmark.p',fact_listrel__Nil1) ).
thf(4945,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)],[606]) ).
thf(1816,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/sandbox/benchmark/theBenchmark.p',fact_pair__lessI2) ).
thf(9527,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)],[1816]) ).
thf(1939,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
<=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__Un__eq) ).
thf(9966,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= A ) )
& ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1939]) ).
thf(2065,axiom,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_emptyE) ).
thf(10464,plain,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2065]) ).
thf(1853,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 ) ) ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ ( tc_prod @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ B ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_Nat_Onat @ D ) @ ( c_Finite__Set_Ocard @ B ) ) @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__SigmaI) ).
thf(9665,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 ) ) ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ ( tc_prod @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ B ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_Nat_Onat @ D ) @ ( c_Finite__Set_Ocard @ B ) ) @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1853]) ).
thf(1195,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oimage @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INTER__eq__Inter__image) ).
thf(7177,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_Oimage @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195]) ).
thf(1315,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ A ) )
=> ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ A ) ) @ c_FunDef_Omax__strict ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smax__emptyI) ).
thf(7627,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ A ) )
=> ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ A ) ) @ c_FunDef_Omax__strict ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1315]) ).
thf(1760,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert) ).
thf(9306,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1760]) ).
thf(1877,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__vimage__image__eq) ).
thf(9760,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1877]) ).
thf(2355,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_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ C @ C @ A ) @ B ) ) @ B ) )
=> ( ( c_Fun_Oinj__on @ C @ C @ A @ B )
=> ( ( hAPP @ ( c_Set_Oimage @ C @ C @ A ) @ B )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_endo__inj__surj) ).
thf(11530,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_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ C @ C @ A ) @ B ) ) @ B ) )
=> ( ( c_Fun_Oinj__on @ C @ C @ A @ B )
=> ( ( hAPP @ ( c_Set_Oimage @ C @ C @ A ) @ B )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2355]) ).
thf(1842,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/sandbox/benchmark/theBenchmark.p',fact_butlast__snoc) ).
thf(9628,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)],[1842]) ).
thf(557,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ E ) @ B ) @ A ) ) @ ( hAPP @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__leI) ).
thf(4763,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ E ) @ B ) @ A ) ) @ ( hAPP @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ B ) ) @ A )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__zminus) ).
thf(2870,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ B ) ) @ A )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(407,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_List_Oconcat @ C @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ ( tc_List_Olist @ C ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ ( c_List_Oconcat @ C @ B ) ) @ ( c_List_Oconcat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat__append) ).
thf(4165,plain,
! [A: $i,B: $i,C: $i] :
( ( c_List_Oconcat @ C @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ ( tc_List_Olist @ C ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ ( c_List_Oconcat @ C @ B ) ) @ ( c_List_Oconcat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(44,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 ) ) )
=> ( ( hAPP @ c_Int_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ B ) ) ) @ ( hAPP @ c_Int_Onat @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__distrib__neg) ).
thf(2828,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 ) ) )
=> ( ( hAPP @ c_Int_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ B ) ) ) @ ( hAPP @ c_Int_Onat @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(1884,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__Diff1) ).
thf(9780,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1884]) ).
thf(751,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/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
thf(5536,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)],[751]) ).
thf(2497,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( ( c_Fun_Oinj__on @ B @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ B @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__inj__surj) ).
thf(11995,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( ( c_Fun_Oinj__on @ B @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ B @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2497]) ).
thf(783,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ E ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ E ) @ B ) ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__finite2__subset) ).
thf(5660,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ E ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ E ) @ B ) ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ tc_Nat_Onat @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(711,axiom,
! [A: $i] :
( ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ c_Int_ORep__Integ @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Rep__Integ__inverse) ).
thf(5386,plain,
! [A: $i] :
( ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ c_Int_ORep__Integ @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(1309,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Set_OPow @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ C ) @ B ) ) @ ( hAPP @ ( c_Set_OPow @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__Int__eq) ).
thf(7606,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Set_OPow @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ C ) @ B ) ) @ ( hAPP @ ( c_Set_OPow @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1309]) ).
thf(471,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( c_List_Ofilter @ C @ B ) @ A ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ tc_HOL_Obool @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( c_List_Onth @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__filter__conv__card) ).
thf(4419,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( c_List_Ofilter @ C @ B ) @ A ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ tc_HOL_Obool @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( c_List_Onth @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(1252,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__Un__nat) ).
thf(7412,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1252]) ).
thf(2336,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_InterI) ).
thf(11450,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2336]) ).
thf(2147,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ c_Nat_OSuc @ B )
= ( hAPP @ c_Nat_OSuc @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Oinject) ).
thf(10774,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)],[2147]) ).
thf(981,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/sandbox/benchmark/theBenchmark.p',fact_Suc__le__eq) ).
thf(6390,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)],[981]) ).
thf(1896,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ E @ D @ C )
=> ( ! [F: $i,G: $i] :
( ( hAPP @ B @ ( hAPP @ ( hAPP @ D @ F ) @ G ) )
= ( hAPP @ ( hAPP @ D @ ( hAPP @ B @ F ) ) @ ( hAPP @ B @ G ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ A ) )
=> ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ B @ ( hAPP @ C @ A ) )
= ( hAPP @ C @ ( hAPP @ ( c_Set_Oimage @ E @ E @ B ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Ohom__commute) ).
thf(9819,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ E @ D @ C )
=> ( ! [F: $i,G: $i] :
( ( hAPP @ B @ ( hAPP @ ( hAPP @ D @ F ) @ G ) )
= ( hAPP @ ( hAPP @ D @ ( hAPP @ B @ F ) ) @ ( hAPP @ B @ G ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ A ) )
=> ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ B @ ( hAPP @ C @ A ) )
= ( hAPP @ C @ ( hAPP @ ( c_Set_Oimage @ E @ E @ B ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1896]) ).
thf(2645,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/sandbox/benchmark/theBenchmark.p',fact_remove1__idem) ).
thf(12633,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)],[2645]) ).
thf(621,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/sandbox/benchmark/theBenchmark.p',fact_one__le__mult__iff) ).
thf(4997,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)],[621]) ).
thf(2403,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ C ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF1__E) ).
thf(11681,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ C ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2403]) ).
thf(2153,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/sandbox/benchmark/theBenchmark.p',fact_pair__box_Oinject) ).
thf(10796,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)],[2153]) ).
thf(1225,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( c_Relation_ORange @ C @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
<=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__empty__iff) ).
thf(7288,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( c_Relation_ORange @ C @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) ) )
& ( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Relation_ORange @ C @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1225]) ).
thf(1668,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Orefl__on @ C @ B @ A )
<=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ C @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ C ) @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ C ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) ) ) @ D ) ) )
& ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ D ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__def_H) ).
thf(8957,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Relation_Orefl__on @ C @ B @ A )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ C @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ C ) @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ C ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) ) ) @ D ) ) )
& ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ D ) ) @ A ) ) ) ) )
& ( ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ C @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ C ) @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ C ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) ) ) @ D ) ) )
& ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ D ) ) @ A ) ) ) )
=> ( c_Relation_Orefl__on @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1668]) ).
thf(1355,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/sandbox/benchmark/theBenchmark.p',fact_o__def) ).
thf(7765,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)],[1355]) ).
thf(718,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ D )
=> ( ( C
= ( c_Inductive_Ocomplete__lattice__class_Ogfp @ D @ B ) )
=> ( ( c_Orderings_Oorder__class_Omono @ D @ D @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ A ) @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ A ) @ C ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__coinduct) ).
thf(5421,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ D )
=> ( ( C
= ( c_Inductive_Ocomplete__lattice__class_Ogfp @ D @ B ) )
=> ( ( c_Orderings_Oorder__class_Omono @ D @ D @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ A ) @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ A ) @ C ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(549,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/sandbox/benchmark/theBenchmark.p',fact_list__ball__nth) ).
thf(4738,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)],[549]) ).
thf(1627,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Int__distrib2) ).
thf(8825,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1627]) ).
thf(1220,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__empty__right) ).
thf(7271,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1220]) ).
thf(411,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ C @ B ) @ C @ ( c_Product__Type_Ofst @ C @ B ) ) @ A )
= ( hAPP @ ( c_Relation_ODomain @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__eq__Domain) ).
thf(4185,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ C @ B ) @ C @ ( c_Product__Type_Ofst @ C @ B ) ) @ A )
= ( hAPP @ ( c_Relation_ODomain @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(263,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/sandbox/benchmark/theBenchmark.p',fact_nth__append) ).
thf(3625,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)],[263]) ).
thf(1517,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ E ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ D @ E @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ E @ E ) @ D ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ E ) ) @ A ) ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__SUPR__fold__sup) ).
thf(8392,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ E ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ D @ E @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ E @ E ) @ D ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ E ) ) @ A ) ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1517]) ).
thf(294,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/sandbox/benchmark/theBenchmark.p',fact_nat__eq__add__iff1) ).
thf(3725,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)],[294]) ).
thf(846,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/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq) ).
thf(5907,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)],[846]) ).
thf(1143,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ A ) ) ) )
=> ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__cartesian__productD1) ).
thf(7007,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ A ) ) ) )
=> ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).
thf(523,axiom,
! [A: $i,B: $i] :
( ( c_Product__Type_Omap__pair @ B @ B @ A @ A @ ( c_Fun_Oid @ B ) @ ( c_Fun_Oid @ A ) )
= ( c_Fun_Oid @ ( tc_prod @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair_Oid) ).
thf(4646,plain,
! [A: $i,B: $i] :
( ( c_Product__Type_Omap__pair @ B @ B @ A @ A @ ( c_Fun_Oid @ B ) @ ( c_Fun_Oid @ A ) )
= ( c_Fun_Oid @ ( tc_prod @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(384,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) @ D ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ B ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ C ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_Nat_Onat ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_Nat_Onat ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) @ ( tc_List_Olist @ C ) ) @ ( c_COMBB @ tc_Nat_Onat @ tc_HOL_Obool @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_List_Olist @ C ) ) @ c_fequal ) @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) ) ) ) @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) ) ) @ D ) ) )
=> ( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ ( tc_List_Olist @ C ) ) ) @ B )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ ( tc_List_Olist @ C ) ) ) @ A ) )
=> ( ( ( c_List_Oconcat @ C @ B )
= ( c_List_Oconcat @ C @ A ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat__eq__concat__iff) ).
thf(4078,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) @ D ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ B ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ C ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_Nat_Onat ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_Nat_Onat ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) @ ( tc_List_Olist @ C ) ) @ ( c_COMBB @ tc_Nat_Onat @ tc_HOL_Obool @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_List_Olist @ C ) ) @ c_fequal ) @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) ) ) ) @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) ) ) @ D ) ) )
=> ( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ ( tc_List_Olist @ C ) ) ) @ B )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ ( tc_List_Olist @ C ) ) ) @ A ) )
=> ( ( ( ( c_List_Oconcat @ C @ B )
= ( c_List_Oconcat @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_List_Oconcat @ C @ B )
= ( c_List_Oconcat @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(1839,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/sandbox/benchmark/theBenchmark.p',fact_rtrancl__listrel1__eq__len) ).
thf(9615,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)],[1839]) ).
thf(1726,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ D @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ C @ C ) @ B ) @ D ) @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ C @ C ) @ B ) @ D ) @ ( hAPP @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funpow__swap1) ).
thf(9141,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ D @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ C @ C ) @ B ) @ D ) @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ C @ C ) @ B ) @ D ) @ ( hAPP @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1726]) ).
thf(2664,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fdisj__1) ).
thf(12722,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2664]) ).
thf(1610,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/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofun__comp__comm) ).
thf(8761,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)],[1610]) ).
thf(712,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/sandbox/benchmark/theBenchmark.p',fact_listrel__Cons2) ).
thf(5389,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)],[712]) ).
thf(2584,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/sandbox/benchmark/theBenchmark.p',fact_ord_OgreaterThanAtMost__iff) ).
thf(12355,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)],[2584]) ).
thf(349,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/sandbox/benchmark/theBenchmark.p',fact_in__set__conv__nth) ).
thf(3929,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)],[349]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Omap @ D @ C ) @ B ) @ ( hAPP @ ( c_List_Otl @ D ) @ A ) )
= ( hAPP @ ( c_List_Otl @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ D @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__tl) ).
thf(2792,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Omap @ D @ C ) @ B ) @ ( hAPP @ ( c_List_Otl @ D ) @ A ) )
= ( hAPP @ ( c_List_Otl @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ D @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ B ) @ ( hAPP @ ( c_List_Otl @ C ) @ A ) )
= ( hAPP @ ( c_List_Otl @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__tl) ).
thf(2907,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ B ) @ ( hAPP @ ( c_List_Otl @ C ) @ A ) )
= ( hAPP @ ( c_List_Otl @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(1098,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ C @ B ) @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__seg__image__imp__finite) ).
thf(6814,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ C @ B ) @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).
thf(2326,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/sandbox/benchmark/theBenchmark.p',fact_antisym__def) ).
thf(11412,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)],[2326]) ).
thf(1847,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/sandbox/benchmark/theBenchmark.p',fact_distinct__butlast) ).
thf(9647,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)],[1847]) ).
thf(1435,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Equiv__Relations_Oequiv @ C @ B @ A )
=> ( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ C ) @ B ) @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__quotient) ).
thf(8075,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Equiv__Relations_Oequiv @ C @ B @ A )
=> ( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ C ) @ B ) @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1435]) ).
thf(2069,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/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__onto) ).
thf(10479,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)],[2069]) ).
thf(1180,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord__eq__le__trans) ).
thf(7131,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1180]) ).
thf(1505,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ A ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ounion__inter) ).
thf(8337,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ A ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1505]) ).
thf(1103,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( c_Fun_Oinj__on @ C @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ C ) @ ( c_Equiv__Relations_Oquotient @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ C ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) @ A ) @ B )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ C ) @ B ) @ A ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__quotient__disjoint) ).
thf(6831,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( c_Fun_Oinj__on @ C @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ C ) @ ( c_Equiv__Relations_Oquotient @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ C ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) @ A ) @ B )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ C ) @ B ) @ A ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).
thf(2631,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/sandbox/benchmark/theBenchmark.p',fact_DomainP_Oequations) ).
thf(12574,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)],[2631]) ).
thf(187,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/sandbox/benchmark/theBenchmark.p',fact_pos__zmult__eq__1__iff) ).
thf(3336,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)],[187]) ).
thf(817,axiom,
( ( hAPP @ ( c_SetInterval_Oord__class_OgreaterThan @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ tc_Nat_Onat @ c_Nat_OSuc ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThan__0) ).
thf(5813,plain,
( ( hAPP @ ( c_SetInterval_Oord__class_OgreaterThan @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ tc_Nat_Onat @ c_Nat_OSuc ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(2054,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/sandbox/benchmark/theBenchmark.p',fact_takeWhile__tail) ).
thf(10428,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)],[2054]) ).
thf(1332,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/sandbox/benchmark/theBenchmark.p',fact_fun__upd__twist) ).
thf(7700,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)],[1332]) ).
thf(1344,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/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__fun__comm) ).
thf(7732,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)],[1344]) ).
thf(1404,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E
= ( c_Inductive_Ocomplete__lattice__class_Ogfp @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Set_OCollect @ D ) ) @ C ) ) )
=> ( ( c_Orderings_Oorder__class_Omono @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Set_OCollect @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ A ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ E ) ) @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__Collect__coinduct) ).
thf(7950,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E
= ( c_Inductive_Ocomplete__lattice__class_Ogfp @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Set_OCollect @ D ) ) @ C ) ) )
=> ( ( c_Orderings_Oorder__class_Omono @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Set_OCollect @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ A ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ E ) ) @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1404]) ).
thf(1967,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/sandbox/benchmark/theBenchmark.p',fact_filter__empty__conv) ).
thf(10072,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)],[1967]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Enum_On__lists @ C @ ( hAPP @ c_Nat_OSuc @ B ) @ A )
= ( c_List_Oconcat @ ( tc_List_Olist @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_List_Olist @ C ) ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ ( tc_List_Olist @ C ) ) ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Omap @ C @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( c_COMBC @ C @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olist_OCons @ C ) ) ) ) @ A ) ) @ ( c_Enum_On__lists @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__lists_Osimps_I2_J) ).
thf(2707,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Enum_On__lists @ C @ ( hAPP @ c_Nat_OSuc @ B ) @ A )
= ( c_List_Oconcat @ ( tc_List_Olist @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_List_Olist @ C ) ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ ( tc_List_Olist @ C ) ) ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Omap @ C @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( c_COMBC @ C @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olist_OCons @ C ) ) ) ) @ A ) ) @ ( c_Enum_On__lists @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(2515,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/sandbox/benchmark/theBenchmark.p',fact_ord_OatLeast__iff) ).
thf(12066,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)],[2515]) ).
thf(1099,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/sandbox/benchmark/theBenchmark.p',fact_R__O__Id) ).
thf(6818,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)],[1099]) ).
thf(1746,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Omax__extp @ D @ C @ B @ A )
<=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) )
& ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ F ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__extp_Osimps) ).
thf(9234,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Wellfounded_Omax__extp @ D @ C @ B @ A )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) )
& ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ F ) ) ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) )
& ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ F ) ) ) ) )
=> ( c_Wellfounded_Omax__extp @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1746]) ).
thf(971,axiom,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OgreaterThan @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OgreaterThan @ tc_Nat_Onat ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThan__Suc) ).
thf(6341,plain,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OgreaterThan @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OgreaterThan @ tc_Nat_Onat ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(230,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) ) @ C ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ A ) @ B ) )
= ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) ) @ C ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) ) @ C ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ A ) @ B ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__minus__const__atLeastLessThan__nat) ).
thf(3484,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) ) @ C ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ A ) @ B ) )
= ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ C ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) ) @ C ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) ) @ C ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ A ) @ B ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(289,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/sandbox/benchmark/theBenchmark.p',fact_nth__drop) ).
thf(3709,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)],[289]) ).
thf(1615,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Int__distrib1) ).
thf(8780,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1615]) ).
thf(320,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/sandbox/benchmark/theBenchmark.p',fact_upt__0) ).
thf(3825,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)],[320]) ).
thf(1238,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/sandbox/benchmark/theBenchmark.p',fact_wf__lex__prod) ).
thf(7359,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)],[1238]) ).
thf(515,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ E @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ E @ ( hAPP @ ( c_Product__Type_Osnd @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ A ) @ C ) @ D ) ) ) @ ( hAPP @ ( c_Product__Type_Ofst @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ A ) @ C ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_exI__realizer) ).
thf(4615,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ E @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ E @ ( hAPP @ ( c_Product__Type_Osnd @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ A ) @ C ) @ D ) ) ) @ ( hAPP @ ( c_Product__Type_Ofst @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ A ) @ C ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(1936,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Predicate_Oconversep @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( c_Predicate_Oconversep @ D @ C @ B ) ) @ ( c_Predicate_Oconversep @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__join) ).
thf(9951,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Predicate_Oconversep @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( c_Predicate_Oconversep @ D @ C @ B ) ) @ ( c_Predicate_Oconversep @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1936]) ).
thf(1063,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ F ) @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( c_Fun_Obij__betw @ G @ D @ A @ F @ C )
=> ( ( c_Fun_Obij__betw @ G @ D @ A @ E @ B )
=> ( c_Fun_Obij__betw @ G @ D @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ F ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__Disj__Un) ).
thf(6689,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ F ) @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( c_Fun_Obij__betw @ G @ D @ A @ F @ C )
=> ( ( c_Fun_Obij__betw @ G @ D @ A @ E @ B )
=> ( c_Fun_Obij__betw @ G @ D @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ F ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).
thf(624,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ B ) ) @ ( c_List_Olists @ D @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ D ) ) @ C ) @ ( c_List_Olists @ D @ A ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ D ) ) @ B ) @ ( c_List_Olists @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__in__lists__conv) ).
thf(5008,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ B ) ) @ ( c_List_Olists @ D @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ D ) ) @ C ) @ ( c_List_Olists @ D @ A ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ D ) ) @ B ) @ ( c_List_Olists @ D @ A ) ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ D ) ) @ C ) @ ( c_List_Olists @ D @ A ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ D ) ) @ B ) @ ( c_List_Olists @ D @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ B ) ) @ ( c_List_Olists @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(385,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/sandbox/benchmark/theBenchmark.p',fact_list__eq__iff__nth__eq) ).
thf(4089,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)],[385]) ).
thf(1420,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A )
= A ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I1_J) ).
thf(8011,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A )
= A ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1420]) ).
thf(670,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ D @ tc_Nat_Onat ) @ D ) @ ( c_Product__Type_Ofst @ D @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_List_Ofilter @ ( tc_prod @ D @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_prod @ D @ tc_Nat_Onat ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_prod @ D @ tc_Nat_Onat ) ) @ ( c_member @ tc_Nat_Onat ) ) @ ( c_Product__Type_Osnd @ D @ tc_Nat_Onat ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ D @ tc_Nat_Onat ) @ B ) @ ( c_List_Oupt @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ B ) ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ D @ tc_Nat_Onat ) @ D ) @ ( c_Product__Type_Ofst @ D @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_List_Ofilter @ ( tc_prod @ D @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_prod @ D @ tc_Nat_Onat ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_prod @ D @ tc_Nat_Onat ) ) @ ( c_member @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_prod @ D @ tc_Nat_Onat ) @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ D @ tc_Nat_Onat ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) ) @ ( c_Product__Type_Osnd @ D @ tc_Nat_Onat ) ) ) @ A ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ D @ tc_Nat_Onat ) @ B ) @ ( c_List_Oupt @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__shift__lemma) ).
thf(5191,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ D @ tc_Nat_Onat ) @ D ) @ ( c_Product__Type_Ofst @ D @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_List_Ofilter @ ( tc_prod @ D @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_prod @ D @ tc_Nat_Onat ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_prod @ D @ tc_Nat_Onat ) ) @ ( c_member @ tc_Nat_Onat ) ) @ ( c_Product__Type_Osnd @ D @ tc_Nat_Onat ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ D @ tc_Nat_Onat ) @ B ) @ ( c_List_Oupt @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ B ) ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ D @ tc_Nat_Onat ) @ D ) @ ( c_Product__Type_Ofst @ D @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_List_Ofilter @ ( tc_prod @ D @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_prod @ D @ tc_Nat_Onat ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_prod @ D @ tc_Nat_Onat ) ) @ ( c_member @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_prod @ D @ tc_Nat_Onat ) @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ D @ tc_Nat_Onat ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) ) @ ( c_Product__Type_Osnd @ D @ tc_Nat_Onat ) ) ) @ A ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ D @ tc_Nat_Onat ) @ B ) @ ( c_List_Oupt @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(2002,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
=> ( ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ E ) @ F ) ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( c_Wellfounded_Omax__ext @ D @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ext_Ointros) ).
thf(10225,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
=> ( ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ E ) @ F ) ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( c_Wellfounded_Omax__ext @ D @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2002]) ).
thf(2223,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ B @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__f__inv__f) ).
thf(11039,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ B @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2223]) ).
thf(654,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/sandbox/benchmark/theBenchmark.p',fact_pair__lessI1) ).
thf(5132,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)],[654]) ).
thf(1415,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ ( hAPP @ ( c_Set_Oimage @ D @ E @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Set_Oimage @ D @ B @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ B @ D ) @ A ) @ C ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__range__imageI) ).
thf(7996,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ ( hAPP @ ( c_Set_Oimage @ D @ E @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Set_Oimage @ D @ B @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ B @ D ) @ A ) @ C ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1415]) ).
thf(2514,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/sandbox/benchmark/theBenchmark.p',fact_split__paired__All) ).
thf(12061,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)],[2514]) ).
thf(1690,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__insert) ).
thf(9029,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1690]) ).
thf(2033,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Set_OPow @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__top) ).
thf(10352,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Set_OPow @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2033]) ).
thf(2588,axiom,
! [A: $i,B: $i] :
( ( B != A )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__2) ).
thf(12370,plain,
! [A: $i,B: $i] :
( ( B != A )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2588]) ).
thf(1145,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_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff__subset) ).
thf(7012,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_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).
thf(2203,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/sandbox/benchmark/theBenchmark.p',fact_prod__caseI) ).
thf(10969,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)],[2203]) ).
thf(394,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ E @ D @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ B @ ( hAPP @ ( c_Product__Type_Ofst @ E @ D ) @ A ) ) @ ( hAPP @ ( c_Product__Type_Osnd @ E @ D ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__def) ).
thf(4126,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ E @ D @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ B @ ( hAPP @ ( c_Product__Type_Ofst @ E @ D ) @ A ) ) @ ( hAPP @ ( c_Product__Type_Osnd @ E @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(1090,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/sandbox/benchmark/theBenchmark.p',fact_converse__rel__comp) ).
thf(6790,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)],[1090]) ).
thf(1192,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( c_member @ tc_Nat_Onat ) ) @ c_Nat_OSuc ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ A ) ) ) ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ tc_Nat_Onat ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__less__Suc) ).
thf(7167,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( c_member @ tc_Nat_Onat ) ) @ c_Nat_OSuc ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ A ) ) ) ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ tc_Nat_Onat ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1192]) ).
thf(372,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ E ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ E ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP__subset) ).
thf(4042,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ E ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ E ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(1654,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/sandbox/benchmark/theBenchmark.p',fact_dropWhile__eq__Cons__conv) ).
thf(8912,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)],[1654]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__left__commute) ).
thf(2811,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)],[39]) ).
thf(1931,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/sandbox/benchmark/theBenchmark.p',fact_listrelp_OCons) ).
thf(9934,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)],[1931]) ).
thf(362,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/sandbox/benchmark/theBenchmark.p',fact_add__is__1) ).
thf(3991,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)],[362]) ).
thf(1119,axiom,
! [A: $i] :
( ( hAPP @ ( c_Set_OPow @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__UNIV) ).
thf(6913,plain,
! [A: $i] :
( ( hAPP @ ( c_Set_OPow @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).
thf(80,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 ) @ B ) @ A ) )
=> ( ( hAPP @ c_Int_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ A ) ) @ ( hAPP @ c_Int_Onat @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__distrib) ).
thf(2971,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 ) @ B ) @ A ) )
=> ( ( hAPP @ c_Int_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ A ) ) @ ( hAPP @ c_Int_Onat @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(2209,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__mono) ).
thf(11001,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2209]) ).
thf(1118,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__UNIV__left) ).
thf(6910,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).
thf(1580,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ D ) )
=> ( c_Fun_Oinj__on @ C @ B @ A @ E ) )
=> ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__Inter) ).
thf(8634,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ D ) )
=> ( c_Fun_Oinj__on @ C @ B @ A @ E ) )
=> ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1580]) ).
thf(2049,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/sandbox/benchmark/theBenchmark.p',fact_rtrancl__into__trancl2) ).
thf(10411,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)],[2049]) ).
thf(1990,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( class_Enum_Oenum @ C )
& ( class_Enum_Oenum @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__all @ ( tc_prod @ B @ C ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__all @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool @ B ) @ ( c_Enum_Oenum__class_Oenum__all @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ B @ C ) ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ B @ C ) @ tc_HOL_Obool @ C ) @ A ) ) @ ( c_Product__Type_OPair @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_enum__all__prod__def) ).
thf(10182,plain,
! [A: $i,B: $i,C: $i] :
( ( ( class_Enum_Oenum @ C )
& ( class_Enum_Oenum @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__all @ ( tc_prod @ B @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__all @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool @ B ) @ ( c_Enum_Oenum__class_Oenum__all @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ B @ C ) ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ B @ C ) @ tc_HOL_Obool @ C ) @ A ) ) @ ( c_Product__Type_OPair @ B @ C ) ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__all @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool @ B ) @ ( c_Enum_Oenum__class_Oenum__all @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ B @ C ) ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ B @ C ) @ tc_HOL_Obool @ C ) @ A ) ) @ ( c_Product__Type_OPair @ B @ C ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__all @ ( tc_prod @ B @ C ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1990]) ).
thf(1648,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I5_J) ).
thf(8897,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1648]) ).
thf(91,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/sandbox/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib) ).
thf(3003,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)],[91]) ).
thf(713,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/sandbox/benchmark/theBenchmark.p',fact_card__distinct) ).
thf(5394,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)],[713]) ).
thf(24,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 ) )
=> ( ( hAPP @ c_Int_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ B ) ) @ ( hAPP @ c_Int_Onat @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__distrib) ).
thf(2764,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 ) )
=> ( ( hAPP @ c_Int_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ B ) ) @ ( hAPP @ c_Int_Onat @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(364,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/sandbox/benchmark/theBenchmark.p',fact_mult__less__mono1) ).
thf(4010,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)],[364]) ).
thf(2395,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ A ) ) )
=> ( ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__vimageD) ).
thf(11663,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ A ) ) )
=> ( ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2395]) ).
thf(1898,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( c_Hoare__Mirabelle_Ohoare__derivs @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_asm) ).
thf(9824,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( c_Hoare__Mirabelle_Ohoare__derivs @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1898]) ).
thf(574,axiom,
! [A: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ A )
=> ( ( c_Complete__Lattice_OInf__class_OInf @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__empty) ).
thf(4834,plain,
! [A: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ A )
=> ( ( c_Complete__Lattice_OInf__class_OInf @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(491,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Groups_Ocomm__monoid__mult @ F )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ D ) )
=> ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ G ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ B @ G ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ F @ E @ ( c_Groups_Otimes__class_Otimes @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ C @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ F @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ F ) @ ( tc_fun @ F @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ F ) ) @ E ) @ ( c_Finite__Set_Ofold__image @ F @ C @ ( c_Groups_Otimes__class_Otimes @ F ) ) ) @ A ) ) @ ( c_Groups_Oone__class_Oone @ F ) ) ) @ B ) ) @ ( c_Groups_Oone__class_Oone @ F ) ) @ D )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ F @ ( tc_prod @ E @ C ) @ ( c_Groups_Otimes__class_Otimes @ F ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ E @ C @ F ) @ A ) ) @ ( c_Groups_Oone__class_Oone @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ C ) @ D ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__Sigma) ).
thf(4495,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Groups_Ocomm__monoid__mult @ F )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ D ) )
=> ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ G ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ B @ G ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ F @ E @ ( c_Groups_Otimes__class_Otimes @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ C @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ F @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ F ) @ ( tc_fun @ F @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ F ) ) @ E ) @ ( c_Finite__Set_Ofold__image @ F @ C @ ( c_Groups_Otimes__class_Otimes @ F ) ) ) @ A ) ) @ ( c_Groups_Oone__class_Oone @ F ) ) ) @ B ) ) @ ( c_Groups_Oone__class_Oone @ F ) ) @ D )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ F @ ( tc_prod @ E @ C ) @ ( c_Groups_Otimes__class_Otimes @ F ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ E @ C @ F ) @ A ) ) @ ( c_Groups_Oone__class_Oone @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ C ) @ D ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(641,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_List_Oconcat @ C @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ ( tc_List_Olist @ C ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ B ) @ ( c_List_Oconcat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat_Osimps_I2_J) ).
thf(5087,plain,
! [A: $i,B: $i,C: $i] :
( ( c_List_Oconcat @ C @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ ( tc_List_Olist @ C ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ B ) @ ( c_List_Oconcat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(1973,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/sandbox/benchmark/theBenchmark.p',fact_remove1__filter__not) ).
thf(10104,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)],[1973]) ).
thf(1176,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ H @ G ) @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ H @ G ) @ E ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ G @ tc_HOL_Obool ) @ H ) @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ G @ C ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ G @ C ) @ D ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ G ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ H @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ H @ G @ C ) @ F ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ H @ C ) @ E ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ H ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__subset__Sigma) ).
thf(7120,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ H @ G ) @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ H @ G ) @ E ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ G @ tc_HOL_Obool ) @ H ) @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ G @ C ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ G @ C ) @ D ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ G ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ H @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ H @ G @ C ) @ F ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ H @ C ) @ E ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ H ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176]) ).
thf(1042,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ C @ C @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ C @ C @ C ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ A ) @ B ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__commute) ).
thf(6618,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ C @ C @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ C @ C @ C ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ A ) @ B ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(332,axiom,
! [A: $i] :
( ( hAPP @ c_Int_Onat @ A )
= ( c_Set_Othe__elem @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ c_Int_ORep__Integ @ A ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ tc_Nat_Onat @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ tc_Nat_Onat ) @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( c_Set_Oinsert @ tc_Nat_Onat ) ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__def) ).
thf(3859,plain,
! [A: $i] :
( ( hAPP @ c_Int_Onat @ A )
= ( c_Set_Othe__elem @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ c_Int_ORep__Integ @ A ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ tc_Nat_Onat @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ tc_Nat_Onat ) @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( c_Set_Oinsert @ tc_Nat_Onat ) ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(12835,plain,
( ( ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ sk2 )
!= ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ sk2 ) )
| ( v_ts != v_G ) ),
inference(simp,[status(thm)],[12809]) ).
thf(12836,plain,
v_ts != v_G,
inference(simp,[status(thm)],[12835]) ).
thf(1795,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_OCollect @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_HOL_OEx @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBS @ D @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool @ D ) ) @ c_fequal ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__eq) ).
thf(9449,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( c_Set_OCollect @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_HOL_OEx @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBS @ D @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool @ D ) ) @ c_fequal ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1795]) ).
thf(1178,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__left__commute) ).
thf(7125,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178]) ).
thf(196,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 ) )
=> ( ( hAPP @ c_Int_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ B ) ) @ ( hAPP @ c_Int_Onat @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__distrib) ).
thf(3368,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 ) )
=> ( ( hAPP @ c_Int_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ B ) ) @ ( hAPP @ c_Int_Onat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(2590,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/sandbox/benchmark/theBenchmark.p',fact_insert__ident) ).
thf(12387,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)],[2590]) ).
thf(1438,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/sandbox/benchmark/theBenchmark.p',fact_add__leD1) ).
thf(8083,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)],[1438]) ).
thf(612,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/sandbox/benchmark/theBenchmark.p',fact_nth__Cons__Suc) ).
thf(4969,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)],[612]) ).
thf(274,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/sandbox/benchmark/theBenchmark.p',fact_listrel__Cons1) ).
thf(3662,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)],[274]) ).
thf(1406,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/sandbox/benchmark/theBenchmark.p',fact_Nil__is__map__conv) ).
thf(7959,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)],[1406]) ).
thf(2214,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/sandbox/benchmark/theBenchmark.p',fact_tranclD) ).
thf(11013,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)],[2214]) ).
thf(2109,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Diff) ).
thf(10627,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2109]) ).
thf(1093,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ F @ B ) @ A ) )
= ( hAPP @ ( c_Set_Oimage @ C @ E @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ E @ C ) @ D ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__image) ).
thf(6799,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ F @ B ) @ A ) )
= ( hAPP @ ( c_Set_Oimage @ C @ E @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ E @ C ) @ D ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).
thf(1870,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/sandbox/benchmark/theBenchmark.p',fact_congruent2D) ).
thf(9736,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)],[1870]) ).
thf(2673,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/sandbox/benchmark/theBenchmark.p',fact_notin__set__remove1) ).
thf(12758,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)],[2673]) ).
thf(2009,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Finite__Set_Ofold1 @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__singleton) ).
thf(10268,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Finite__Set_Ofold1 @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2009]) ).
thf(1961,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/sandbox/benchmark/theBenchmark.p',fact_take__map) ).
thf(10050,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)],[1961]) ).
thf(768,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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 ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) ) @ c_Int_Ointrel ) )
<=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_intrel__iff) ).
thf(5600,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( 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 ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) ) @ c_Int_Ointrel ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) ) )
& ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ 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 ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) ) @ c_Int_Ointrel ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(1035,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
<=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INTER__UNIV__conv_I2_J) ).
thf(6584,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
& ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(849,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/sandbox/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
thf(5922,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)],[849]) ).
thf(2476,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( c_Predicate_OPowp @ C @ B ) ) @ ( c_Predicate_OPowp @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Powp__mono) ).
thf(11918,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( c_Predicate_OPowp @ C @ B ) ) @ ( c_Predicate_OPowp @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2476]) ).
thf(1448,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/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).
thf(8119,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)],[1448]) ).
thf(1948,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/sandbox/benchmark/theBenchmark.p',fact_acc_Osimps) ).
thf(9999,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)],[1948]) ).
thf(990,axiom,
! [A: $i,B: $i] : ( c_Relation_Oirrefl @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) @ ( c_Relation_OId @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_irrefl__diff__Id) ).
thf(6430,plain,
! [A: $i,B: $i] : ( c_Relation_Oirrefl @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) @ ( c_Relation_OId @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(444,axiom,
c_FunDef_Oreduction__pair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) ) @ c_FunDef_Omin__strict ) @ c_FunDef_Omin__weak ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__rpair__set) ).
thf(4321,plain,
c_FunDef_Oreduction__pair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) ) @ c_FunDef_Omin__strict ) @ c_FunDef_Omin__weak ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(987,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I3_J) ).
thf(6412,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(651,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ B ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ B ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ B ) ) @ ( hAPP @ D @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Oinsert) ).
thf(5119,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ B ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ A ) @ B ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ B ) ) @ ( hAPP @ D @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(2392,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Obij__betw @ D @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__imp__surj) ).
thf(11653,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Obij__betw @ D @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2392]) ).
thf(1718,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/sandbox/benchmark/theBenchmark.p',fact_le__diff__conv2) ).
thf(9115,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)],[1718]) ).
thf(1606,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/sandbox/benchmark/theBenchmark.p',fact_add__less__mono) ).
thf(8749,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)],[1606]) ).
thf(2192,axiom,
! [A: $i] :
( ( c_Predicate_Oconversep @ A @ A @ c_fequal )
= c_fequal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_conversep__eq) ).
thf(10937,plain,
! [A: $i] :
( ( c_Predicate_Oconversep @ A @ A @ c_fequal )
= c_fequal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2192]) ).
thf(75,axiom,
! [A: $i,B: $i] :
( ( B
!= ( c_List_Olist_ONil @ A ) )
=> ( ( hAPP @ ( c_List_Ohd @ A ) @ B )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ A ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__conv__nth) ).
thf(2956,plain,
! [A: $i,B: $i] :
( ( B
!= ( c_List_Olist_ONil @ A ) )
=> ( ( hAPP @ ( c_List_Ohd @ A ) @ B )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ A ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(1380,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/sandbox/benchmark/theBenchmark.p',fact_Cons__listrel1__Cons) ).
thf(7855,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)],[1380]) ).
thf(962,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 ) ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) @ B ) @ A ) ) )
=> ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( D != C ) )
=> ~ ! [F: $i,G: $i] :
( ( B
= ( hAPP @ c_Nat_OSuc @ 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 @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ F ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) @ G ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__E2) ).
thf(6305,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 ) ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) @ B ) @ A ) ) )
=> ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( D != C ) )
=> ~ ! [F: $i,G: $i] :
( ( B
= ( hAPP @ c_Nat_OSuc @ 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 @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ F ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) @ G ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(524,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/sandbox/benchmark/theBenchmark.p',fact_listrel__rtrancl__eq__rtrancl__listrel1) ).
thf(4649,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)],[524]) ).
thf(1106,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/sandbox/benchmark/theBenchmark.p',fact_append__is__Nil__conv) ).
thf(6854,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)],[1106]) ).
thf(2161,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__lower) ).
thf(10828,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2161]) ).
thf(983,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_Oconverse @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_Oconverse @ D @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__Un) ).
thf(6397,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_Oconverse @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_Oconverse @ D @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(232,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/sandbox/benchmark/theBenchmark.p',fact_listrel__sym) ).
thf(3497,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)],[232]) ).
thf(403,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/sandbox/benchmark/theBenchmark.p',fact_diff__mult__distrib2) ).
thf(4153,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)],[403]) ).
thf(1515,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Osym @ C @ B )
=> ( ( c_Relation_Osym @ C @ A )
=> ( c_Relation_Osym @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sym__Un) ).
thf(8388,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Osym @ C @ B )
=> ( ( c_Relation_Osym @ C @ A )
=> ( c_Relation_Osym @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1515]) ).
thf(327,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_Onth @ B ) @ ( hAPP @ ( c_List_Orev @ B ) @ A ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) @ ( hAPP @ c_Nat_OSuc @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__nth) ).
thf(3844,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_Onth @ B ) @ ( hAPP @ ( c_List_Orev @ B ) @ A ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) @ ( hAPP @ c_Nat_OSuc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(1547,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( c_Set_Oimage @ D @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Union) ).
thf(8501,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ ( c_Set_Oimage @ D @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1547]) ).
thf(212,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ tc_Nat_Onat ) @ C ) @ A ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__diff) ).
thf(3430,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ tc_Nat_Onat ) @ C ) @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(790,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ F )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ F ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ F ) @ F @ E ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ F ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ F ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ F ) @ F @ C ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ F ) @ D ) ) @ ( hAPP @ ( c_COMBC @ E @ C @ F ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__commute) ).
thf(5692,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ F )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ F ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ F ) @ F @ E ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ F ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ F ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ F ) @ F @ C ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ F ) @ D ) ) @ ( hAPP @ ( c_COMBC @ E @ C @ F ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(511,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
thf(4591,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(1921,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DiffE) ).
thf(9908,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1921]) ).
thf(2520,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ C @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Respects__def) ).
thf(12080,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2520]) ).
thf(871,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/sandbox/benchmark/theBenchmark.p',fact_split__conv) ).
thf(6018,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)],[871]) ).
thf(1886,axiom,
! [A: $i,B: $i] :
( ( c_Hilbert__Choice_OEps @ B @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ B @ tc_HOL_Obool ) @ c_fequal ) @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_some__eq__trivial) ).
thf(9792,plain,
! [A: $i,B: $i] :
( ( c_Hilbert__Choice_OEps @ B @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ B @ tc_HOL_Obool ) @ c_fequal ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1886]) ).
thf(1472,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ D ) @ C ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ C ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ A ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ D ) @ C ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__times__insert) ).
thf(8203,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ D ) @ C ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ C ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ A ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ D ) @ C ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1472]) ).
thf(560,axiom,
! [A: $i,B: $i] :
( ( ( c_List_Olist_ONil @ B )
= ( hAPP @ ( c_List_Orev @ B ) @ A ) )
<=> ( A
= ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nil__is__rev__conv) ).
thf(4774,plain,
! [A: $i,B: $i] :
( ( ( ( c_List_Olist_ONil @ B )
= ( hAPP @ ( c_List_Orev @ B ) @ A ) )
=> ( A
= ( c_List_Olist_ONil @ B ) ) )
& ( ( A
= ( c_List_Olist_ONil @ B ) )
=> ( ( c_List_Olist_ONil @ B )
= ( hAPP @ ( c_List_Orev @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(1792,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( ( D != E )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__partition) ).
thf(9434,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( ( D != E )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1792]) ).
thf(1495,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ 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 ) ) @ ( hAPP @ ( c_List_Ofilter @ C @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ C ) @ c_fNot ) @ B ) ) @ A ) ) )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__length__filter__compl) ).
thf(8304,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ 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 ) ) @ ( hAPP @ ( c_List_Ofilter @ C @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ C ) @ c_fNot ) @ B ) ) @ A ) ) )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1495]) ).
thf(631,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ D )
=> ( ( C
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ D ) @ C ) @ ( hAPP @ ( c_COMBK @ D @ B ) @ A ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__const) ).
thf(5040,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ D )
=> ( ( C
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ D ) @ C ) @ ( hAPP @ ( c_COMBK @ D @ B ) @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(825,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_Olist__update @ C @ B ) @ D ) @ A )
= B )
<=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ B ) @ D )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__same__conv) ).
thf(5837,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_Olist__update @ C @ B ) @ D ) @ A )
= B )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ B ) @ D )
= A ) )
& ( ( ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ B ) @ D )
= A )
=> ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ C @ B ) @ D ) @ A )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(1349,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ ( c_List_Olist_ONil @ B ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__Nil) ).
thf(7747,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)],[1349]) ).
thf(2427,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/sandbox/benchmark/theBenchmark.p',fact_card__insert__if) ).
thf(11755,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)],[2427]) ).
thf(2394,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/sandbox/benchmark/theBenchmark.p',fact_comm__monoid__big_OF__eq) ).
thf(11658,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)],[2394]) ).
thf(132,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/sandbox/benchmark/theBenchmark.p',fact_finite__atLeastZeroLessThan__int) ).
thf(3149,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)],[132]) ).
thf(339,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/sandbox/benchmark/theBenchmark.p',fact_id__take__nth__drop) ).
thf(3896,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)],[339]) ).
thf(2315,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/sandbox/benchmark/theBenchmark.p',fact_single__valued__def) ).
thf(11366,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)],[2315]) ).
thf(462,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ A ) @ C ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__infI2) ).
thf(4387,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ A ) @ C ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(2323,axiom,
class_Enum_Oenum @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Enum_Oenum) ).
thf(11405,plain,
class_Enum_Oenum @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2323]) ).
thf(486,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ E @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ C ) @ B ) ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ D ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__length) ).
thf(4478,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ E @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ C ) @ B ) ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ D ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(952,axiom,
c_Wellfounded_Owf @ tc_Nat_Onat @ c_Wellfounded_Opred__nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__pred__nat) ).
thf(6277,plain,
c_Wellfounded_Owf @ tc_Nat_Onat @ c_Wellfounded_Opred__nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(2641,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/sandbox/benchmark/theBenchmark.p',fact_semilattice__big_OF__eq) ).
thf(12620,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)],[2641]) ).
thf(2261,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/sandbox/benchmark/theBenchmark.p',fact_in__set__butlast__appendI) ).
thf(11172,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)],[2261]) ).
thf(1385,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I4_J) ).
thf(7887,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1385]) ).
thf(2603,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ c_fequal @ A ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__mem) ).
thf(12448,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)],[2603]) ).
thf(2656,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/sandbox/benchmark/theBenchmark.p',fact_part__equivp__def) ).
thf(12675,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)],[2656]) ).
thf(1965,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__subset__eq) ).
thf(10065,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1965]) ).
thf(1444,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( c_Equiv__Relations_Oequiv @ J @ I @ H )
=> ( ( c_Equiv__Relations_Oequiv @ G @ F @ E )
=> ( ( c_Equiv__Relations_Ocongruent2 @ J @ G @ ( tc_fun @ D @ tc_HOL_Obool ) @ H @ E @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ J ) @ B ) @ I ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ A ) @ F ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ J @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ J @ J @ H ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ J ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ J @ tc_HOL_Obool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ G @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ J ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ G @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ G @ G @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) ) ) @ C ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__equiv__class2) ).
thf(8102,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( c_Equiv__Relations_Oequiv @ J @ I @ H )
=> ( ( c_Equiv__Relations_Oequiv @ G @ F @ E )
=> ( ( c_Equiv__Relations_Ocongruent2 @ J @ G @ ( tc_fun @ D @ tc_HOL_Obool ) @ H @ E @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ J ) @ B ) @ I ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ A ) @ F ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ J @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ J @ J @ H ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ J ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ J @ tc_HOL_Obool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ G @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ J ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ G @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ G @ G @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) ) ) @ C ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1444]) ).
thf(916,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ A ) ) @ c_FunDef_Omax__weak ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wmax__emptyI) ).
thf(6166,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ A ) ) @ c_FunDef_Omax__weak ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(2405,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_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ A ) @ C ) )
=> ( ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__image__Int) ).
thf(11685,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_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ A ) @ C ) )
=> ( ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2405]) ).
thf(2523,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/sandbox/benchmark/theBenchmark.p',fact_image__iff) ).
thf(12093,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)],[2523]) ).
thf(1288,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Ozip @ G @ F ) @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ G @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ F @ B ) @ D ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ ( tc_prod @ G @ F ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ G @ F ) @ E ) @ B ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__update) ).
thf(7530,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Ozip @ G @ F ) @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ G @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ F @ B ) @ D ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ ( tc_prod @ G @ F ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ G @ F ) @ E ) @ B ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1288]) ).
thf(2493,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/sandbox/benchmark/theBenchmark.p',fact_Id__onE) ).
thf(11982,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)],[2493]) ).
thf(765,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
thf(5590,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(1743,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_prod @ H @ G ) @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ H @ G ) @ D ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ G @ tc_HOL_Obool ) @ H ) @ C ) ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ H @ G @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ H @ ( tc_fun @ G @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ ( tc_fun @ G @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ G @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ ( tc_fun @ G @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) ) @ H ) @ ( c_COMBB @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ G ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ H ) @ ( c_Product__Type_OSigma @ F @ E ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ G ) @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) ) @ A ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ H @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ D ) @ B ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ G @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__Times__distrib) ).
thf(9211,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_prod @ H @ G ) @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ H @ G ) @ D ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ G @ tc_HOL_Obool ) @ H ) @ C ) ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ H @ G @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ H @ ( tc_fun @ G @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ ( tc_fun @ G @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ G @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ ( tc_fun @ G @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) ) @ H ) @ ( c_COMBB @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ G ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ H ) @ ( c_Product__Type_OSigma @ F @ E ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ G ) @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) ) @ A ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ F @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ H @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ D ) @ B ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ G @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1743]) ).
thf(2187,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Obij__betw @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ C @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__is__surj) ).
thf(10924,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Obij__betw @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ C @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2187]) ).
thf(1032,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/sandbox/benchmark/theBenchmark.p',fact_trancl__range) ).
thf(6569,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)],[1032]) ).
thf(786,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/sandbox/benchmark/theBenchmark.p',fact_le__cube) ).
thf(5672,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)],[786]) ).
thf(1600,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ B ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord__le__eq__trans) ).
thf(8721,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ B ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1600]) ).
thf(746,axiom,
! [A: $i,B: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ B )
=> ( ( c_Complete__Lattice_OSup__class_OSup @ B @ A )
= ( c_Complete__Lattice_OInf__class_OInf @ B @ ( hAPP @ ( c_Set_OCollect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool @ B ) @ ( c_HOL_OAll @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) @ B ) @ ( hAPP @ ( c_COMBS @ B @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ B ) @ c_fimplies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ B ) ) @ A ) ) ) ) @ ( hAPP @ ( c_COMBC @ B @ B @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless__eq @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__Inf) ).
thf(5517,plain,
! [A: $i,B: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ B )
=> ( ( c_Complete__Lattice_OSup__class_OSup @ B @ A )
= ( c_Complete__Lattice_OInf__class_OInf @ B @ ( hAPP @ ( c_Set_OCollect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool @ B ) @ ( c_HOL_OAll @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) @ B ) @ ( hAPP @ ( c_COMBS @ B @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ B ) @ c_fimplies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ B ) ) @ A ) ) ) ) @ ( hAPP @ ( c_COMBC @ B @ B @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless__eq @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zmult__distrib2) ).
thf(2739,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)],[16]) ).
thf(2467,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/sandbox/benchmark/theBenchmark.p',fact_finite__acyclic__wf) ).
thf(11894,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)],[2467]) ).
thf(582,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/sandbox/benchmark/theBenchmark.p',fact_upt__eq__Cons__conv) ).
thf(4869,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)],[582]) ).
thf(1733,axiom,
! [A: $i] : ( c_Wellfounded_OwfP @ A @ ( hAPP @ ( c_COMBK @ ( tc_fun @ A @ tc_HOL_Obool ) @ A ) @ ( hAPP @ ( c_COMBK @ tc_HOL_Obool @ A ) @ c_fFalse ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__empty) ).
thf(9162,plain,
! [A: $i] : ( c_Wellfounded_OwfP @ A @ ( hAPP @ ( c_COMBK @ ( tc_fun @ A @ tc_HOL_Obool ) @ A ) @ ( hAPP @ ( c_COMBK @ tc_HOL_Obool @ A ) @ c_fFalse ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1733]) ).
thf(671,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/sandbox/benchmark/theBenchmark.p',fact_le__0__eq) ).
thf(5194,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)],[671]) ).
thf(2410,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/sandbox/benchmark/theBenchmark.p',fact_le__SucI) ).
thf(11700,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)],[2410]) ).
thf(600,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ D )
=> ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ D ) @ B ) @ A )
= ( c_Complete__Lattice_OSup__class_OSup @ D @ ( hAPP @ ( c_Set_OCollect @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool @ D ) @ ( c_HOL_OEx @ ( tc_fun @ C @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_COMBS @ ( tc_fun @ C @ D ) @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_fun @ C @ D ) ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ C @ D ) @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ ( tc_fun @ C @ D ) ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_fun @ C @ D ) @ D ) @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_fun @ C @ D ) @ D ) @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBB @ D @ tc_HOL_Obool @ ( tc_fun @ C @ D ) ) ) @ c_fequal ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ C @ D ) @ C @ D ) @ ( c_COMBI @ ( tc_fun @ C @ D ) ) ) @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fun__def) ).
thf(4927,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ D )
=> ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ D ) @ B ) @ A )
= ( c_Complete__Lattice_OSup__class_OSup @ D @ ( hAPP @ ( c_Set_OCollect @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool @ D ) @ ( c_HOL_OEx @ ( tc_fun @ C @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_COMBS @ ( tc_fun @ C @ D ) @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_fun @ C @ D ) ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ C @ D ) @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ ( tc_fun @ C @ D ) ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_fun @ C @ D ) @ D ) @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_fun @ C @ D ) @ D ) @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBB @ D @ tc_HOL_Obool @ ( tc_fun @ C @ D ) ) ) @ c_fequal ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ C @ D ) @ C @ D ) @ ( c_COMBI @ ( tc_fun @ C @ D ) ) ) @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(1181,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/sandbox/benchmark/theBenchmark.p',fact_append__Cons) ).
thf(7135,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)],[1181]) ).
thf(705,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ B @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBK @ tc_Nat_Onat @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__eq__setsum) ).
thf(5336,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ B @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBK @ tc_Nat_Onat @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(2539,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/sandbox/benchmark/theBenchmark.p',fact_rp__inv__image__rp) ).
thf(12171,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)],[2539]) ).
thf(2270,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Un) ).
thf(11208,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2270]) ).
thf(832,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Olexn @ C @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ ( tc_prod @ C @ ( tc_List_Olist @ C ) ) @ ( tc_prod @ C @ ( tc_List_Olist @ C ) ) ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_Product__Type_Omap__pair @ ( tc_prod @ C @ ( tc_List_Olist @ C ) ) @ ( tc_List_Olist @ C ) @ ( tc_prod @ C @ ( tc_List_Olist @ C ) ) @ ( tc_List_Olist @ C ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ C @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olist_OCons @ C ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ C @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olist_OCons @ C ) ) ) ) @ ( c_Wellfounded_Olex__prod @ C @ ( tc_List_Olist @ C ) @ B @ ( hAPP @ ( c_List_Olexn @ C @ B ) @ A ) ) ) ) @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ C ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) @ ( tc_List_Olist @ C ) ) @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_List_Olist @ C ) ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ C ) @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_List_Olist @ C ) ) @ c_fequal ) @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ C ) @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_List_Olist @ C ) ) @ c_fequal ) @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexn_Osimps_I2_J) ).
thf(5864,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Olexn @ C @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ ( tc_prod @ C @ ( tc_List_Olist @ C ) ) @ ( tc_prod @ C @ ( tc_List_Olist @ C ) ) ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_Product__Type_Omap__pair @ ( tc_prod @ C @ ( tc_List_Olist @ C ) ) @ ( tc_List_Olist @ C ) @ ( tc_prod @ C @ ( tc_List_Olist @ C ) ) @ ( tc_List_Olist @ C ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ C @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olist_OCons @ C ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ C @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olist_OCons @ C ) ) ) ) @ ( c_Wellfounded_Olex__prod @ C @ ( tc_List_Olist @ C ) @ B @ ( hAPP @ ( c_List_Olexn @ C @ B ) @ A ) ) ) ) @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ C ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) @ ( tc_List_Olist @ C ) ) @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_List_Olist @ C ) ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ C ) @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_List_Olist @ C ) ) @ c_fequal ) @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ C ) @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_List_Olist @ C ) ) @ c_fequal ) @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) ) ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(1169,axiom,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeast @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeast @ tc_Nat_Onat ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast__Suc) ).
thf(7093,plain,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeast @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeast @ tc_Nat_Onat ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).
thf(1750,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( hAPP @ ( c_List_Oset @ C ) @ B ) ) )
=> ( ( c_List_OdropWhile @ C @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ C ) @ c_fNot ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ C @ tc_HOL_Obool ) @ c_fequal ) @ A ) ) @ ( hAPP @ ( c_List_Orev @ C ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ A ) @ ( hAPP @ ( c_List_Orev @ C ) @ ( c_List_OtakeWhile @ C @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ C ) @ c_fNot ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ C @ tc_HOL_Obool ) @ c_fequal ) @ A ) ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dropWhile__neq__rev) ).
thf(9262,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( hAPP @ ( c_List_Oset @ C ) @ B ) ) )
=> ( ( c_List_OdropWhile @ C @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ C ) @ c_fNot ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ C @ tc_HOL_Obool ) @ c_fequal ) @ A ) ) @ ( hAPP @ ( c_List_Orev @ C ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ A ) @ ( hAPP @ ( c_List_Orev @ C ) @ ( c_List_OtakeWhile @ C @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ C ) @ c_fNot ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ C @ tc_HOL_Obool ) @ c_fequal ) @ A ) ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1750]) ).
thf(2554,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/sandbox/benchmark/theBenchmark.p',fact_same__fstI) ).
thf(12230,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)],[2554]) ).
thf(1960,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ? [E: $i] :
( ( c_Fun_Oinj__on @ C @ B @ E @ D )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ C @ B @ E ) @ D ) ) @ A ) ) )
<=> ? [E: $i] :
( ( hAPP @ ( c_Set_Oimage @ B @ C @ E ) @ A )
= D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__surj) ).
thf(10041,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( ? [E: $i] :
( ( c_Fun_Oinj__on @ C @ B @ E @ D )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ C @ B @ E ) @ D ) ) @ A ) ) )
=> ? [E: $i] :
( ( hAPP @ ( c_Set_Oimage @ B @ C @ E ) @ A )
= D ) )
& ( ? [E: $i] :
( ( hAPP @ ( c_Set_Oimage @ B @ C @ E ) @ A )
= D )
=> ? [E: $i] :
( ( c_Fun_Oinj__on @ C @ B @ E @ D )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ C @ B @ E ) @ D ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1960]) ).
thf(2549,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/sandbox/benchmark/theBenchmark.p',fact_notin__set__sublistI) ).
thf(12213,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)],[2549]) ).
thf(735,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 @ ( c_List_Orev @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ C @ B ) @ D ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ C @ ( hAPP @ ( c_List_Orev @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) @ D ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__update) ).
thf(5477,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 @ ( c_List_Orev @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ C @ B ) @ D ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ C @ ( hAPP @ ( c_List_Orev @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) @ D ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(527,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/sandbox/benchmark/theBenchmark.p',fact_zero__less__diff) ).
thf(4663,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)],[527]) ).
thf(2422,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/sandbox/benchmark/theBenchmark.p',fact_Least__le) ).
thf(11744,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)],[2422]) ).
thf(199,axiom,
( ( hAPP @ c_Int_Onat @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__1) ).
thf(3379,plain,
( ( hAPP @ c_Int_Onat @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(583,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Nat_Onat_Onat__case @ C @ B @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__case__0) ).
thf(4880,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Nat_Onat_Onat__case @ C @ B @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(2165,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__inject) ).
thf(10838,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2165]) ).
thf(1319,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/sandbox/benchmark/theBenchmark.p',fact_append__eq__append__conv2) ).
thf(7649,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)],[1319]) ).
thf(2534,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fimplies__1) ).
thf(12153,plain,
! [A: $i,B: $i] :
( ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2534]) ).
thf(1165,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Int) ).
thf(7081,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).
thf(1292,axiom,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Otrancl @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ B @ B @ B ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__unfold) ).
thf(7542,plain,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Otrancl @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ B @ B @ B ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1292]) ).
thf(596,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/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
thf(4917,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)],[596]) ).
thf(2371,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/sandbox/benchmark/theBenchmark.p',fact_image__insert) ).
thf(11580,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)],[2371]) ).
thf(1587,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/sandbox/benchmark/theBenchmark.p',fact_map__pair_Ocompositionality) ).
thf(8660,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)],[1587]) ).
thf(966,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/sandbox/benchmark/theBenchmark.p',fact_insert__remdups) ).
thf(6326,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)],[966]) ).
thf(1735,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/sandbox/benchmark/theBenchmark.p',fact_trans__le__add2) ).
thf(9166,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)],[1735]) ).
thf(1255,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Relation_ORange @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_ORange @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_ORange @ D @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Un__eq) ).
thf(7419,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Relation_ORange @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_ORange @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_ORange @ D @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1255]) ).
thf(390,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mult__distrib) ).
thf(4114,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)],[390]) ).
thf(926,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__partition) ).
thf(6201,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(465,axiom,
class_Complete__Lattice_Ocomplete__lattice @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice) ).
thf(4399,plain,
class_Complete__Lattice_Ocomplete__lattice @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(541,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/sandbox/benchmark/theBenchmark.p',fact_takeWhile__eq__take__P__nth) ).
thf(4706,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)],[541]) ).
thf(311,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
<=> ( ( B = A )
| ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__cancel1) ).
thf(3785,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)],[311]) ).
thf(1890,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ball__empty) ).
thf(9806,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1890]) ).
thf(2016,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 @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__I) ).
thf(10291,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 @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2016]) ).
thf(459,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/sandbox/benchmark/theBenchmark.p',fact_card__atLeastLessThan) ).
thf(4378,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)],[459]) ).
thf(2536,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/sandbox/benchmark/theBenchmark.p',fact_pair__box_Orecs) ).
thf(12162,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)],[2536]) ).
thf(2120,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( hAPP @ c_Int_ORep__Integ @ A ) ) @ c_Int_OInteg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Rep__Integ) ).
thf(10681,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( hAPP @ c_Int_ORep__Integ @ A ) ) @ c_Int_OInteg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2120]) ).
thf(868,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/sandbox/benchmark/theBenchmark.p',fact_in__measure) ).
thf(6007,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)],[868]) ).
thf(343,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( c_List_Olist_ONil @ B ) )
=> ( ( c_List_Olast @ B @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ A ) @ C ) )
= ( c_List_Olast @ B @ A ) ) )
& ( ( C
!= ( c_List_Olist_ONil @ B ) )
=> ( ( c_List_Olast @ B @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ A ) @ C ) )
= ( c_List_Olast @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__append) ).
thf(3907,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( c_List_Olist_ONil @ B ) )
=> ( ( c_List_Olast @ B @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ A ) @ C ) )
= ( c_List_Olast @ B @ A ) ) )
& ( ( C
!= ( c_List_Olist_ONil @ B ) )
=> ( ( c_List_Olast @ B @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ A ) @ C ) )
= ( c_List_Olast @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(1470,axiom,
! [A: $i,B: $i] :
( ( ( c_List_Oremdups @ B @ A )
= A )
<=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remdups__id__iff__distinct) ).
thf(8193,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)],[1470]) ).
thf(1461,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ E @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ E @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ E @ D ) ) ) ) @ ( c_Product__Type_OPair @ E @ D ) ) ) ) ) @ C ) ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__INT__eq2) ).
thf(8162,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ E @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ E @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ E @ D ) ) ) ) @ ( c_Product__Type_OPair @ E @ D ) ) ) ) ) @ C ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ C ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ F ) @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ E @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ E @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ E @ D ) ) ) ) @ ( c_Product__Type_OPair @ E @ D ) ) ) ) ) @ C ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1461]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ B @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Oinsert__remove) ).
thf(2983,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ B @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(334,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/sandbox/benchmark/theBenchmark.p',fact_nat__diff__split) ).
thf(3865,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)],[334]) ).
thf(429,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/sandbox/benchmark/theBenchmark.p',fact_distinct__card) ).
thf(4254,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)],[429]) ).
thf(568,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
!= ( c_List_Olist_ONil @ C ) )
=> ( ( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ D ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
=> ( ( c_List_Olast @ C @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ C @ D ) @ B ) @ A ) )
= A ) )
& ( ( B
!= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ D ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
=> ( ( c_List_Olast @ C @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ C @ D ) @ B ) @ A ) )
= ( c_List_Olast @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__list__update) ).
thf(4811,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
!= ( c_List_Olist_ONil @ C ) )
=> ( ( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ D ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
=> ( ( c_List_Olast @ C @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ C @ D ) @ B ) @ A ) )
= A ) )
& ( ( B
!= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ D ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
=> ( ( c_List_Olast @ C @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ C @ D ) @ B ) @ A ) )
= ( c_List_Olast @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(1348,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/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__Suc) ).
thf(7744,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)],[1348]) ).
thf(1187,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_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff__singleton) ).
thf(7153,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_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1187]) ).
thf(2589,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/sandbox/benchmark/theBenchmark.p',fact_list__ex1__iff__raw) ).
thf(12374,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)],[2589]) ).
thf(1030,axiom,
! [A: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ ( c_Relation_OId @ A ) )
= ( c_Relation_OId @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__Id) ).
thf(6563,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)],[1030]) ).
thf(513,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/sandbox/benchmark/theBenchmark.p',fact_take__upt) ).
thf(4596,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)],[513]) ).
thf(903,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__Int__distrib1) ).
thf(6131,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ C ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ E @ D ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(1377,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/sandbox/benchmark/theBenchmark.p',fact_dropWhile__eq__Nil__conv) ).
thf(7836,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)],[1377]) ).
thf(2021,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ B @ A ) @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ B @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__mono) ).
thf(10312,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ B @ A ) @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ B @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2021]) ).
thf(1738,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A )
= A ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I2_J) ).
thf(9183,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A )
= A ) )
& ( ( E
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1738]) ).
thf(542,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__1) ).
thf(4719,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(2415,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/sandbox/benchmark/theBenchmark.p',fact_refl__onD1) ).
thf(11722,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)],[2415]) ).
thf(223,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/sandbox/benchmark/theBenchmark.p',fact_drop__upt) ).
thf(3464,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)],[223]) ).
thf(1337,axiom,
! [A: $i] : ( c_Finite__Set_Ofun__left__comm__idem @ A @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_COMBC @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem__remove) ).
thf(7712,plain,
! [A: $i] : ( c_Finite__Set_Ofun__left__comm__idem @ A @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_COMBC @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1337]) ).
thf(2051,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_Owf @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__trancl) ).
thf(10418,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)],[2051]) ).
thf(2453,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) ) @ B ) @ A ) )
<=> ! [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ ( hAPP @ B @ E ) ) @ ( hAPP @ A @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__fun__def) ).
thf(11843,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) ) @ B ) @ A ) )
=> ! [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ ( hAPP @ B @ E ) ) @ ( hAPP @ A @ E ) ) ) )
& ( ! [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ ( hAPP @ B @ E ) ) @ ( hAPP @ A @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2453]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Osemiring__0 @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ E @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__right__distrib) ).
thf(2736,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Osemiring__0 @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ E @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(2285,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Diff__insert) ).
thf(11263,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2285]) ).
thf(625,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/sandbox/benchmark/theBenchmark.p',fact_take__Suc__conv__app__nth) ).
thf(5014,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)],[625]) ).
thf(934,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ F @ E @ D ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBS__1) ).
thf(6226,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ F @ E @ D ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(1542,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__UN__distrib) ).
thf(8489,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) @ C ) @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1542]) ).
thf(682,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).
thf(5247,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(2474,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/sandbox/benchmark/theBenchmark.p',fact_trancl__into__rtrancl) ).
thf(11914,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)],[2474]) ).
thf(1903,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) )
=> ~ ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ D ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnionE) ).
thf(9844,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) )
=> ~ ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ D ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1903]) ).
thf(1764,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff2__less) ).
thf(9331,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ D ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1764]) ).
thf(2367,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Equiv__Relations_Oequiv @ G @ F @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ G ) @ F ) @ E ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ G ) @ F ) @ E ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ B ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ G @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ G ) @ B ) @ A ) ) @ E ) )
=> ( D = C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__eqI) ).
thf(11563,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Equiv__Relations_Oequiv @ G @ F @ E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ G ) @ F ) @ E ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ G ) @ F ) @ E ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ B ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ G @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ G ) @ B ) @ A ) ) @ E ) )
=> ( D = C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2367]) ).
thf(147,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ ( hAPP @ c_Int_Onat @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__less__nat__eq) ).
thf(3203,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ ( hAPP @ c_Int_Onat @ A ) ) )
=> ( 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 ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ 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 @ c_Int_Onat @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(1659,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/sandbox/benchmark/theBenchmark.p',fact_r__comp__rtrancl__eq) ).
thf(8933,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)],[1659]) ).
thf(1996,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A ) @ F ) @ E ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup2I2) ).
thf(10205,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A ) @ F ) @ E ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1996]) ).
thf(2620,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ B ) @ A ) )
| ( hBOOL @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fconj__2) ).
thf(12515,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ B ) @ A ) )
| ( hBOOL @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2620]) ).
thf(1620,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Finite__Set_Ofold__image @ D @ C @ B ) @ A )
= ( c_Finite__Set_Ofold @ C @ D @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ D @ D ) @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__def) ).
thf(8801,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Finite__Set_Ofold__image @ D @ C @ B ) @ A )
= ( c_Finite__Set_Ofold @ C @ D @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ D @ D ) @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1620]) ).
thf(1022,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl3) ).
thf(6535,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)],[1022]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ E @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ E @ E ) @ D ) @ ( c_Groups_Oplus__class_Oplus @ E ) ) @ C ) ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__addf) ).
thf(2800,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ E @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ E @ E ) @ D ) @ ( c_Groups_Oplus__class_Oplus @ E ) ) @ C ) ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(2237,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__upper2) ).
thf(11082,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2237]) ).
thf(178,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/sandbox/benchmark/theBenchmark.p',fact_finite__atLeastLessThan__int) ).
thf(3309,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)],[178]) ).
thf(359,axiom,
! [A: $i,B: $i] :
( ( c_Set_Othe__elem @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__elem__eq) ).
thf(3982,plain,
! [A: $i,B: $i] :
( ( c_Set_Othe__elem @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(95,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ A @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__diff1_H) ).
thf(3015,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ E ) @ ( hAPP @ A @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(2048,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/sandbox/benchmark/theBenchmark.p',fact_distinct__remove1__removeAll) ).
thf(10408,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)],[2048]) ).
thf(2255,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__left__if1) ).
thf(11155,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2255]) ).
thf(2483,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Equiv__Relations_Oequiv @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( hAPP @ ( c_Relation_OImage @ D @ D @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__class__self) ).
thf(11943,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Equiv__Relations_Oequiv @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( hAPP @ ( c_Relation_OImage @ D @ D @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2483]) ).
thf(1520,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ ( tc_List_Olist @ B ) ) @ A ) )
=> ( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ B ) ) @ C ) @ ( hAPP @ ( c_List_Oset @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ B ) @ C ) ) )
=> ( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ B ) ) @ C ) @ ( hAPP @ ( c_List_Oset @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ B ) ) @ D ) @ ( hAPP @ ( c_List_Oset @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ( ( C != D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ B ) @ C ) ) @ ( hAPP @ ( c_List_Oset @ B ) @ D ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ B ) @ ( c_List_Oconcat @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__concat) ).
thf(8400,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ ( tc_List_Olist @ B ) ) @ A ) )
=> ( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ B ) ) @ C ) @ ( hAPP @ ( c_List_Oset @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ B ) @ C ) ) )
=> ( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ B ) ) @ C ) @ ( hAPP @ ( c_List_Oset @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ B ) ) @ D ) @ ( hAPP @ ( c_List_Oset @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ( ( C != D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ B ) @ C ) ) @ ( hAPP @ ( c_List_Oset @ B ) @ D ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ B ) @ ( c_List_Oconcat @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1520]) ).
thf(2155,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__absorb1) ).
thf(10809,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2155]) ).
thf(1958,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate2D) ).
thf(10036,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1958]) ).
thf(1924,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__insert__right) ).
thf(9915,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1924]) ).
thf(2272,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Obij__betw @ E @ D @ C @ B @ A )
=> ( c_Fun_Obij__betw @ D @ E @ ( c_Hilbert__Choice_Oinv__into @ E @ D @ B @ C ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__inv__into) ).
thf(11214,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Obij__betw @ E @ D @ C @ B @ A )
=> ( c_Fun_Obij__betw @ D @ E @ ( c_Hilbert__Choice_Oinv__into @ E @ D @ B @ C ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2272]) ).
thf(662,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ A ) @ B ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
thf(5159,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ A ) @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(1554,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__partition) ).
thf(8521,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1554]) ).
thf(555,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/sandbox/benchmark/theBenchmark.p',fact_nth__eq__iff__index__eq) ).
thf(4755,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)],[555]) ).
thf(959,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_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff__singleton__if) ).
thf(6294,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_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(250,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/sandbox/benchmark/theBenchmark.p',fact_mult__Suc) ).
thf(3560,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)],[250]) ).
thf(588,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofun__left__comm__idem @ D @ C @ B )
=> ( ( hAPP @ ( c_Fun_Ocomp @ C @ C @ C @ ( hAPP @ B @ A ) ) @ ( hAPP @ B @ A ) )
= ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofun__comp__idem) ).
thf(4895,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofun__left__comm__idem @ D @ C @ B )
=> ( ( hAPP @ ( c_Fun_Ocomp @ C @ C @ C @ ( hAPP @ B @ A ) ) @ ( hAPP @ B @ A ) )
= ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(2124,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ G @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ D @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_splitD_H) ).
thf(10691,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ G @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ D @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2124]) ).
thf(189,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( c_Fun_Oinj__on @ D @ D @ B @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ ( hAPP @ ( c_Set_Oimage @ D @ D @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ ( hAPP @ ( c_Fun_Ocomp @ D @ E @ D @ A ) @ B ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Oreindex) ).
thf(3347,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( c_Fun_Oinj__on @ D @ D @ B @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ A ) @ ( hAPP @ ( c_Set_Oimage @ D @ D @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ ( hAPP @ ( c_Fun_Ocomp @ D @ E @ D @ A ) @ B ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(897,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/sandbox/benchmark/theBenchmark.p',fact_diff__le__self) ).
thf(6114,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)],[897]) ).
thf(438,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
thf(4286,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(1513,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/sandbox/benchmark/theBenchmark.p',fact_dropWhile_Osimps_I2_J) ).
thf(8373,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)],[1513]) ).
thf(863,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/sandbox/benchmark/theBenchmark.p',fact_le__antisym) ).
thf(5990,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)],[863]) ).
thf(1753,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/sandbox/benchmark/theBenchmark.p',fact_diff__add__assoc2) ).
thf(9271,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)],[1753]) ).
thf(249,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ C ) ) @ B ) @ ( c_List_Olists @ C @ ( c_Wellfounded_Oacc @ C @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ C ) ) @ B ) @ ( c_Wellfounded_Oacc @ ( tc_List_Olist @ C ) @ ( c_List_Olistrel1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists__accD) ).
thf(3558,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ C ) ) @ B ) @ ( c_List_Olists @ C @ ( c_Wellfounded_Oacc @ C @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ C ) ) @ B ) @ ( c_Wellfounded_Oacc @ ( tc_List_Olist @ C ) @ ( c_List_Olistrel1 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(2638,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/sandbox/benchmark/theBenchmark.p',fact_CollectI) ).
thf(12605,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)],[2638]) ).
thf(1421,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ C ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_union__fold__insert) ).
thf(8019,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ C ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1421]) ).
thf(1018,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hAPP @ ( c_Set_Oimage @ F @ C @ ( c_Fun_Ofun__upd @ F @ C @ B @ E @ A ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( hAPP @ ( c_Set_Oimage @ F @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hAPP @ ( c_Set_Oimage @ F @ C @ ( c_Fun_Ofun__upd @ F @ C @ B @ E @ A ) ) @ D )
= ( hAPP @ ( c_Set_Oimage @ F @ C @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__image) ).
thf(6520,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hAPP @ ( c_Set_Oimage @ F @ C @ ( c_Fun_Ofun__upd @ F @ C @ B @ E @ A ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( hAPP @ ( c_Set_Oimage @ F @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hAPP @ ( c_Set_Oimage @ F @ C @ ( c_Fun_Ofun__upd @ F @ C @ B @ E @ A ) ) @ D )
= ( hAPP @ ( c_Set_Oimage @ F @ C @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(139,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_Onat @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__nat__eq) ).
thf(3177,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_Onat @ 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 @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ c_Int_Onat @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(2040,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__trans) ).
thf(10379,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2040]) ).
thf(315,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_COMBI @ B ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBI__1) ).
thf(3804,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_COMBI @ B ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(1725,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) )
<=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__Compl__self__eq) ).
thf(9134,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1725]) ).
thf(1821,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/sandbox/benchmark/theBenchmark.p',fact_diff__less__Suc) ).
thf(9541,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)],[1821]) ).
thf(363,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_List_Oset__Cons @ C @ B @ A )
= ( hAPP @ ( c_Set_OCollect @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool @ ( tc_List_Olist @ C ) ) @ ( c_HOL_OEx @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool @ C ) @ ( c_HOL_OEx @ ( tc_List_Olist @ C ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ C ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) ) @ ( tc_fun @ ( tc_fun @ C @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) ) @ ( tc_List_Olist @ C ) ) @ ( c_COMBS @ C @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_List_Olist @ C ) @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) ) @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_List_Olist @ C ) @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) @ C ) @ ( c_COMBS @ ( tc_List_Olist @ C ) @ tc_HOL_Obool @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_List_Olist @ C ) @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) ) @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_List_Olist @ C ) ) @ c_fconj ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ C ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ C @ ( tc_fun @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) ) @ ( tc_List_Olist @ C ) ) @ ( c_COMBB @ ( tc_fun @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) @ ( tc_List_Olist @ C ) ) @ ( c_COMBB @ ( tc_List_Olist @ C ) @ tc_HOL_Obool @ ( tc_List_Olist @ C ) ) ) @ c_fequal ) ) ) @ ( c_List_Olist_OCons @ C ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) @ C ) @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ C ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ C ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ ( tc_List_Olist @ C ) ) ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__Cons__def) ).
thf(4007,plain,
! [A: $i,B: $i,C: $i] :
( ( c_List_Oset__Cons @ C @ B @ A )
= ( hAPP @ ( c_Set_OCollect @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool @ ( tc_List_Olist @ C ) ) @ ( c_HOL_OEx @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool @ C ) @ ( c_HOL_OEx @ ( tc_List_Olist @ C ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ C ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) ) @ ( tc_fun @ ( tc_fun @ C @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) ) @ ( tc_List_Olist @ C ) ) @ ( c_COMBS @ C @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_List_Olist @ C ) @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) ) @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_List_Olist @ C ) @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) @ C ) @ ( c_COMBS @ ( tc_List_Olist @ C ) @ tc_HOL_Obool @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_List_Olist @ C ) @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) ) @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_List_Olist @ C ) ) @ c_fconj ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ C ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ C @ ( tc_fun @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) ) @ ( tc_List_Olist @ C ) ) @ ( c_COMBB @ ( tc_fun @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) @ ( tc_List_Olist @ C ) ) @ ( c_COMBB @ ( tc_List_Olist @ C ) @ tc_HOL_Obool @ ( tc_List_Olist @ C ) ) ) @ c_fequal ) ) ) @ ( c_List_Olist_OCons @ C ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) ) @ C ) @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ C ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ C ) @ ( tc_fun @ ( tc_List_Olist @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ ( tc_List_Olist @ C ) ) ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(1075,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_HOL_OThe @ ( tc_prod @ D @ C ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) @ ( hAPP @ c_fequal @ B ) ) ) ) @ ( hAPP @ c_fequal @ A ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_The__split__eq) ).
thf(6735,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_HOL_OThe @ ( tc_prod @ D @ C ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) @ ( hAPP @ c_fequal @ B ) ) ) ) @ ( hAPP @ c_fequal @ A ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).
thf(646,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_HOL_OThe @ ( tc_prod @ C @ B ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ C @ B @ tc_HOL_Obool ) @ A ) )
= ( c_HOL_OThe @ ( tc_prod @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ ( tc_prod @ C @ B ) @ B @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_prod @ C @ B ) ) @ A ) @ ( c_Product__Type_Ofst @ C @ B ) ) ) @ ( c_Product__Type_Osnd @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_The__split) ).
thf(5105,plain,
! [A: $i,B: $i,C: $i] :
( ( c_HOL_OThe @ ( tc_prod @ C @ B ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ C @ B @ tc_HOL_Obool ) @ A ) )
= ( c_HOL_OThe @ ( tc_prod @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ ( tc_prod @ C @ B ) @ B @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_prod @ C @ B ) ) @ A ) @ ( c_Product__Type_Ofst @ C @ B ) ) ) @ ( c_Product__Type_Osnd @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(1051,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__cancel) ).
thf(6644,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(1655,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Hilbert__Choice_OEps @ D @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ c_fequal ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__def) ).
thf(8921,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Hilbert__Choice_OEps @ D @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ c_fequal ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1655]) ).
thf(1751,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/sandbox/benchmark/theBenchmark.p',fact_trancl__domain) ).
thf(9265,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)],[1751]) ).
thf(1641,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ A ) ) ) )
=> ( ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__cartesian__productD2) ).
thf(8869,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ C ) @ B ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ A ) ) ) )
=> ( ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1641]) ).
thf(1526,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/sandbox/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
thf(8424,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)],[1526]) ).
thf(1028,axiom,
! [A: $i] : ( class_Nat_Osize @ ( tc_List_Olist @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_List__Olist__Nat_Osize) ).
thf(6558,plain,
! [A: $i] : ( class_Nat_Osize @ ( tc_List_Olist @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(2679,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/sandbox/benchmark/theBenchmark.p',fact_eq__mem__trans) ).
thf(12781,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)],[2679]) ).
thf(2363,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/sandbox/benchmark/theBenchmark.p',fact_equivp__reflp__symp__transp) ).
thf(11548,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)],[2363]) ).
thf(329,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/sandbox/benchmark/theBenchmark.p',fact_lexord__Nil__right) ).
thf(3850,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)],[329]) ).
thf(802,axiom,
! [A: $i,B: $i] :
( ( c_List_Opartition @ B @ A @ ( c_List_Olist_ONil @ 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 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partition_Osimps_I1_J) ).
thf(5741,plain,
! [A: $i,B: $i] :
( ( c_List_Opartition @ B @ A @ ( c_List_Olist_ONil @ 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 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(1518,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_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__psubset) ).
thf(8395,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_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1518]) ).
thf(2258,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/sandbox/benchmark/theBenchmark.p',fact_trancl__converseI) ).
thf(11162,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)],[2258]) ).
thf(2618,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/sandbox/benchmark/theBenchmark.p',fact_ord_OgreaterThan__iff) ).
thf(12503,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)],[2618]) ).
thf(2068,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
<=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF1__iff) ).
thf(10472,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ A ) ) ) )
& ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2068]) ).
thf(2561,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fdisj__2) ).
thf(12253,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2561]) ).
thf(12800,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ sk2 ) @ v_ts ) )
!= ( hBOOL @ c_fFalse ) ),
inference(paramod_ordered,[status(thm)],[2685,12369]) ).
thf(12801,plain,
( ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ sk2 ) @ v_ts )
!= c_fFalse ),
inference(simp,[status(thm)],[12800]) ).
thf(706,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_List_Orev @ B ) @ ( c_List_Oconcat @ B @ A ) )
= ( c_List_Oconcat @ B @ ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Orev @ B ) ) @ ( hAPP @ ( c_List_Orev @ ( tc_List_Olist @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__concat) ).
thf(5339,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_List_Orev @ B ) @ ( c_List_Oconcat @ B @ A ) )
= ( c_List_Oconcat @ B @ ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Orev @ B ) ) @ ( hAPP @ ( c_List_Orev @ ( tc_List_Olist @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(945,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_ORange @ C @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_ORange @ C @ D ) @ B ) ) @ ( hAPP @ ( c_Relation_ORange @ C @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Int__subset) ).
thf(6258,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_ORange @ C @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_ORange @ C @ D ) @ B ) ) @ ( hAPP @ ( c_Relation_ORange @ C @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(1875,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubsetD) ).
thf(9752,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1875]) ).
thf(64,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/sandbox/benchmark/theBenchmark.p',fact_zless__le) ).
thf(2913,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)],[64]) ).
thf(978,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Oord @ B )
=> ( class_Orderings_Oord @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
thf(6380,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Oord @ B )
=> ( class_Orderings_Oord @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(1112,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
<=> ? [C: $i,D: $i] :
( A
= ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ B @ D ) @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__conv__nat__seg__image) ).
thf(6889,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ? [C: $i,D: $i] :
( A
= ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ B @ D ) @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ C ) ) ) ) )
& ( ? [C: $i,D: $i] :
( A
= ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ B @ D ) @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ C ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).
thf(1417,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Int) ).
thf(8002,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1417]) ).
thf(182,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_List_OdropWhile @ C @ B @ A )
!= ( c_List_Olist_ONil @ C ) )
=> ~ ( hBOOL @ ( hAPP @ B @ ( hAPP @ ( c_List_Ohd @ C ) @ ( c_List_OdropWhile @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__dropWhile) ).
thf(3323,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_List_OdropWhile @ C @ B @ A )
!= ( c_List_Olist_ONil @ C ) )
=> ~ ( hBOOL @ ( hAPP @ B @ ( hAPP @ ( c_List_Ohd @ C ) @ ( c_List_OdropWhile @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(1223,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Relation_OImage @ D @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ A ) ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__singleton) ).
thf(7280,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Relation_OImage @ D @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ A ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1223]) ).
thf(833,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ D @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ D @ C ) @ F ) @ B ) ) @ E ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ D @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ D @ C ) @ E ) @ A ) ) @ F ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__swap) ).
thf(5867,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ D @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ D @ C ) @ F ) @ B ) ) @ E ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ D @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ D @ C ) @ E ) @ A ) ) @ F ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
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/sandbox/benchmark/theBenchmark.p',fact_self__quotient__aux1) ).
thf(2714,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(2666,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/sandbox/benchmark/theBenchmark.p',fact_inj__onD) ).
thf(12729,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)],[2666]) ).
thf(683,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/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I3_J) ).
thf(5251,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)],[683]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_List_Otranspose @ D @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ ( tc_List_Olist @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ C ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ ( tc_List_Olist @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ C ) @ ( c_List_Oconcat @ D @ ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( c_List_Olist_Olist__case @ ( tc_List_Olist @ D ) @ D @ ( c_List_Olist_ONil @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_List_Olist @ D ) @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ D ) @ ( c_COMBK @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( c_List_Olist_OCons @ D ) ) @ ( c_List_Olist_ONil @ D ) ) ) ) ) @ A ) ) ) ) @ ( c_List_Otranspose @ D @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ ( tc_List_Olist @ D ) ) @ B ) @ ( c_List_Oconcat @ ( tc_List_Olist @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ ( tc_List_Olist @ D ) ) ) @ ( c_List_Olist_Olist__case @ ( tc_List_Olist @ ( tc_List_Olist @ D ) ) @ D @ ( c_List_Olist_ONil @ ( tc_List_Olist @ D ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ ( tc_List_Olist @ D ) ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ ( tc_List_Olist @ D ) ) @ ( tc_List_Olist @ ( tc_List_Olist @ D ) ) ) @ ( c_List_Olist_OCons @ ( tc_List_Olist @ D ) ) ) @ ( c_List_Olist_ONil @ ( tc_List_Olist @ D ) ) ) ) ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose_Osimps_I3_J) ).
thf(3030,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_List_Otranspose @ D @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ ( tc_List_Olist @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ C ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ ( tc_List_Olist @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ D ) @ C ) @ ( c_List_Oconcat @ D @ ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( c_List_Olist_Olist__case @ ( tc_List_Olist @ D ) @ D @ ( c_List_Olist_ONil @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_List_Olist @ D ) @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ D ) @ ( c_COMBK @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( c_List_Olist_OCons @ D ) ) @ ( c_List_Olist_ONil @ D ) ) ) ) ) @ A ) ) ) ) @ ( c_List_Otranspose @ D @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ ( tc_List_Olist @ D ) ) @ B ) @ ( c_List_Oconcat @ ( tc_List_Olist @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ ( tc_List_Olist @ D ) ) ) @ ( c_List_Olist_Olist__case @ ( tc_List_Olist @ ( tc_List_Olist @ D ) ) @ D @ ( c_List_Olist_ONil @ ( tc_List_Olist @ D ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ ( tc_List_Olist @ D ) ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ ( tc_List_Olist @ D ) ) @ ( tc_List_Olist @ ( tc_List_Olist @ D ) ) ) @ ( c_List_Olist_OCons @ ( tc_List_Olist @ D ) ) ) @ ( c_List_Olist_ONil @ ( tc_List_Olist @ D ) ) ) ) ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(2397,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Wellfounded_Oaccp @ C @ A ) ) @ ( c_Wellfounded_Oaccp @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp__subset) ).
thf(11668,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Wellfounded_Oaccp @ C @ A ) ) @ ( c_Wellfounded_Oaccp @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2397]) ).
thf(1887,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Int) ).
thf(9795,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1887]) ).
thf(1061,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/sandbox/benchmark/theBenchmark.p',fact_lexord__append__rightI) ).
thf(6682,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)],[1061]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ E @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ E @ ( tc_fun @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ E @ ( tc_fun @ E @ E ) ) @ D ) @ ( c_If @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ D @ tc_HOL_Obool ) @ c_fequal ) @ B ) ) ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ E ) ) ) @ C )
= ( hAPP @ A @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ E @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ E @ ( tc_fun @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ E @ ( tc_fun @ E @ E ) ) @ D ) @ ( c_If @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ D @ tc_HOL_Obool ) @ c_fequal ) @ B ) ) ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ E ) ) ) @ C )
= ( c_Groups_Ozero__class_Ozero @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__delta) ).
thf(2795,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ E @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ E @ ( tc_fun @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ E @ ( tc_fun @ E @ E ) ) @ D ) @ ( c_If @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ D @ tc_HOL_Obool ) @ c_fequal ) @ B ) ) ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ E ) ) ) @ C )
= ( hAPP @ A @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ D @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ E @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ E @ ( tc_fun @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ E @ ( tc_fun @ E @ E ) ) @ D ) @ ( c_If @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ D @ tc_HOL_Obool ) @ c_fequal ) @ B ) ) ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ E ) ) ) @ C )
= ( c_Groups_Ozero__class_Ozero @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(414,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/sandbox/benchmark/theBenchmark.p',fact_listrel__rtrancl__trans) ).
thf(4193,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)],[414]) ).
thf(594,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/sandbox/benchmark/theBenchmark.p',fact_length__dropWhile__le) ).
thf(4912,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)],[594]) ).
thf(2239,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Obij__betw @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( c_Hilbert__Choice_Oinv__into @ B @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__inv__eq) ).
thf(11099,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Obij__betw @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( c_Hilbert__Choice_Oinv__into @ B @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2239]) ).
thf(1929,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E
= ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ E ) @ ( hAPP @ ( c_Set_Oimage @ A @ B @ D ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__eqI) ).
thf(9927,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E
= ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ E ) @ ( hAPP @ ( c_Set_Oimage @ A @ B @ D ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1929]) ).
thf(1758,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__disjoint) ).
thf(9293,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1758]) ).
thf(2390,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__greatest) ).
thf(11649,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2390]) ).
thf(2107,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Int) ).
thf(10622,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2107]) ).
thf(2503,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_OCollect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ B ) ) @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__mem__eq) ).
thf(12022,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_OCollect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ B ) ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2503]) ).
thf(1129,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
<=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNION__empty__conv_I2_J) ).
thf(6952,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
& ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ( ( hAPP @ A @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).
thf(104,axiom,
( ( c_Groups_Oone__class_Oone @ tc_Int_Oint )
= ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_One__int__def) ).
thf(3045,plain,
( ( c_Groups_Oone__class_Oone @ tc_Int_Oint )
= ( hAPP @ c_Int_OAbs__Integ @ ( hAPP @ ( c_Relation_OImage @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Int_Ointrel ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(1791,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__set__diff) ).
thf(9431,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oinj__on @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1791]) ).
thf(1785,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( c_List_Oset @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
<=> ( A
= ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__empty) ).
thf(9409,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( c_List_Oset @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( A
= ( c_List_Olist_ONil @ B ) ) )
& ( ( A
= ( c_List_Olist_ONil @ B ) )
=> ( ( hAPP @ ( c_List_Oset @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1785]) ).
thf(1828,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/sandbox/benchmark/theBenchmark.p',fact_add__leE) ).
thf(9564,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)],[1828]) ).
thf(1944,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ ( c_List_Osublist @ C @ B @ A ) ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__sublist__subset) ).
thf(9987,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ ( c_List_Osublist @ C @ B @ A ) ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1944]) ).
thf(2465,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Obij__betw @ E @ D @ C @ B @ A )
=> ( c_Fun_Obij__betw @ D @ E @ ( c_Fun_Othe__inv__into @ E @ D @ B @ C ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__the__inv__into) ).
thf(11890,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Obij__betw @ E @ D @ C @ B @ A )
=> ( c_Fun_Obij__betw @ D @ E @ ( c_Fun_Othe__inv__into @ E @ D @ B @ C ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2465]) ).
thf(2316,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/sandbox/benchmark/theBenchmark.p',fact_card__insert__disjoint) ).
thf(11377,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)],[2316]) ).
thf(2541,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/sandbox/benchmark/theBenchmark.p',fact_ord_OatMost__iff) ).
thf(12175,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)],[2541]) ).
thf(2245,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__insert__left) ).
thf(11114,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2245]) ).
thf(2148,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ C ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ C ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Otrancl @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ C ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__subset__Sigma) ).
thf(10781,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ C ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ C ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Otrancl @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ C ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2148]) ).
thf(2586,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/sandbox/benchmark/theBenchmark.p',fact_vimage__code) ).
thf(12363,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)],[2586]) ).
thf(1286,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/sandbox/benchmark/theBenchmark.p',fact_distinct__removeAll) ).
thf(7525,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)],[1286]) ).
thf(443,axiom,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeast @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( c_SetInterval_Oord__class_OgreaterThan @ tc_Nat_Onat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast__Suc__greaterThan) ).
thf(4318,plain,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeast @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( c_SetInterval_Oord__class_OgreaterThan @ tc_Nat_Onat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(1163,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ D ) ) @ C ) @ ( c_List_Olists @ D @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ D ) ) @ C ) @ ( c_List_Olists @ D @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ D @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ A ) ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists__IntI) ).
thf(7076,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ D ) ) @ C ) @ ( c_List_Olists @ D @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ D ) ) @ C ) @ ( c_List_Olists @ D @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ D @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ A ) ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).
thf(1396,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( ( c_Wellfounded_Owf @ C @ A )
=> ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_ODomain @ C @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_ORange @ C @ C ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( c_Wellfounded_Owf @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__Un) ).
thf(7925,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( ( c_Wellfounded_Owf @ C @ A )
=> ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_ODomain @ C @ C ) @ B ) ) @ ( hAPP @ ( c_Relation_ORange @ C @ C ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( c_Wellfounded_Owf @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1396]) ).
thf(1594,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Osym @ B @ A )
<=> ( ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sym__conv__converse__eq) ).
thf(8692,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)],[1594]) ).
thf(853,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Relation_ODomain @ C @ B ) @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ C @ B ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ C @ B @ tc_HOL_Obool ) @ A ) ) )
= ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool @ C ) @ ( c_HOL_OEx @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Collect__split) ).
thf(5945,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Relation_ODomain @ C @ B ) @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ C @ B ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ C @ B @ tc_HOL_Obool ) @ A ) ) )
= ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool @ C ) @ ( c_HOL_OEx @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(2207,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/sandbox/benchmark/theBenchmark.p',fact_remove1__append) ).
thf(10988,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)],[2207]) ).
thf(2472,axiom,
! [A: $i] : ( c_Equiv__Relations_Oequivp @ A @ c_fequal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_identity__equivp) ).
thf(11910,plain,
! [A: $i] : ( c_Equiv__Relations_Oequivp @ A @ c_fequal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2472]) ).
thf(2442,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_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ C @ B ) @ D ) ) @ ( hAPP @ A @ ( hAPP @ ( c_Set_Oimage @ F @ C @ B ) @ D ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ E ) ) @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_weak__coinduct__image) ).
thf(11803,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_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ C @ B ) @ D ) ) @ ( hAPP @ A @ ( hAPP @ ( c_Set_Oimage @ F @ C @ B ) @ D ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ E ) ) @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ ( tc_fun @ C @ tc_HOL_Obool ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2442]) ).
thf(905,axiom,
! [A: $i,B: $i] :
( ! [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ ( hAPP @ B @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) ) @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__less__ub) ).
thf(6136,plain,
! [A: $i,B: $i] :
( ! [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ ( hAPP @ B @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( hAPP @ ( c_Set_OCollect @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) ) @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(194,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ ( tc_prod @ D @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ D @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ B ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__zip) ).
thf(3362,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ ( tc_prod @ D @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ D @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ B ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(1774,axiom,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ ( c_Relation_OId @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ B @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__unfold) ).
thf(9367,plain,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ ( c_Relation_OId @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ B @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1774]) ).
thf(2595,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ B @ ( c_Hilbert__Choice_OEps @ A @ B ) ) )
<=> ? [C: $i] : ( hBOOL @ ( hAPP @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_some__eq__ex) ).
thf(12406,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)],[2595]) ).
thf(673,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__infE) ).
thf(5204,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_List_Olist_ONil @ B ) )
=> ( ( hAPP @ ( c_List_Ohd @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ C ) @ A ) )
= ( hAPP @ ( c_List_Ohd @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__append2) ).
thf(3128,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_List_Olist_ONil @ B ) )
=> ( ( hAPP @ ( c_List_Ohd @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ B ) @ C ) @ A ) )
= ( hAPP @ ( c_List_Ohd @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(395,axiom,
! [A: $i] :
( ( hAPP @ ( c_List_Orev @ A ) @ ( c_List_Olist_ONil @ A ) )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev_Osimps_I1_J) ).
thf(4129,plain,
! [A: $i] :
( ( hAPP @ ( c_List_Orev @ A ) @ ( c_List_Olist_ONil @ A ) )
= ( c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(1432,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/sandbox/benchmark/theBenchmark.p',fact_wf__converse__trancl) ).
thf(8066,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)],[1432]) ).
thf(2087,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( hBOOL @ ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ B @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ B ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1CI) ).
thf(10554,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( hBOOL @ ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ B @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ B ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2087]) ).
thf(357,axiom,
! [A: $i,B: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__self__implies__10) ).
thf(3974,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)],[357]) ).
thf(1502,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Relation_OField @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ ( hAPP @ ( c_Relation_OField @ D ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__insert) ).
thf(8328,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Relation_OField @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) @ ( hAPP @ ( c_Relation_OField @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1502]) ).
thf(2164,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__trans) ).
thf(10836,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2164]) ).
thf(1413,axiom,
! [A: $i,B: $i] : ( c_Relation_Orefl__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) @ ( c_Relation_OId @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__reflcl) ).
thf(7987,plain,
! [A: $i,B: $i] : ( c_Relation_Orefl__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) @ ( c_Relation_OId @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1413]) ).
thf(2283,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__absorb1) ).
thf(11258,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2283]) ).
thf(2643,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/sandbox/benchmark/theBenchmark.p',fact_rev__image__eqI) ).
thf(12626,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)],[2643]) ).
thf(108,axiom,
! [A: $i,B: $i] :
( ( B
!= ( c_List_Olist_ONil @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ ( hAPP @ ( c_List_Ohd @ A ) @ B ) ) @ ( hAPP @ ( c_List_Oset @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__in__set) ).
thf(3057,plain,
! [A: $i,B: $i] :
( ( B
!= ( c_List_Olist_ONil @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ ( hAPP @ ( c_List_Ohd @ A ) @ B ) ) @ ( hAPP @ ( c_List_Oset @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(912,axiom,
! [A: $i,B: $i] :
( ( c_List_Oset__Cons @ B @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_List_Olist @ B ) ) @ ( c_List_Olist_ONil @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_List_Olist @ B ) @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( c_Set_Oimage @ B @ ( tc_List_Olist @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olist_OCons @ B ) ) @ ( c_List_Olist_ONil @ B ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__Cons__sing__Nil) ).
thf(6155,plain,
! [A: $i,B: $i] :
( ( c_List_Oset__Cons @ B @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_List_Olist @ B ) ) @ ( c_List_Olist_ONil @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_List_Olist @ B ) @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( c_Set_Oimage @ B @ ( tc_List_Olist @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olist_OCons @ B ) ) @ ( c_List_Olist_ONil @ B ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Otl @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ B ) @ A ) )
= ( hAPP @ ( c_List_Olist_Olist__case @ ( tc_List_Olist @ C ) @ C @ ( hAPP @ ( c_List_Otl @ C ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Oappend @ C ) ) @ A ) ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tl__append) ).
thf(2803,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Otl @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ B ) @ A ) )
= ( hAPP @ ( c_List_Olist_Olist__case @ ( tc_List_Olist @ C ) @ C @ ( hAPP @ ( c_List_Otl @ C ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Oappend @ C ) ) @ A ) ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(426,axiom,
! [A: $i] : ( c_Finite__Set_Ofun__left__comm__idem @ A @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem__insert) ).
thf(4242,plain,
! [A: $i] : ( c_Finite__Set_Ofun__left__comm__idem @ A @ ( tc_fun @ A @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(967,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ B @ C @ C @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) @ A )
= ( c_Fun_Oid @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__o__cancel) ).
thf(6329,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Oinj__on @ C @ B @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ B @ C @ C @ ( c_Hilbert__Choice_Oinv__into @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) @ A )
= ( c_Fun_Oid @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(2383,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__mono) ).
thf(11621,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2383]) ).
thf(2622,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/sandbox/benchmark/theBenchmark.p',fact_equivp__def) ).
thf(12530,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)],[2622]) ).
thf(1878,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_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ C ) ) @ B ) )
=> ( ( c_Fun_Oinj__on @ E @ F @ A @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ F @ A ) @ B ) ) @ C ) )
=> ? [G: $i] : ( c_Fun_Obij__betw @ F @ E @ G @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cantor__Bernstein) ).
thf(9763,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_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ E @ D ) @ C ) ) @ B ) )
=> ( ( c_Fun_Oinj__on @ E @ F @ A @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ F @ A ) @ B ) ) @ C ) )
=> ? [G: $i] : ( c_Fun_Obij__betw @ F @ E @ G @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1878]) ).
thf(613,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Oset @ C ) @ ( c_List_Osublist @ C @ B @ A ) )
= ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool @ C ) @ ( c_HOL_OEx @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ C ) @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ tc_Nat_Onat @ C ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ C ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ C ) @ ( c_COMBB @ C @ tc_HOL_Obool @ tc_Nat_Onat ) ) @ c_fequal ) ) @ ( hAPP @ ( c_List_Onth @ C ) @ B ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ tc_Nat_Onat ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__sublist) ).
thf(4972,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Oset @ C ) @ ( c_List_Osublist @ C @ B @ A ) )
= ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool @ C ) @ ( c_HOL_OEx @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ C ) @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ tc_Nat_Onat @ C ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ C ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ C ) @ ( c_COMBB @ C @ tc_HOL_Obool @ tc_Nat_Onat ) ) @ c_fequal ) ) @ ( hAPP @ ( c_List_Onth @ C ) @ B ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ tc_Nat_Onat ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(657,axiom,
! [A: $i,B: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) )
= ( c_SetInterval_Oord_OatLeastAtMost @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B @ A ) )
<=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeastatMost__empty__iff2) ).
thf(5140,plain,
! [A: $i,B: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) )
= ( c_SetInterval_Oord_OatLeastAtMost @ tc_Nat_Onat @ ( 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 ) @ A ) )
=> ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) )
= ( c_SetInterval_Oord_OatLeastAtMost @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(992,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_fun @ B @ A ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_fun @ B @ A ) @ tc_HOL_Obool ) ) ) )
=> ( ( ( hAPP @ ( c_Finite__Set_Ocard @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
!= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__fun__UNIVD1) ).
thf(6435,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_fun @ B @ A ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ ( tc_fun @ B @ A ) @ tc_HOL_Obool ) ) ) )
=> ( ( ( hAPP @ ( c_Finite__Set_Ocard @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
!= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(2227,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF1__D) ).
thf(11050,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2227]) ).
thf(2489,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) )
<=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__not__in__conv) ).
thf(11958,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2489]) ).
thf(1802,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I8_J) ).
thf(9474,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1802]) ).
thf(1065,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Orefl__on @ E @ D @ C )
=> ( ( c_Relation_Orefl__on @ E @ B @ A )
=> ( c_Relation_Orefl__on @ E @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__Un) ).
thf(6697,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Orefl__on @ E @ D @ C )
=> ( ( c_Relation_Orefl__on @ E @ B @ A )
=> ( c_Relation_Orefl__on @ E @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).
thf(306,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ tc_HOL_Obool ) ) @ ( c_List_Olistrel @ C @ B ) ) @ ( c_List_Olistrel @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__mono) ).
thf(3772,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ tc_HOL_Obool ) ) @ ( c_List_Olistrel @ C @ B ) ) @ ( c_List_Olistrel @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(2556,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/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Opos__single__def) ).
thf(12235,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)],[2556]) ).
thf(2619,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/sandbox/benchmark/theBenchmark.p',fact_Bex__set__list__ex) ).
thf(12508,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)],[2619]) ).
thf(2626,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ B ) @ A ) )
| ( hBOOL @ B )
| ( hBOOL @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fdisj__3) ).
thf(12560,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ B ) @ A ) )
| ( hBOOL @ B )
| ( hBOOL @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2626]) ).
thf(2675,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/sandbox/benchmark/theBenchmark.p',fact_type__definition_OAbs__inverse) ).
thf(12761,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)],[2675]) ).
thf(381,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/sandbox/benchmark/theBenchmark.p',fact_nat__0__less__mult__iff) ).
thf(4066,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)],[381]) ).
thf(488,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/sandbox/benchmark/theBenchmark.p',fact_length__upt) ).
thf(4484,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)],[488]) ).
thf(692,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/sandbox/benchmark/theBenchmark.p',fact_drop__Cons_H) ).
thf(5280,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)],[692]) ).
thf(1794,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Relation_OImage @ E @ D @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ E @ D @ C ) @ A ) ) @ ( hAPP @ ( c_Relation_OImage @ E @ D @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Image) ).
thf(9446,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Relation_OImage @ E @ D @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Relation_OImage @ E @ D @ C ) @ A ) ) @ ( hAPP @ ( c_Relation_OImage @ E @ D @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1794]) ).
thf(1149,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_Olist__update @ F @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ E @ ( hAPP @ ( hAPP @ ( c_List_Omap @ F @ E ) @ D ) @ C ) ) @ B ) @ ( hAPP @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__update) ).
thf(7035,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_Olist__update @ F @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ E @ ( hAPP @ ( hAPP @ ( c_List_Omap @ F @ E ) @ D ) @ C ) ) @ B ) @ ( hAPP @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).
thf(469,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Fun_Obij__betw @ C @ C @ ( c_Fun_Oid @ C ) @ B @ A )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__id__iff) ).
thf(4410,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Fun_Obij__betw @ C @ C @ ( c_Fun_Oid @ C ) @ B @ A )
=> ( B = A ) )
& ( ( B = A )
=> ( c_Fun_Obij__betw @ C @ C @ ( c_Fun_Oid @ C ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(573,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_Ovimage @ B @ B @ ( c_Fun_Oid @ B ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__id) ).
thf(4831,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_Ovimage @ B @ B @ ( c_Fun_Oid @ B ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(1740,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/sandbox/benchmark/theBenchmark.p',fact_Nil__is__append__conv) ).
thf(9193,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)],[1740]) ).
thf(2298,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Predicate_Oconversep @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( c_Predicate_Oconversep @ D @ C @ B ) ) @ ( c_Predicate_Oconversep @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__meet) ).
thf(11309,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Predicate_Oconversep @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ ( c_Predicate_Oconversep @ D @ C @ B ) ) @ ( c_Predicate_Oconversep @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2298]) ).
thf(2019,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Transitive__Closure_Ortrancl @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) )
= ( c_Transitive__Closure_Ortrancl @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Un__rtrancl) ).
thf(10308,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Transitive__Closure_Ortrancl @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) )
= ( c_Transitive__Closure_Ortrancl @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2019]) ).
thf(2167,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 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) )
<=> ( ( hAPP @ B @ D )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__singleton__eq) ).
thf(10845,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 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) )
=> ( ( hAPP @ B @ D )
= A ) )
& ( ( ( hAPP @ B @ D )
= A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Set_Ovimage @ E @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2167]) ).
thf(2346,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ E ) ) )
<=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ( hBOOL @ ( hAPP @ A @ E ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ball__Un) ).
thf(11479,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ E ) ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ( hBOOL @ ( hAPP @ A @ E ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ E ) ) ) ) )
& ( ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ( hBOOL @ ( hAPP @ A @ E ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ E ) ) ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2346]) ).
thf(1699,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/sandbox/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).
thf(9055,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)],[1699]) ).
thf(1352,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/sandbox/benchmark/theBenchmark.p',fact_Suc__lessI) ).
thf(7755,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)],[1352]) ).
thf(2345,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/sandbox/benchmark/theBenchmark.p',fact_rel__compI) ).
thf(11477,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)],[2345]) ).
thf(2544,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/sandbox/benchmark/theBenchmark.p',fact_in__set__member) ).
thf(12188,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)],[2544]) ).
thf(998,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Diff) ).
thf(6452,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(2341,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/sandbox/benchmark/theBenchmark.p',fact_not__less__Least) ).
thf(11462,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)],[2341]) ).
thf(1311,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/sandbox/benchmark/theBenchmark.p',fact_Field__converse) ).
thf(7617,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)],[1311]) ).
thf(2175,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Equiv__Relations_Oequiv @ G @ F @ E )
=> ( ( c_Equiv__Relations_Ocongruent @ G @ ( tc_fun @ D @ tc_HOL_Obool ) @ E @ C )
=> ( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ G @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ G @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ G ) @ F ) @ E ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ G ) @ F ) @ E ) ) )
=> ( ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ F ) )
=> ! [I: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ I ) @ F ) )
=> ( ( ( hAPP @ C @ H )
= ( hAPP @ C @ I ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ G @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ G ) @ H ) @ I ) ) @ E ) ) ) ) )
=> ( B = A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__equiv__class__inject) ).
thf(10877,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Equiv__Relations_Oequiv @ G @ F @ E )
=> ( ( c_Equiv__Relations_Ocongruent @ G @ ( tc_fun @ D @ tc_HOL_Obool ) @ E @ C )
=> ( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ G @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ G @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ G ) @ F ) @ E ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ G @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ G ) @ F ) @ E ) ) )
=> ( ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ H ) @ F ) )
=> ! [I: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ I ) @ F ) )
=> ( ( ( hAPP @ C @ H )
= ( hAPP @ C @ I ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ G @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ G ) @ H ) @ I ) ) @ E ) ) ) ) )
=> ( B = A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2175]) ).
thf(1977,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ F ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate2D) ).
thf(10124,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ F ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1977]) ).
thf(1571,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ B ) @ C ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ D ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__cartesian__product) ).
thf(8585,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ ( tc_prod @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ D @ B ) @ C ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ D ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1571]) ).
thf(676,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) )
=> ( ( ? [D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Ounion__inter__neutral) ).
thf(5219,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) )
=> ( ( ? [D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(2112,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/sandbox/benchmark/theBenchmark.p',fact_in__set__conv__decomp__last) ).
thf(10642,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)],[2112]) ).
thf(1258,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( D
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ A ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__constant) ).
thf(7430,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( D
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1258]) ).
thf(1590,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__empty2) ).
thf(8680,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1590]) ).
thf(1614,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Int__assoc__eq) ).
thf(8773,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ C ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1614]) ).
thf(298,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oorder__class_Omono @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gfp__fun__UnI2) ).
thf(3740,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oorder__class_Omono @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(896,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/sandbox/benchmark/theBenchmark.p',fact_acyclicP__converse) ).
thf(6109,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)],[896]) ).
thf(1775,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Oantisym @ B @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) )
<=> ( c_Relation_Oantisym @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisym__converse) ).
thf(9370,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)],[1775]) ).
thf(368,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( c_Finite__Set_Ofolding @ K @ J @ I @ H )
=> ( ( 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/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__comps_I1_J) ).
thf(4019,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( c_Finite__Set_Ofolding @ K @ J @ I @ H )
=> ( ( 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)],[368]) ).
thf(1330,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__Compl__image__subset) ).
thf(7694,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1330]) ).
thf(1835,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__Un) ).
thf(9605,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1835]) ).
thf(535,axiom,
! [A: $i] :
( ( class_Lattices_Osemilattice__inf @ A )
=> ( c_Finite__Set_Ofun__left__comm__idem @ A @ A @ ( c_Lattices_Osemilattice__inf__class_Oinf @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem__inf) ).
thf(4691,plain,
! [A: $i] :
( ( class_Lattices_Osemilattice__inf @ A )
=> ( c_Finite__Set_Ofun__left__comm__idem @ A @ A @ ( c_Lattices_Osemilattice__inf__class_Oinf @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__add @ D )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ D ) @ A ) @ B )
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Oinfinite) ).
thf(2699,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__add @ D )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum @ C @ D ) @ A ) @ B )
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(231,axiom,
! [A: $i] :
( ( c_List_Oconcat @ A @ ( c_List_Olist_ONil @ ( tc_List_Olist @ A ) ) )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat_Osimps_I1_J) ).
thf(3494,plain,
! [A: $i] :
( ( c_List_Oconcat @ A @ ( c_List_Olist_ONil @ ( tc_List_Olist @ A ) ) )
= ( c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(2462,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/sandbox/benchmark/theBenchmark.p',fact_wf__iff__no__infinite__down__chain) ).
thf(11875,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)],[2462]) ).
thf(452,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).
thf(4345,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(1834,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
=> ( ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ F ) ) ) )
=> ( c_Wellfounded_Omax__extp @ D @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__extp_Ointros) ).
thf(9600,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
=> ( ( B
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ F ) ) ) )
=> ( c_Wellfounded_Omax__extp @ D @ A @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1834]) ).
thf(2096,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ C @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ C ) @ c_fdisj ) @ B ) ) @ A ) ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ B ) ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__disjI) ).
thf(10586,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ C @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ C ) @ c_fdisj ) @ B ) ) @ A ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ B ) ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ A ) ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ B ) ) )
& ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ C @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ C ) @ c_fdisj ) @ B ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2096]) ).
thf(2521,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/sandbox/benchmark/theBenchmark.p',fact_f__inv__into__f) ).
thf(12085,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)],[2521]) ).
thf(1228,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Product__Type_Omap__pair @ F @ E @ D @ C @ B @ A )
= ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ F @ D @ ( tc_prod @ E @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ D @ C ) @ ( tc_fun @ D @ ( tc_prod @ E @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ E @ C ) ) @ ( tc_fun @ ( tc_fun @ D @ C ) @ ( tc_fun @ D @ ( tc_prod @ E @ C ) ) ) @ F ) @ ( c_COMBB @ C @ ( tc_prod @ E @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ C @ ( tc_prod @ E @ C ) ) @ F ) @ ( c_Product__Type_OPair @ E @ C ) ) @ B ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair__def) ).
thf(7299,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Product__Type_Omap__pair @ F @ E @ D @ C @ B @ A )
= ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ F @ D @ ( tc_prod @ E @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ D @ C ) @ ( tc_fun @ D @ ( tc_prod @ E @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ E @ C ) ) @ ( tc_fun @ ( tc_fun @ D @ C ) @ ( tc_fun @ D @ ( tc_prod @ E @ C ) ) ) @ F ) @ ( c_COMBB @ C @ ( tc_prod @ E @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ C @ ( tc_prod @ E @ C ) ) @ F ) @ ( c_Product__Type_OPair @ E @ C ) ) @ B ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1228]) ).
thf(421,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ D @ tc_Nat_Onat ) @ D ) @ ( c_Product__Type_Ofst @ D @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_List_Ofilter @ ( tc_prod @ D @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ tc_HOL_Obool @ ( tc_prod @ D @ tc_Nat_Onat ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ tc_Nat_Onat @ ( tc_prod @ D @ tc_Nat_Onat ) ) @ c_Nat_OSuc ) @ ( c_Product__Type_Osnd @ D @ tc_Nat_Onat ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ D @ tc_Nat_Onat ) @ B ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ D @ tc_Nat_Onat ) @ D ) @ ( c_Product__Type_Ofst @ D @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_List_Ofilter @ ( tc_prod @ D @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ tc_HOL_Obool @ ( tc_prod @ D @ tc_Nat_Onat ) ) @ C ) @ ( c_Product__Type_Osnd @ D @ tc_Nat_Onat ) ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ D @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Nat_OSuc ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__shift__lemma__Suc) ).
thf(4221,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ D @ tc_Nat_Onat ) @ D ) @ ( c_Product__Type_Ofst @ D @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_List_Ofilter @ ( tc_prod @ D @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ tc_HOL_Obool @ ( tc_prod @ D @ tc_Nat_Onat ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ tc_Nat_Onat @ ( tc_prod @ D @ tc_Nat_Onat ) ) @ c_Nat_OSuc ) @ ( c_Product__Type_Osnd @ D @ tc_Nat_Onat ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ D @ tc_Nat_Onat ) @ B ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ D @ tc_Nat_Onat ) @ D ) @ ( c_Product__Type_Ofst @ D @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_List_Ofilter @ ( tc_prod @ D @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ tc_HOL_Obool @ ( tc_prod @ D @ tc_Nat_Onat ) ) @ C ) @ ( c_Product__Type_Osnd @ D @ tc_Nat_Onat ) ) ) @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ D @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Nat_OSuc ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(733,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/sandbox/benchmark/theBenchmark.p',fact_card__ge__0__finite) ).
thf(5473,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)],[733]) ).
thf(2217,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ B ) @ A ) ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__drop__subset) ).
thf(11021,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ B ) @ A ) ) ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2217]) ).
thf(1672,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Otrans @ B @ A )
=> ( ( c_Relation_Oantisym @ B @ A )
=> ( c_Relation_Otrans @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) @ ( c_Relation_OId @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__diff__Id) ).
thf(8978,plain,
! [A: $i,B: $i] :
( ( c_Relation_Otrans @ B @ A )
=> ( ( c_Relation_Oantisym @ B @ A )
=> ( c_Relation_Otrans @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) @ A ) @ ( c_Relation_OId @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1672]) ).
thf(827,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hAPP @ ( c_Product__Type_Ofst @ G @ F ) @ ( hAPP @ ( c_Product__Type_Omap__pair @ E @ G @ D @ F @ C @ B ) @ A ) )
= ( hAPP @ C @ ( hAPP @ ( c_Product__Type_Ofst @ E @ D ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__map__pair) ).
thf(5845,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hAPP @ ( c_Product__Type_Ofst @ G @ F ) @ ( hAPP @ ( c_Product__Type_Omap__pair @ E @ G @ D @ F @ C @ B ) @ A ) )
= ( hAPP @ C @ ( hAPP @ ( c_Product__Type_Ofst @ E @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(208,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 @ B @ C ) )
<=> ( hBOOL @ ( hAPP @ A @ C ) ) ) )
=> ( ( hAPP @ ( c_Set_OCollect @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Int_Oint @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Int_Oint ) @ c_fconj ) @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) @ B ) )
= ( hAPP @ ( c_Set_OCollect @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Int_Oint @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Int_Oint ) @ c_fconj ) @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__set__cong) ).
thf(3405,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 @ B @ C ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) )
& ( ( hBOOL @ ( hAPP @ A @ C ) )
=> ( hBOOL @ ( hAPP @ B @ C ) ) ) ) )
=> ( ( hAPP @ ( c_Set_OCollect @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Int_Oint @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Int_Oint ) @ c_fconj ) @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) @ B ) )
= ( hAPP @ ( c_Set_OCollect @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Int_Oint @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Int_Oint ) @ c_fconj ) @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(50,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/sandbox/benchmark/theBenchmark.p',fact_zadd__strict__right__mono) ).
thf(2866,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)],[50]) ).
thf(1486,axiom,
! [A: $i,B: $i] :
~ ( c_List_Olist__ex1 @ B @ A @ ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__ex1__simps_I1_J) ).
thf(8273,plain,
! [A: $i,B: $i] :
~ ( c_List_Olist__ex1 @ B @ A @ ( c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1486]) ).
thf(105,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/sandbox/benchmark/theBenchmark.p',fact_zless__imp__add1__zle) ).
thf(3047,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)],[105]) ).
thf(2145,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ C @ D @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__image__comp) ).
thf(10768,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ C @ D @ ( c_Hilbert__Choice_Oinv__into @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2145]) ).
thf(1125,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ C @ ( c_List_Olist_ONil @ C ) ) @ B ) @ A )
= ( c_List_Olist_ONil @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update_Osimps_I1_J) ).
thf(6933,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ C @ ( c_List_Olist_ONil @ C ) ) @ B ) @ A )
= ( c_List_Olist_ONil @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).
thf(303,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 ) ) @ ( hAPP @ ( c_List_Olexn @ E @ B ) @ A ) ) )
=> ( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ D )
= A )
& ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ C )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexn__length) ).
thf(3753,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 ) ) @ ( hAPP @ ( c_List_Olexn @ E @ B ) @ A ) ) )
=> ( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ D )
= A )
& ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ C )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(2671,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/sandbox/benchmark/theBenchmark.p',fact_vimageI2) ).
thf(12749,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)],[2671]) ).
thf(240,axiom,
! [A: $i,B: $i] : ( c_Fun_Oinj__on @ B @ B @ ( c_Fun_Oid @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__id) ).
thf(3526,plain,
! [A: $i,B: $i] : ( c_Fun_Oinj__on @ B @ B @ ( c_Fun_Oid @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(1200,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/sandbox/benchmark/theBenchmark.p',fact_take__zip) ).
thf(7195,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)],[1200]) ).
thf(1826,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__empty__left) ).
thf(9558,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1826]) ).
thf(2129,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image @ H @ G @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ C ) )
=> ( ( c_Fun_Oinj__on @ G @ G @ B @ C )
=> ( ( hAPP @ ( hAPP @ D @ A ) @ ( hAPP @ ( c_Set_Oimage @ G @ G @ B ) @ C ) )
= ( hAPP @ ( hAPP @ D @ ( hAPP @ ( c_Fun_Ocomp @ G @ H @ G @ A ) @ B ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image_Oreindex) ).
thf(10706,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image @ H @ G @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ C ) )
=> ( ( c_Fun_Oinj__on @ G @ G @ B @ C )
=> ( ( hAPP @ ( hAPP @ D @ A ) @ ( hAPP @ ( c_Set_Oimage @ G @ G @ B ) @ C ) )
= ( hAPP @ ( hAPP @ D @ ( hAPP @ ( c_Fun_Ocomp @ G @ H @ G @ A ) @ B ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2129]) ).
thf(241,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_List_Oset @ B ) @ ( c_List_Oconcat @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_List_Olist @ B ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ ( tc_List_Olist @ B ) ) @ A ) ) @ ( c_List_Oset @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__concat) ).
thf(3528,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_List_Oset @ B ) @ ( c_List_Oconcat @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( tc_List_Olist @ B ) @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_List_Oset @ ( tc_List_Olist @ B ) ) @ A ) ) @ ( c_List_Oset @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(448,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ? [C: $i] : ( c_Fun_Obij__betw @ tc_Nat_Onat @ B @ C @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__bij__betw__nat__finite) ).
thf(4335,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ A ) )
=> ? [C: $i] : ( c_Fun_Obij__betw @ tc_Nat_Onat @ B @ C @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(1294,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Transitive__Closure_Otrancl @ D @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ D @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ D @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ D @ ( tc_prod @ D @ D ) ) @ ( c_Product__Type_OPair @ D @ D ) ) @ C ) ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ D @ D ) ) ) @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__insert) ).
thf(7548,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Transitive__Closure_Otrancl @ D @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) @ ( hAPP @ ( c_Set_OCollect @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ D @ D @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ D ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ D @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ D @ ( tc_prod @ D @ D ) ) @ ( c_Product__Type_OPair @ D @ D ) ) @ C ) ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D ) @ ( c_member @ ( tc_prod @ D @ D ) ) ) @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1294]) ).
thf(2400,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_OPow @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_PowI) ).
thf(11675,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_OPow @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2400]) ).
thf(1937,axiom,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__iff) ).
thf(9954,plain,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1937]) ).
thf(661,axiom,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).
thf(5155,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(354,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/sandbox/benchmark/theBenchmark.p',fact_distinct__conv__nth) ).
thf(3950,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)],[354]) ).
thf(629,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
<=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__1__iff) ).
thf(5029,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)],[629]) ).
thf(2189,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/sandbox/benchmark/theBenchmark.p',fact_converseI) ).
thf(10931,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)],[2189]) ).
thf(2070,axiom,
! [A: $i,B: $i] :
( ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) )
<=> ? [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bex__UNIV) ).
thf(10482,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) )
=> ? [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) ) )
& ( ? [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2070]) ).
thf(2072,axiom,
! [A: $i] :
( ( c_List_Omember @ A )
= ( c_List_Oset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_member__set) ).
thf(10492,plain,
! [A: $i] :
( ( c_List_Omember @ A )
= ( c_List_Oset @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2072]) ).
thf(1359,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/sandbox/benchmark/theBenchmark.p',fact_finite__acyclic__wf__converse) ).
thf(7776,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)],[1359]) ).
thf(1450,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ D @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( hAPP @ ( c_Relation_ODomain @ D @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainP__Domain__eq) ).
thf(8125,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ D @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( hAPP @ ( c_Relation_ODomain @ D @ C ) @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( hAPP @ ( c_Relation_ODomain @ D @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ D @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1450]) ).
thf(2290,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ C ) @ B ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ G @ F ) @ A ) ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ E ) @ D )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ C ) @ B ) )
=> ~ ! [H: $i,I: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ H ) @ I ) ) ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ H ) @ I ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ C ) @ B ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ G @ F ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rtranclE2) ).
thf(11286,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ C ) @ B ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ G @ F ) @ A ) ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ E ) @ D )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ C ) @ B ) )
=> ~ ! [H: $i,I: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ H ) @ I ) ) ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ H ) @ I ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ C ) @ B ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ G @ F ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2290]) ).
thf(753,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding__idem @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ B ) ) @ ( hAPP @ D @ A ) )
= ( hAPP @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__idem_Oin__comp__idem) ).
thf(5542,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Finite__Set_Ofolding__idem @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ B ) )
=> ( ( hAPP @ ( c_Fun_Ocomp @ E @ E @ E @ ( hAPP @ C @ B ) ) @ ( hAPP @ D @ A ) )
= ( hAPP @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(519,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Ozip @ B @ B ) @ A ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ B @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ B @ B @ ( tc_prod @ B @ B ) ) @ ( c_Product__Type_OPair @ B @ B ) ) @ ( c_COMBI @ B ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__same__conv__map) ).
thf(4627,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Ozip @ B @ B ) @ A ) @ A )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ B @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ B @ B @ ( tc_prod @ B @ B ) ) @ ( c_Product__Type_OPair @ B @ B ) ) @ ( c_COMBI @ B ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(1662,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ E @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ D ) @ C ) ) @ B ) @ A )
= ( c_Nat_Onat_Onat__case @ ( tc_List_Olist @ E ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ E @ ( tc_List_Olist @ E ) ) @ ( c_List_Olist__update @ E @ C ) ) @ A ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update_Osimps_I2_J) ).
thf(8940,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ E @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ D ) @ C ) ) @ B ) @ A )
= ( c_Nat_Onat_Onat__case @ ( tc_List_Olist @ E ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_List_Olist @ E ) @ ( tc_List_Olist @ E ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ E @ ( tc_List_Olist @ E ) ) @ ( c_List_Olist__update @ E @ C ) ) @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1662]) ).
thf(508,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= ( c_Relation_OId @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_relpow_Osimps_I1_J) ).
thf(4584,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= ( c_Relation_OId @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(1992,axiom,
! [A: $i,B: $i] : ( class_Nat_Osize @ ( tc_prod @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_prod__Nat_Osize) ).
thf(10187,plain,
! [A: $i,B: $i] : ( class_Nat_Osize @ ( tc_prod @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1992]) ).
thf(699,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ A ) @ B ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym) ).
thf(5307,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ A ) @ B ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(701,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/sandbox/benchmark/theBenchmark.p',fact_listrel__iff__nth) ).
thf(5312,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)],[701]) ).
thf(739,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ D )
=> ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ D ) @ B ) @ A )
= ( c_Complete__Lattice_OSup__class_OSup @ D @ ( hAPP @ ( c_Set_OCollect @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool @ D ) @ ( c_HOL_OEx @ ( tc_fun @ C @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_COMBS @ ( tc_fun @ C @ D ) @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_fun @ C @ D ) ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ C @ D ) @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ ( tc_fun @ C @ D ) ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_fun @ C @ D ) @ D ) @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_fun @ C @ D ) @ D ) @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBB @ D @ tc_HOL_Obool @ ( tc_fun @ C @ D ) ) ) @ c_fequal ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ C @ D ) @ C @ D ) @ ( c_COMBI @ ( tc_fun @ C @ D ) ) ) @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__apply) ).
thf(5494,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ D )
=> ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ C @ D ) @ B ) @ A )
= ( c_Complete__Lattice_OSup__class_OSup @ D @ ( hAPP @ ( c_Set_OCollect @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool @ D ) @ ( c_HOL_OEx @ ( tc_fun @ C @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) @ D ) @ ( hAPP @ ( c_COMBS @ ( tc_fun @ C @ D ) @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( tc_fun @ C @ D ) ) @ c_fconj ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ C @ D ) @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ ( tc_fun @ C @ D ) ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_fun @ C @ D ) @ D ) @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ ( tc_fun @ C @ D ) @ D ) @ ( tc_fun @ ( tc_fun @ C @ D ) @ tc_HOL_Obool ) ) @ D ) @ ( c_COMBB @ D @ tc_HOL_Obool @ ( tc_fun @ C @ D ) ) ) @ c_fequal ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ C @ D ) @ C @ D ) @ ( c_COMBI @ ( tc_fun @ C @ D ) ) ) @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(2280,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__mono) ).
thf(11251,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2280]) ).
thf(1057,axiom,
! [A: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__empty__eq) ).
thf(6663,plain,
! [A: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).
thf(913,axiom,
! [A: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__UNIV__eq) ).
thf(6158,plain,
! [A: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(1677,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ D @ D @ D ) @ C ) @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ D @ D @ D ) @ C ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ D @ D @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_union__comp__emptyR) ).
thf(8991,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ D @ D @ D ) @ C ) @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ D @ D @ D ) @ C ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ D @ D @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1677]) ).
thf(2288,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/sandbox/benchmark/theBenchmark.p',fact_DomainI) ).
thf(11281,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)],[2288]) ).
thf(150,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/sandbox/benchmark/theBenchmark.p',fact_unique__quotient__lemma__neg) ).
thf(3212,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)],[150]) ).
thf(2632,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_New__DSequence_Opos__empty @ B ) @ A )
= ( c_Lazy__Sequence_Oempty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Opos__empty__def) ).
thf(12579,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)],[2632]) ).
thf(175,axiom,
! [A: $i,B: $i] :
( ( B
!= ( c_List_Olist_ONil @ A ) )
=> ( ( hAPP @ ( c_List_Ohd @ A ) @ ( hAPP @ ( c_List_Orev @ A ) @ B ) )
= ( c_List_Olast @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__rev) ).
thf(3299,plain,
! [A: $i,B: $i] :
( ( B
!= ( c_List_Olist_ONil @ A ) )
=> ( ( hAPP @ ( c_List_Ohd @ A ) @ ( hAPP @ ( c_List_Orev @ A ) @ B ) )
= ( c_List_Olast @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(779,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/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono1) ).
thf(5649,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)],[779]) ).
thf(1341,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/sandbox/benchmark/theBenchmark.p',fact_append__assoc) ).
thf(7723,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)],[1341]) ).
thf(1074,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ tc_HOL_Obool ) ) @ ( c_List_Olistrel1 @ C @ B ) ) @ ( c_List_Olistrel1 @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1__mono) ).
thf(6733,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ tc_HOL_Obool ) ) @ ( c_List_Olistrel1 @ C @ B ) ) @ ( c_List_Olistrel1 @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(562,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( c_List_Olist_ONil @ ( tc_List_Olist @ B ) ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ ( tc_List_Olist @ B ) ) ) @ C ) ) )
=> ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Onth @ ( tc_List_Olist @ B ) ) @ C ) @ D ) )
= A ) )
=> ( ( c_List_Otranspose @ B @ C )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ tc_Nat_Onat @ ( tc_List_Olist @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ ( tc_List_Olist @ tc_Nat_Onat ) @ ( tc_List_Olist @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ B ) @ ( tc_fun @ ( tc_List_Olist @ tc_Nat_Onat ) @ ( tc_List_Olist @ B ) ) @ tc_Nat_Onat ) @ ( c_List_Omap @ tc_Nat_Onat @ B ) ) @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_List_Olist @ B ) @ ( tc_fun @ tc_Nat_Onat @ B ) @ tc_Nat_Onat ) @ ( c_List_Onth @ B ) ) @ ( hAPP @ ( c_List_Onth @ ( tc_List_Olist @ B ) ) @ C ) ) ) ) ) @ ( c_List_Oupt @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ ( tc_List_Olist @ B ) ) ) @ C ) ) ) ) @ ( c_List_Oupt @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__rectangle) ).
thf(4784,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( c_List_Olist_ONil @ ( tc_List_Olist @ B ) ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ ( tc_List_Olist @ B ) ) ) @ C ) ) )
=> ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Onth @ ( tc_List_Olist @ B ) ) @ C ) @ D ) )
= A ) )
=> ( ( c_List_Otranspose @ B @ C )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ tc_Nat_Onat @ ( tc_List_Olist @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ ( tc_List_Olist @ tc_Nat_Onat ) @ ( tc_List_Olist @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ B ) @ ( tc_fun @ ( tc_List_Olist @ tc_Nat_Onat ) @ ( tc_List_Olist @ B ) ) @ tc_Nat_Onat ) @ ( c_List_Omap @ tc_Nat_Onat @ B ) ) @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_List_Olist @ B ) @ ( tc_fun @ tc_Nat_Onat @ B ) @ tc_Nat_Onat ) @ ( c_List_Onth @ B ) ) @ ( hAPP @ ( c_List_Onth @ ( tc_List_Olist @ B ) ) @ C ) ) ) ) ) @ ( c_List_Oupt @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ ( tc_List_Olist @ B ) ) ) @ C ) ) ) ) @ ( c_List_Oupt @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(4,axiom,
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__0) ).
thf(2690,plain,
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(668,axiom,
! [A: $i] :
( ( c_Hilbert__Choice_Oinv__into @ A @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Fun_Oid @ A ) )
= ( c_Fun_Oid @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__id) ).
thf(5183,plain,
! [A: $i] :
( ( c_Hilbert__Choice_Oinv__into @ A @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Fun_Oid @ A ) )
= ( c_Fun_Oid @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(89,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/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).
thf(2998,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)],[89]) ).
thf(2386,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/sandbox/benchmark/theBenchmark.p',fact_finite__Domain) ).
thf(11631,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)],[2386]) ).
thf(2609,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/sandbox/benchmark/theBenchmark.p',fact_takeWhile__eq__all__conv) ).
thf(12471,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)],[2609]) ).
thf(814,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ D @ D @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__inf__le__inf) ).
thf(5788,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ D @ D @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(685,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Nitpick_Ofold__graph_H @ D @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_H_Ointros_I1_J) ).
thf(5261,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Nitpick_Ofold__graph_H @ D @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(1466,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ B ) @ ( c_List_Oremdups @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__remdups) ).
thf(8179,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ B ) @ ( c_List_Oremdups @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1466]) ).
thf(723,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ F @ E ) )
=> ( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( hBOOL @ ( hAPP @ F @ ( hAPP @ ( c_Product__Type_Ofst @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ A ) @ E ) @ C ) ) ) )
& ( hBOOL @ ( hAPP @ D @ ( hAPP @ ( c_Product__Type_Osnd @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ A ) @ E ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_conjI__realizer) ).
thf(5436,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ F @ E ) )
=> ( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( hBOOL @ ( hAPP @ F @ ( hAPP @ ( c_Product__Type_Ofst @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ A ) @ E ) @ C ) ) ) )
& ( hBOOL @ ( hAPP @ D @ ( hAPP @ ( c_Product__Type_Osnd @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ A ) @ E ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(503,axiom,
! [A: $i,B: $i] :
( ( ( c_List_Oconcat @ B @ A )
= ( c_List_Olist_ONil @ B ) )
<=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ B ) ) @ C ) @ ( hAPP @ ( c_List_Oset @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ( C
= ( c_List_Olist_ONil @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat__eq__Nil__conv) ).
thf(4547,plain,
! [A: $i,B: $i] :
( ( ( ( c_List_Oconcat @ B @ A )
= ( c_List_Olist_ONil @ B ) )
=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ B ) ) @ C ) @ ( hAPP @ ( c_List_Oset @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ( C
= ( c_List_Olist_ONil @ B ) ) ) )
& ( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_List_Olist @ B ) ) @ C ) @ ( hAPP @ ( c_List_Oset @ ( tc_List_Olist @ B ) ) @ A ) ) )
=> ( C
= ( c_List_Olist_ONil @ B ) ) )
=> ( ( c_List_Oconcat @ B @ A )
= ( c_List_Olist_ONil @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(2185,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/sandbox/benchmark/theBenchmark.p',fact_rtrancl__converseI) ).
thf(10916,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)],[2185]) ).
thf(759,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
| ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less) ).
thf(5569,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
| ( B = A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ A ) )
| ( B = A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(2446,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
<=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ A @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__subset__iff) ).
thf(11822,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ A @ F ) ) ) ) )
& ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2446]) ).
thf(1759,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Obij__betw @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( c_Fun_Obij__betw @ B @ E @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( c_Hilbert__Choice_Oinv__into @ B @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Fun_Ocomp @ E @ D @ B @ C ) @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ B @ D @ ( c_Hilbert__Choice_Oinv__into @ B @ E @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) @ ( c_Hilbert__Choice_Oinv__into @ E @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__inv__distrib) ).
thf(9303,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Obij__betw @ E @ D @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( c_Fun_Obij__betw @ B @ E @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
=> ( ( c_Hilbert__Choice_Oinv__into @ B @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Fun_Ocomp @ E @ D @ B @ C ) @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ E @ B @ D @ ( c_Hilbert__Choice_Oinv__into @ B @ E @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) @ ( c_Hilbert__Choice_Oinv__into @ E @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1759]) ).
thf(2105,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/sandbox/benchmark/theBenchmark.p',fact_pair__imageI) ).
thf(10618,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)],[2105]) ).
thf(2195,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( c_Finite__Set_Ofold1 @ C @ B ) )
=> ( ( hAPP @ D @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__singleton__def) ).
thf(10949,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( c_Finite__Set_Ofold1 @ C @ B ) )
=> ( ( hAPP @ D @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2195]) ).
thf(1451,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ F @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ ( tc_fun @ E @ tc_HOL_Obool ) @ D ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I10_J) ).
thf(8130,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ F @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ F @ ( tc_fun @ E @ tc_HOL_Obool ) @ D ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1451]) ).
thf(2226,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_Oimage @ E @ C @ A ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__surj) ).
thf(11048,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( c_Set_Oimage @ E @ C @ A ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2226]) ).
thf(1221,axiom,
! [A: $i,B: $i] :
( ( c_List_Osublist @ B @ ( c_List_Olist_ONil @ B ) @ A )
= ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__nil) ).
thf(7274,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)],[1221]) ).
thf(1218,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/sandbox/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).
thf(7267,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)],[1218]) ).
thf(592,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__le1) ).
thf(4908,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(2158,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ D @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ D @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsp__infI) ).
thf(10817,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ D @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_List_Olistsp @ D @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2158]) ).
thf(1837,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_List_Omeasures @ B @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ ( tc_fun @ B @ tc_Nat_Onat ) ) @ E ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_measures__less) ).
thf(9611,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_List_Omeasures @ B @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ ( tc_fun @ B @ tc_Nat_Onat ) ) @ E ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1837]) ).
thf(377,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/sandbox/benchmark/theBenchmark.p',fact_diff__is__0__eq_H) ).
thf(4056,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)],[377]) ).
thf(1062,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/sandbox/benchmark/theBenchmark.p',fact_map__pair__simp) ).
thf(6686,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)],[1062]) ).
thf(2122,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/sandbox/benchmark/theBenchmark.p',fact_drop__butlast) ).
thf(10686,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)],[2122]) ).
thf(107,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__mult @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( ( hAPP @ A @ F )
= ( c_Groups_Oone__class_Oone @ E ) ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__Un__one) ).
thf(3052,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ocomm__monoid__mult @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ B ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( ( hAPP @ A @ F )
= ( c_Groups_Oone__class_Oone @ E ) ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E ) ) @ A ) @ ( c_Groups_Oone__class_Oone @ E ) ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(180,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/sandbox/benchmark/theBenchmark.p',fact_zadd__zless__mono) ).
thf(3316,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)],[180]) ).
thf(46,axiom,
class_Groups_Ocomm__monoid__add @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).
thf(2834,plain,
class_Groups_Ocomm__monoid__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(1047,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
thf(6632,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)],[1047]) ).
thf(1514,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ C @ B ) @ B @ ( c_Product__Type_Osnd @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ B ) @ D ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ A ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( D
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ C @ B ) @ B @ ( c_Product__Type_Osnd @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ B ) @ D ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ A ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__image__times) ).
thf(8380,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ C @ B ) @ B @ ( c_Product__Type_Osnd @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ B ) @ D ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ A ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( D
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ C @ B ) @ B @ ( c_Product__Type_Osnd @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OSigma @ C @ B ) @ D ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C ) @ A ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1514]) ).
thf(875,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/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Oeq__fold__g) ).
thf(6035,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)],[875]) ).
thf(1708,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ ( c_Set_Oimage @ D @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ E @ B @ ( hAPP @ ( c_Fun_Ocomp @ D @ B @ E @ A ) @ C ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comp__surj) ).
thf(9087,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( ( ( hAPP @ ( c_Set_Oimage @ D @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( hAPP @ ( c_Set_Oimage @ E @ B @ ( hAPP @ ( c_Fun_Ocomp @ D @ B @ E @ A ) @ C ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_HOL_Obool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1708]) ).
thf(1157,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ C @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ C ) @ c_fconj ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ B ) ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__conj__eq) ).
thf(7057,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Set_OCollect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ C @ tc_HOL_Obool @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ C ) @ c_fconj ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ B ) ) @ ( hAPP @ ( c_Set_OCollect @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).
thf(1226,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ ( c_HOL_OThe @ D @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ c_fequal ) @ B ) ) @ A ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__vimage__singleton) ).
thf(7295,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ ( c_HOL_OThe @ D @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ D ) @ c_fequal ) @ B ) ) @ A ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1226]) ).
thf(1070,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Ofun__upd @ D @ C @ B @ A @ ( hAPP @ B @ A ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__triv) ).
thf(6722,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)],[1070]) ).
thf(2468,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( c_Relation_Oantisym @ C @ A )
=> ( c_Relation_Oantisym @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisym__subset) ).
thf(11896,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
=> ( ( c_Relation_Oantisym @ C @ A )
=> ( c_Relation_Oantisym @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2468]) ).
thf(1481,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ ( c_Set_Ovimage @ D @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ C ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__eq__UN) ).
thf(8232,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Set_Ovimage @ D @ C @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) @ C ) @ ( c_Set_Ovimage @ D @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ C ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1481]) ).
thf(1111,axiom,
! [A: $i,B: $i] :
( ( ( c_SetInterval_Oord_OgreaterThanAtMost @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) ) @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ tc_Nat_Onat ) @ c_fNot ) ) @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) )
<=> ~ ( ( 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/sandbox/benchmark/theBenchmark.p',fact_dvd_OgreaterThanAtMost__empty__iff) ).
thf(6879,plain,
! [A: $i,B: $i] :
( ( ( ( c_SetInterval_Oord_OgreaterThanAtMost @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) ) @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ tc_Nat_Onat ) @ c_fNot ) ) @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) )
=> ~ ( ( 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 ) ) )
=> ( ( c_SetInterval_Oord_OgreaterThanAtMost @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ c_fconj ) ) @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_Nat_Onat ) @ ( hAPP @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ tc_Nat_Onat ) @ c_fNot ) ) @ ( hAPP @ ( c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) ) ) ) @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).
thf(892,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_Set_OPow @ D ) ) @ A ) ) ) @ ( hAPP @ ( c_Set_OPow @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__Pow__subset) ).
thf(6094,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C ) @ ( c_Set_OPow @ D ) ) @ A ) ) ) @ ( hAPP @ ( c_Set_OPow @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(1113,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__Compl__subset) ).
thf(6896,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ C @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ D @ C @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).
thf(82,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/sandbox/benchmark/theBenchmark.p',fact_incr__mult__lemma) ).
thf(2980,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)],[82]) ).
thf(276,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ C @ B ) @ E ) @ A ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__list__update__neq) ).
thf(3669,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ C @ B ) @ E ) @ A ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(882,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A )
= ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( A
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__eq__UNIV__imp__eq__UNIV) ).
thf(6067,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ A )
= ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( A
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(15500,plain,
$false,
inference(cvc4,[status(thm)],[8607,3021,4201,3944,6405,6979,9077,4729,4852,6512,9864,5509,2822,9131,4188,4447,11472,12055,10166,6355,10259,10373,6669,12607,11445,4571,9653,5857,9886,5896,6231,2778,8288,6530,11211,8663,6976,4062,3399,10452,12116,4899,3798,12570,11517,7922,8514,9754,7673,6283,4290,11164,8507,6285,10495,10812,2787,5654,6121,6172,11998,6555,11898,8415,4682,8639,5733,11318,6263,8887,10976,6566,12468,8828,6014,5582,4992,6374,12699,6527,12462,8200,12738,9032,6808,10507,11350,10431,6744,10694,4532,12500,11175,10658,3534,6142,11688,8005,8417,11352,7477,3072,7905,8450,9573,6177,7935,12129,12649,6918,4500,4075,6868,11880,6495,2808,3905,6106,10927,5644,11603,5069,6463,2776,10277,11409,9901,9120,2953,6458,9045,3460,6796,10061,9918,5625,7726,10562,9717,5173,6323,11122,8447,6338,10314,7198,5982,10017,5224,5669,9191,12221,5405,4215,7182,10886,8943,7781,3402,5237,8563,4408,10039,6602,11724,11440,7208,9152,8988,5348,9268,4487,12013,9003,11080,6194,6971,3439,2686,7697,2712,7467,10341,8320,5425,6278,12193,10282,10959,8765,11945,6505,9460,5565,3049,3745,11072,5755,3648,10869,10395,3365,7556,9052,4026,5288,7873,7096,10346,9428,10864,6089,9813,6727,9000,3693,7147,11160,10940,8370,5674,11239,7422,11513,6241,12421,7188,3481,5005,6996,6759,10594,9801,12165,12494,5782,5178,5708,11786,3717,5412,6046,9672,8851,6236,7944,8578,11588,7311,5533,4941,12617,9443,6138,4047,10336,7018,10230,4343,8848,3350,6466,3915,6268,9746,3502,11542,10599,11382,8539,11907,6623,8133,4679,7235,9096,9159,9994,7729,6904,11863,8122,3281,5301,4198,11731,9465,9396,4137,6754,8025,8546,8699,11912,8504,2825,10807,10530,4322,12785,4156,5269,6608,5750,12324,11831,6291,9394,7043,4948,4467,5024,10584,5797,5342,8357,5274,8951,8834,6332,9123,7386,3891,12351,3248,8610,3442,3263,10903,7241,10955,6766,7620,10121,5585,9989,10935,3195,7277,3029,4348,4866,6552,9099,2814,4422,10630,7825,3275,8494,9828,11798,8996,9597,3131,4956,11203,8875,3116,7401,8089,8225,6274,11025,3689,9561,10053,9084,12718,4224,8647,12046,4761,11299,9128,3821,10221,7771,11448,11458,9360,8214,3776,6968,5150,11812,10010,4023,10606,3089,7000,4568,3353,8022,11628,5108,8242,4428,10469,2745,8880,7665,11760,11183,2989,8483,3231,8257,8770,8907,5744,11453,12745,9877,7156,11986,11696,6253,11232,4119,3517,3374,8590,3638,9480,12804,8902,6455,4617,11773,10516,11321,8310,6149,7060,6626,11538,11859,2767,8468,6599,4492,5323,5397,5622,5480,3216,8235,6781,6936,8367,10967,3470,9529,11741,6923,10650,5851,3657,12180,7047,11991,3734,5829,9869,3014,8220,5727,9973,3835,11849,10665,9725,9039,10945,4265,4460,6828,10702,4507,11716,12657,4400,7464,8352,6487,8558,11495,7509,12517,6382,6594,9768,10157,7588,11533,8293,9425,9401,4396,12051,6657,11748,6054,5985,6081,10913,10519,10454,4696,5957,4988,9204,5433,7107,11314,7792,8190,9103,7786,5892,10746,11778,7144,4329,12706,11064,11656,3199,5888,5526,5084,3075,4072,8229,10189,3393,11293,11926,7818,7369,5333,10271,3163,7104,3453,10918,6189,8972,2880,4847,7376,9811,5558,4050,12296,12105,11389,4724,2925,11691,11838,4134,11709,7015,8642,3923,3290,7581,8759,6438,12582,12735,3152,6717,10734,4162,7899,6204,11036,9309,5834,3068,4033,12430,8817,8173,2750,5045,7707,12330,11939,10070,4751,11242,5738,11312,12638,9749,11325,12311,6777,11119,7807,10551,5384,3712,9452,8823,8141,11104,7336,3036,11136,5772,7909,12008,6347,5296,6498,12036,12101,8686,4924,9035,10965,9700,10350,4825,6863,12411,10388,10895,10390,3243,6021,9347,11783,10574,11954,4643,8892,2965,11596,8443,5629,4519,11143,8939,7830,5137,10459,4892,7051,5819,7688,10933,9923,3606,7758,9024,11357,2718,6210,4475,7170,9896,4065,5695,10523,7305,8924,9822,3151,11555,9090,8078,5545,9252,10216,5298,9026,9048,11677,4700,8751,2954,8975,3899,2922,11528,3229,7254,12732,8170,3011,7533,8486,7849,6560,11993,2910,12078,8655,4753,4589,11253,11255,6482,11395,9340,10742,8927,3169,11791,12623,5017,3531,3635,12200,12333,6064,8795,6250,4557,8397,5291,8613,5117,3318,7269,11456,11069,9164,6865,12489,4370,4910,8842,6741,7078,4059,12073,11499,12300,11704,6092,7110,3795,5122,12232,9881,7735,3679,9722,3603,5266,9618,8856,11003,8878,12110,9488,6635,9705,8211,8783,6079,12260,7989,7870,4016,7703,10171,6605,8994,7353,4920,10699,4375,8756,9817,6773,5579,5512,9949,7229,10858,11865,5815,3742,12809,8334,3069,7084,3884,5470,9981,3371,11106,8081,3134,12715,7692,7984,12215,4821,2986,8714,10441,5594,7244,11074,3682,4044,5843,7957,9455,8683,6163,5690,6402,3033,3445,6709,10721,3166,7308,4295,12640,8810,5826,4280,5879,2873,5937,3269,6629,6432,10502,4140,9217,8788,4849,4053,12147,8085,12340,8145,3198,6427,7762,6043,4994,11152,3499,3750,8736,7361,5460,7902,7625,3600,5988,5779,9391,12025,6143,7545,8181,5038,4746,4402,11683,10367,7501,6096,10006,5201,7591,11646,11670,12603,4417,6168,11948,3926,11042,9291,6666,8031,9613,12020,11702,3667,4732,12709,5993,5330,8518,5515,4668,5345,11762,11435,9333,11304,8238,6215,3731,4808,8354,7750,5854,4123,12760,3467,3699,11736,8530,6748,8471,12353,3782,5904,8068,6677,3831,11133,5053,6101,12404,3122,2946,7205,6335,2685,7065,3862,10126,10413,10154,10791,8282,7623,7173,9328,3381,7389,5502,9608,10566,4544,11007,11221,10266,8063,2692,8931,4525,4693,5428,9936,7593,4930,10318,11128,5919,3632,3119,10398,3078,4883,10771,5081,11189,4012,6128,7222,4109,5233,8138,11278,5497,5475,3001,3060,9772,3018,11019,11923,4817,4263,5830,4276,8864,4315,9477,6395,2781,4676,11801,6299,8176,7101,9872,8544,3311,10107,2877,4301,3326,3143,12768,8105,9640,10830,10185,9508,8985,7054,11364,7453,3622,9662,5705,7717,5651,4772,6116,10015,7846,3094,7981,4425,10761,10528,3714,6661,10381,2868,4389,7998,8008,9419,9957,5253,10671,4938,10620,5263,5547,4744,11046,5932,6256,10195,11666,9288,5662,6837,11442,7480,7417,6539,8390,3643,6946,7404,4444,4457,12724,10752,11651,7895,6271,7682,7821,8159,11892,3573,8820,7668,9012,6805,9620,9144,11061,12005,3703,11432,2968,5576,8599,8458,12418,6134,11608,11023,9365,7609,3654,10423,4384,12481,8072,8658,12393,11965,10834,8326,10560,9149,11052,12218,7138,7966,5134,6788,8036,9893,6207,10603,6475,5973,9739,7485,6876,4244,7738,9581,10285,3390,10148,4934,4540,10961,10207,3937,7789,7597,5776,8732,5683,10533,8587,8455,3967,10302,11833,4902,3333,11261,4953,8307,6152,5026,3920,6186,11916,7333,8980,9942,11873,3201,6171,8512,4889,4765,3190,10783,8708,10406,10058,3824,4148,11673,3903,7150,5747,3834,11593,11216,5310,8527,5153,6533,10815,12751,9468,11084,8839,9913,8739,11856,2702,3563,2761,12282,4195,12305,5402,5090,7407,2883,10689,10377,11546,3856,8422,8049,8279,11544,3592,10819,2748,5964,6260,6070,6647,5447,12486,12255,12553,9171,11196,12346,11328,7941,9925,12361,12123,9168,6038,6931,6400,2995,3841,7802,7527,9517,3807,12173,12155,2936,3660,5722,7128,6084,9650,11578,6901,10592,10683,12238,5996,11110,9416,9352,10571,12168,4470,11033,4685,10175,9765,6026,10971,2904,8095,9677,4354,3042,7512,5969,7459,2717,6699,7010,9939,11591,10030,7225,8290,12660,3985,8110,4657,8480,9021,12265,11016,6243,8112,10327,6001,7491,12704,10321,9853,11464,4797,10420,4340,7165,3523,7257,4503,9154,5882,6546,3111,6492,12287,10625,11561,5758,2894,4599,7212,11011,3396,7372,10890,11920,5043,8807,11805,11323,3266,7041,10461,7472,12636,3536,8217,12028,7709,7162,6234,7833,3387,3547,5456,9798,7714,4268,7968,7938,6468,12483,8909,11633,3234,6916,11333,7639,11566,3504,10906,4283,5488,7497,8900,3240,6949,2789,3609,4159,11615,9733,10334,10963,8580,12301,7073,3472,9543,3086,9157,6581,8711,12210,7440,3081,3758,5940,9471,3272,10709,8222,11861,6229,10100,5050,9521,5876,2806,5097,6344,8167,6898,9057,10557,10435,7180,5271,8092,4381,4975,2817,7828,12787,5752,10874,10525,12663,7815,4505,7038,2959,8872,3964,12566,11201,7671,4433,7741,7795,4251,12349,8767,11819,4978,10611,12592,10034,9125,6385,8549,9659,11846,2891,4837,10393,3646,12053,4112,12401,3695,3330,11951,11502,4171,3208,8665,4218,10348,8624,11423,6302,8492,11291,9538,11968,11515,6649,3123,12423,5207,3436,9555,6638,8059,5539,9808,3619,7536,4640,6123,11750,3416,11841,8524,10974,6549,12280,10596,3304,11618,11900,9354,11765,3302,7394,10953,8301,11525,9483,9670,7482,9835,11169,8419,6024,7783,9702,10766,10842,5870,7415,2721,10088,8452,4337,8276,9422,6572,10151,7519,7933,10910,3251,11283,11117,3815,12668,9375,9312,6920,3238,5244,12131,9867,5103,11932,5520,8135,9377,7907,6443,5848,4620,6461,8970,10279,10677,10675,3287,12034,4828,3779,7379,3419,4914,5631,5303,7438,8688,5491,5901,11733,9118,11355,11829,12182,11268,4805,8313,9570,5610,10888,9015,3182,3586,3384,11438,5616,11586,10696,12369,11406,4107,9713,7238,5657,4462,4985,2757,12246,9931,3219,5563,6834,4203,5114,7504,9042,12248,6004,6087,8620,9857,7768,3747,11470,2742,10375,11623,4103,10253,5730,12433,9079,10995,12712,5175,11205,9691,6989,11392,8983,12572,5439,7302,6725,6974,11746,7551,11158,7928,10732,7978,9553,10219,3977,7778,3006,3451,10755,7141,4652,12562,8998,5466,10489,5885,11583,3583,9905,8473,9511,12587,11767,7450,6802,4726,9074,9674,6446,12810,9101,6692,2928,8652,2974,7297,8340,8413,3893,2710,10467,9018,6377,7911,2931,5976,7366,6730,3539,2770,8052,8853,4844,12460,10793,10660,8440,7603,2962,6811,4232,12655,11348,10444,11558,6449,5216,3838,2835,6907,8573,7383,10275,8719,10020,10549,5641,10852,12797,9741,9899,6738,4373,11775,12465,9975,3917,9841,9249,7469,6223,6288,11102,11245,3687,11380,10893,7805,12497,9106,9698,12765,11605,11130,3706,7200,5725,4703,11781,9345,7339,10576,6180,12224,9921,7630,10119,9398,7507,7356,7232,6485,6212,8560,12557,11359,11535,11361,4481,9503,5619,4473,3881,2952,9727,9111,5463,7260,4331,4741,12207,8954,9524,5587,6320,10311,10824,4441,9403,3193,3427,4013,12492,7578,4886,4260,2994,4580,7975,12368,10759,12118,2784,10354,9259,9514,9069,3293,5785,10223,7447,9884,8804,10867,12599,3672,4735,6659,8936,9826,7562,7539,6751,6962,10449,7897,8949,3146,11030,6056,10132,4177,8323,8836,4859,9656,2684,5165,6517,7679,9546,6076,7773,7122,3455,4688,5916,3278,10788,9783,12075,6440,6821,8477,6998,4722,12043,5003,9202,4168,11679,7070,6641,6266,6621,4922,7159,8904,10521,10246,5790,6012,11230,7283,3988,9631,11738,11937,7600,5047,9879,7026,5229,5716,3737,7087,8569,8725,3640,7705,2863,6238,7635,5607,6472,9847,3507,11460,12088,11540,11573,8143,5125,11753,11694,8537,5111,3214,6597,3260,5499,9710,4950,9535,6826,11956,5074,5592,10371,12807,7045,5523,3209,9005,4630,8364,4593,2888,10027,2831,6146,2689,6280,3063,10164,3722,3554,5948,4117,3769,10608,3246,11066,10636,3448,4522,5431,6762,8498,9214,10504,9991,12071,4905,10439,3940,6981,7494,9634,5467,9281,4190,11974,3818,12455,3691,3114,2688,11429,7568,9050,10095,3344,8496,11295,7522,11297,3202,10717,10724,3475,10861,7090,9567,7947,9815,8845,4145,6508,7879,8509,3801,6125,9082,3774,12396,4351,6352,3544,6174,3828,4132,8148,7583,3847,11198,9093,8206,10012,3359,3329,3174,4781,9911,11637,3853,10739,5186,5277,11788,4510,12548,2949,8433,6992,9775,5147,10129,9109,7752,12647,7876,4802,9495,10097,7456,12439,4959,2838,6073,12630,5736,8331,11835,12262,12771,2992,7919,7580,10293,9500,4624,6318,7461,6775,3356,11386,7067,11054,11882,9363,4991,8061,5453,4143,4932,8185,11005,9983,4235,8734,3024,9406,7202,9637,7426,4225,2939,12241,8552,7192,9274,8087,6511,6161,5100,11108,8798,4795,3520,8151,10178,8861,7720,7690,5895,7488,4257,12039,4671,3684,6220,6420,11302,9770,6793,12277,10193,8285,5832,2875,10332,12145,8830,3284,6706,10712,2760,10261,7099,9532,3478,3433,3946,3139,5873,8946,9060,12343,4698,7676,6965,10082,3589,5179,8028,4587,4945,9527,9966,10464,9665,7177,7627,9306,9760,11530,9628,4763,2870,4165,2828,9780,5536,11995,5660,5386,7606,4419,7412,11450,10774,6390,9819,12633,4997,11681,10796,7288,8957,7765,5421,4738,8825,7271,4185,3625,8392,3725,5907,7007,4646,4078,9615,9141,12722,8761,5389,12355,3929,2792,2907,6814,11412,9647,8075,10479,7131,8337,6831,12574,3336,5813,10428,7700,7732,7950,10072,2707,12066,6818,9234,6341,3484,3709,8780,3825,7359,4615,9951,6689,5008,4089,8011,5191,10225,11039,5132,7996,12061,9029,10352,12370,7012,10969,4126,6790,7167,4042,8912,2811,9934,3991,6913,2971,11001,6910,8634,10411,10182,8897,3003,5394,2764,4010,11663,9824,4834,4495,5087,10104,7120,6618,3859,12836,9449,7125,3368,12387,8083,4969,3662,7959,11013,10627,6799,9736,12758,10268,10050,5600,6584,5922,11918,8119,9999,6430,4321,6412,5119,11653,9115,8749,10937,2956,7855,6305,4649,6854,10828,6397,3497,4153,8388,3844,8501,3430,5692,4591,9908,12080,6018,9792,8203,4774,9434,8304,5040,5837,7747,11755,11658,3149,3896,11366,4387,11405,4478,6277,12620,11172,7887,12448,12675,10065,8102,6166,11685,12093,7530,11982,5590,9211,10924,6569,5672,8721,5517,2739,11894,4869,9162,5194,11700,4927,7135,5336,12171,11208,5864,7093,9262,12230,10041,12213,5477,4663,11744,3379,4880,10838,7649,12153,7081,7542,4917,11580,8660,6326,2683,9166,7419,4114,6201,4399,4706,3785,9806,10291,4378,12162,10681,6007,3907,8193,8162,2983,3865,4254,4811,7744,7153,12374,6563,4596,6131,7836,10312,9183,4719,11722,3464,7712,10418,11843,2736,11263,5014,6226,8489,5247,11914,9844,9331,11563,3203,8933,10205,12515,8801,6535,2800,11082,3309,3982,3015,10408,11155,11943,8400,10809,10036,9915,11214,5159,8521,4755,6294,3560,4895,10691,3347,6114,4286,8373,5990,9271,3558,12605,8019,6520,3177,10379,3804,9134,9541,4007,6735,5105,6644,8921,9265,8869,8424,6558,12781,11548,3850,5741,8395,11162,12503,10472,12253,12801,5339,6258,9752,2913,6380,6889,8002,3323,7280,5867,2714,12729,5251,3030,11668,9795,6682,2795,4193,4912,11099,9927,9293,11649,10622,12022,6952,3045,9431,9409,9564,9987,11890,11377,12175,11114,10781,12363,7525,4318,7076,7925,8692,5945,10988,11910,11803,6136,3362,9367,12406,5204,3128,4129,8066,10554,3974,8328,10836,7987,11258,12626,3057,6155,2803,4242,6329,11621,12530,9763,4972,5140,6435,11050,11958,9474,6697,3772,12235,12508,12560,12761,4066,4484,5280,9446,7035,4410,4831,9193,11309,10308,10845,11479,9055,7755,11477,12188,6452,11462,7617,10877,10124,8585,5219,10642,7430,8680,8773,2687,3740,6109,9370,4019,7694,9605,4691,2699,3494,11875,4345,9600,10586,12085,7299,4221,5473,11021,8978,5845,3405,2866,8273,3047,10768,6933,3753,12749,3526,7195,9558,10706,3528,4335,7548,11675,9954,5155,3950,5029,10931,10482,10492,7776,8125,11286,5542,4627,8940,4584,10187,5307,5312,5494,11251,6663,6158,8991,11281,3212,12579,3299,5649,7723,6733,4784,2690,5183,2998,11631,12471,5788,5261,8179,5436,4547,10916,5569,11822,9303,10618,10949,8130,11048,7274,7267,4908,10817,9611,4056,6686,10686,3052,3316,2834,6632,6141,8380,6035,9087,7057,7295,6722,11896,8232,6879,6094,6896,2980,3669,6067]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWW337+1 : TPTP v8.1.2. Released v5.2.0.
% 0.13/0.14 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 18 22:25:16 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.94/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.79/1.42 % [INFO] Parsing done (562ms).
% 2.79/1.44 % [INFO] Running in sequential loop mode.
% 3.22/1.66 % [INFO] eprover registered as external prover.
% 3.22/1.67 % [INFO] cvc4 registered as external prover.
% 3.22/1.67 % [INFO] Scanning for conjecture ...
% 4.53/2.07 % [INFO] Found a conjecture and 5225 axioms. Running axiom selection ...
% 7.48/3.53 % [INFO] Axiom selection finished. Selected 2680 axioms (removed 2545 axioms).
% 11.03/5.01 % [INFO] Problem is first-order (TPTP FOF).
% 11.17/5.07 % [INFO] Type checking passed.
% 11.17/5.08 % [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 ...
% 91.70/31.08 % External prover 'cvc4' found a proof!
% 91.70/31.08 % [INFO] Killing All external provers ...
% 91.70/31.08 % Time passed: 30547ms (effective reasoning time: 29639ms)
% 91.70/31.08 % 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)>
% 91.70/31.10 % Axioms used in derivation (2680): fact_wf__not__refl, fact_insertCI, fact_Union__upper, fact_Sigma__Un__distrib1, fact_order__le__neq__trans, fact_INT__simps_I6_J, fact_SUP1__I, fact_remdups_Osimps_I1_J, fact_rtrancl__Int__subset, fact_bex__empty, fact_Int__insert__left__if1, fact_card__partition, fact_Nat_Oadd__0__right, fact_converseI, fact_insert__partition, fact_converse__meet, fact_atLeastLessThan__upt, fact_all__nat, fact_insert__compr, fact_Un__absorb1, fact_Sigma__Diff__distrib2, fact_xt1_I1_J, fact_Inf__Sup, fact_le__SucI, fact_notin__set__remove1, fact_UN__simps_I3_J, fact_set__drop__subset, fact_setsum__cases, fact_converse__rtrancl__induct2, fact_singleton__iff, fact_wmin__emptyI, fact_divmod__nat__zero, fact_single__valued__Id__on, fact_divmod__nat__rel__divmod__nat, fact_append__Nil2, fact_Diff__insert__absorb, fact_concat_Osimps_I1_J, fact_wfP__SUP, fact_card__image__le, arity_fun__Orderings_Oorder, fact_divmod__nat__base, fact_nth__Cons__0, fact_folding__image__simple__idem_Osubset__idem, fact_rel__pow__Suc__I, fact_nat_Osimps_I3_J, fact_wf__union__merge, fact_surj__f__inv__f, fact_le__imp__diff__is__add, fact_bij__betw__same__card, fact_Compl__UNIV__eq, fact_wf, fact_set__zip, fact_vimage__insert, fact_ImageE, fact_inj__graph, fact_InterE, fact_Compl__UN, fact_length__filter__less, fact_folding__one_Osingleton, fact_New__DSequence_Opos__map__def, fact_finite__vimageI, fact_wf__not__sym, fact_finite__UN__I, fact_mult, fact_rel__pow__E2, arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice, fact_lexn_Osimps_I1_J, fact_refl__onD2, fact_Int__lower1, fact_inv__def, fact_def__coinduct, fact_wf__inv__image, fact_setsum__shift__lb__Suc0__0__upt, fact_drop__butlast, fact_def__gfp__unfold, fact_sequence__trans, fact_converse__converse, fact_dropWhile_Osimps_I2_J, fact_pos__union__def, fact_finite_Oequations_I1_J, fact_sym__conv__converse__eq, fact_fold1Set_Ointros, fact_incr__mult__lemma, fact_in__set__conv__decomp, fact_le__inf__iff, fact_sup1I1, fact_atLeastLessThan__empty__iff2, fact_finite__lists__length__le, fact_diff__0__eq__0, fact_zle__refl, fact_inj__comp, fact_rel__pow__E, fact_transfer__nat__int__numerals_I1_J, fact_Field__empty, fact_Sigma__def, fact_bij__imp__bij__inv, fact_inj__on__diff__nat, fact_Domain__Id, fact_le__eq__less__or__eq, fact_rev__swap, fact_UnI1, fact_curry__split, fact_trans__less__add1, fact_folding__image__simple__idem_Oin__idem, fact_comp__inj__on__iff, fact_less__eq__nat_Osimps_I2_J, fact_accp_Oequations, fact_q__pos__lemma, fact_listrel__refl__on, fact_inf__INFI__fold__inf, fact_setsum__Un__nat, fact_length__0__conv, fact_inj__imp__surj__inv, fact_card__Diff__subset__Int, fact_map__fst__zip, fact_subset__UNIV, fact_map__pair__inj__on, fact_Range__Id, fact_inf2I, fact_notin__set__sublistI, fact_lexord__append__leftI, fact_finite_OemptyI, fact_list__eq__iff__nth__eq, fact_set__Cons__sing__Nil, fact_lexord__take__index__conv, fact_Compl__Times__UNIV1, fact_nat__add__left__commute, fact_set__append, fact_nth__upt, fact_image__constant__conv, fact_Range__Int__subset, fact_Image__Int__eq, fact_inf_Oassoc, fact_pair__lessI2, fact_smax__insertI, fact_listrel1E, fact_inv__into__into, fact_insert__iff, fact_INT__Un, fact_zip__append1, fact_image__insert, fact_setsum__empty, fact_monoD, fact_diff__add__inverse, fact_ex__bij__betw__finite__nat, fact_INT__extend__simps_I2_J, fact_part__equivp__transp, fact_last__appendR, fact_fun__left__comm__idem__insert, fact_take__drop, fact_minus__fold__remove, fact_fst__eq__Domain, fact_min__diff, fact_card__gt__0__iff, fact_funpow_Osimps_I1_J, fact_fst__map__pair, fact_nat__less__cases, fact_drop__upt, fact_one__is__add, fact_diff__le__mono2, arity_prod__Enum_Oenum, fact_xt1_I4_J, fact_listrel__Cons1, fact_zip__Nil, fact_termination__basic__simps_I5_J, fact_insert__subset, fact_Rep__Integ__inverse, fact_odd__nonzero, fact_diff__Suc, fact_SUP1__iff, fact_image__Pow__mono, fact_map_Osimps_I1_J, fact_zip__takeWhile__snd, fact_injD, fact_equivI, fact_set__take__subset__set__take, fact_conversep_Oequations, fact_zminus__zminus, fact_Inf__insert, fact_less__imp__le__nat, fact_length__tl, fact_finite__Collect__subsets, fact_greaterThan__iff, fact_divmod__nat__eq, fact_in__listrel1__converse, fact_Suc__nat__eq__nat__zadd1, fact_zless__nat__conj, fact_below__fold1__iff, fact_rtranclD, fact_set__empty2, fact_lists__IntI, arity_Nat__Onat__Orderings_Oorder, fact_curry__def, fact_UNION__empty__conv_I1_J, fact_drop__eq__Nil, fact_fun__left__comm__idem__remove, fact_card__Diff__subset, fact_setsum__Un__zero, fact_pred__nat__trancl__eq__le, fact_rel__comp__distrib, fact_setsum_Oreindex, fact_Inter__insert, fact_le__imp__0__less, fact_add__leD1, fact_Times__Diff__distrib1, fact_UN__eq, fact_INF1__iff, fact_Compl__Int, fact_converse__UNION, fact_Un__mono, fact_finite__INT, fact_equivp__reflp__symp__transp, fact_double__complement, fact_n__lists_Osimps_I2_J, fact_n__less__m__mult__n, fact_fold__image__Un__one, fact_Transitive__Closure_Otrancl__into__trancl, fact_fun__left__comm_Ofold__equality, fact_prod_Orecs, fact_union__comp__emptyR, fact_UN__finite__subset, fact_eq__Abs__Integ, fact_Suc__mono, fact_bij__betw__empty2, fact_concat__eq__Nil__conv, fact_Int__UNIV__right, fact_distinct__remdups, fact_self__append__conv, fact_O__assoc, fact_less__nat__zero__code, fact_hd__rev, fact_trancl__id, fact_List_Omap_Ocompositionality, fact_mono__Field, fact_fun__lub__def, fact_nat_Osize_I4_J, fact_finite__lists__length__eq, fact_min__ext__wf, fact_setsum__diff__nat, fact_equivp__transp, fact_setsum__setsum__restrict, fact_list__update__append, fact_add__less__mono, fact_curry__conv, fact_UN__simps_I10_J, fact_zadd__commute, fact_INT__simps_I10_J, fact_image__Int, fact_IdI, fact_List_Omap_Ocomp, fact_lexn__length, fact_diff__Suc__less, fact_insertI1, fact_rel__comp__distrib2, fact_mult__0, fact_vimage__UNIV, fact_zip__Cons__Cons, fact_wf__no__loop, fact_Zero__int__def, fact_Un__empty__left, fact_sup2I2, fact_pair__box_Oinject, fact_folding__one_Ounion__inter, fact_flat__lub__def, fact_last__rev, arity_Int__Oint__Lattices_Osemilattice__inf, fact_image__add__atLeastLessThan, fact_gr0__conv__Suc, fact_CollectI, fact_UNIV__not__empty, fact_zip__map1, fact_Range__rtrancl, fact_image__constant, fact_Un__insert__left, fact_Int__Union, fact_Un__Pow__subset, fact_comm__monoid__big_Oinfinite, fact_List_Omember__def, fact_pred__nat__def, fact_INT__D, fact_dropWhile__eq__drop, fact_INFI__fold__inf, fact_finite__induct, fact_folding__image__simple_Oeq__fold__g, fact_hoare__derivs_Oinsert, fact_less, fact_max__ext__additive, fact_rtrancl_Ortrancl__refl, fact_inf__absorb1, fact_tl__take, fact_ex__bij__betw__nat__finite, fact_inj__image__mem__iff, fact_map__butlast, fact_equiv__def, fact_prod__eqI, fact_SUP2__E, fact_zero__less__diff, fact_conversep__noteq, fact_INT__eq, fact_remove1_Osimps_I1_J, fact_card_Oempty, fact_acc_Osimps, arity_Nat__Onat__Lattices_Osemilattice__inf, fact_atLeastLessThanSuc, fact_hd__map, fact_setsum__insert, fact_finite__range__imageI, fact_diff__diff__cancel, fact_list__update__code_I2_J, fact_equiv__class__eq, fact_measures__lesseq, fact_funpow__add, fact_nat__add__right__cancel, fact_distinct__append, fact_type__definition__Integ, fact_set__subset__Cons, fact_quotient__diff1, fact_inf__Inf__fold__inf, fact_o__eq__elim, fact_inj__on__the__inv__into, fact_finite__Collect__bounded__ex, fact_listrel__subset__rtrancl__listrel1, fact_listrelp_Oequations_I2_J, fact_last__drop, fact_Compl__Un, fact_curryE, fact_takeWhile__eq__all__conv, fact_Ex__inj__on__UNION__Sigma, fact_setsum__commute, fact_the__inv__f__f, fact_take__upt, fact_dvd_OatLeastLessThan__empty__iff2, fact_Int__left__commute, fact_empty__not__insert, fact_UN__extend__simps_I5_J, fact_image__vimage__eq, fact_SigmaE2, fact_trans__Id__on, fact_mult__le__mono2, help_c__fconj__3, fact_Suc__diff__diff, fact_image__Int__subset, fact_rtrancl__empty, fact_sym__trans__comp__subset, fact_Union__Int__subset, fact_Suc__le__mono, fact_Image__UN, fact_distinct__zipI2, fact_divmod__nat__rel__unique, fact_length__takeWhile__less__P__nth, fact_inj__on__id, arity_Int__Oint__Orderings_Oord, fact_List_Oset__insert, fact_Cons__acc__listrel1I, fact_int__0__less__1, arity_fun__Enum_Oenum, fact_inj__on__Un, fact_set__take__subset, fact_r__into__trancl_H, fact_max__ext__compat, fact_Bex__set__list__ex, fact_rel__compI, fact_atLeast__iff, fact_Int__UN__distrib, fact_singleton__rev__conv, fact_surj__iff__all, fact_Un__UNIV__left, fact_filter__empty__conv, fact_setsum__right__distrib, fact_setsum__multicount, fact_infinite__UNIV__int, help_c__fequal__2, fact_UNION__empty__conv_I2_J, fact_mult__eq__self__implies__10, fact_Image__eq__UN, fact_wf__Int1, fact_acyclic__impl__antisym__rtrancl, fact_Pow__Compl, fact_le__neq__implies__less, fact_tranclD2, fact_wf__less, fact_sublist__shift__lemma, fact_transfer__nat__int__numerals_I2_J, fact_list__all__iff, fact_Collect__imp__eq, fact_snd__eqD, fact_filter__concat, fact_zle__linear, fact_append__eq__conv__conj, fact_neg__single__def, fact_INT__greaterThan__UNIV, fact_weak__coinduct, fact_folding_Oinsert, fact_comp__inj__on, fact_nat__add__distrib, fact_image__UN, fact_ComplD, fact_setsum__reindex, fact_SUP__UN__eq2, fact_list__update_Osimps_I2_J, fact_INT__E, fact_le__funI, fact_pred__equals__eq2, fact_setsum__multicount__gen, fact_Compl__eq__Diff__UNIV, fact_nat__add__left__cancel__less, fact_map__pair__def, fact_finite__UnionD, fact_nth__Cons__Suc, fact_INT__subset__iff, fact_bij__is__inj, fact_rtrancl__listrel1__if__listrel, help_c__fFalse__1, fact_setsum__eq__Suc0__iff, fact_order__less__imp__not__eq, fact_remdups__filter, fact_hd__drop__conv__nth, fact_o__apply, fact_min__strict__def, fact_INF__commute, fact_max__rpair__set, fact_dropWhile__eq__Cons__conv, fact_swap__inj__on, fact_rtrancl__mono, fact_image__Pow__surj, fact_rtrancl__subset__rtrancl, fact_listsp_Oequations_I2_J, help_c__COMBC__1, fact_Powp__Pow__eq, fact_surj__image__vimage__eq, fact_fun__left__comm_Ofun__left__comm, fact_list_Osimps_I3_J, fact_inf1D2, fact_inj__on__imageI2, fact_measures__less, fact_last__list__update, fact_insert__not__empty, fact_take__Suc__conv__app__nth, fact_setsum__0, fact_inv__image__def, fact_folding_Ocommute__left__comp, fact_equiv__intrel__iff, fact_dvd_OatLeastAtMost__singleton, fact_ivl__disj__int_I8_J, fact_UN__equiv__class__type, fact_UN__atLeast__UNIV, fact_prod_Osimps_I2_J, fact_bij__betw__inv__into, fact_Field__Union, fact_subset__Compl__self__eq, fact_THE__default__def, fact_smax__emptyI, fact_converse__rtranclE2, fact_hd_Osimps, fact_nth__take, fact_image__image, fact_Least__Suc, fact_rtrancl__converse, fact_Int__insert__right, fact_Sigma__empty1, fact_finite__SigmaI, fact_ex__nat, fact_folding__image_Ocong, fact_less__infI2, fact_transpose__aux__filter__head, fact_type__definition_OAbs__inject, fact_inj__on__fun__updI, fact_exE__realizer, fact_part__equivp__symp, fact_transfer__nat__int__relations_I1_J, fact_zadd__left__mono, fact_exI__realizer, fact_listrel__iff__nth, fact_split__paired__All, fact_Un__Diff__Int, fact_list__ex__simps_I1_J, fact_append__is__Nil__conv, fact_Int__eq__Inter, fact_Diff__subset, fact_distinct_Osimps_I2_J, fact_card__eq__UNIV__imp__eq__UNIV, fact_nat__mult__distrib__neg, fact_upt__eq__Nil__conv, fact_Field__Un, fact_less__eq, fact_sup__Un__eq2, fact_acyclic__converse, fact_setsum__Un__disjoint, fact_rp__inv__image__def, fact_Range__empty, fact_folding_Oinsert__remove, fact_rev__ImageI, fact_fun__left__comm_Ofold__graph__insertE, fact_upt__conv__Cons, fact_Cons__in__lists__iff, fact_finite__Collect__conjI, fact_nat, fact_nth__map, fact_finite__atLeastZeroLessThan__int, fact_INT__lower, fact_lists_ONil, fact_inv__into__image__cancel, fact_concat__injective, fact_folding__image__simple_Oremove, fact_bij__image__INT, fact_trans__finite__psubset, fact_image__Un, fact_INT__simps_I3_J, fact_acc_OaccI, fact_length__zip, fact_transpose_Osimps_I2_J, fact_sublists__powset, fact_equalityD2, fact_finite__cartesian__productD1, fact_butlast__take, fact_append1__eq__conv, fact_inf_Oleft__commute, fact_remove1__filter__not, fact_image__Suc__atLeastLessThan, arity_HOL__Obool__Nat_Osize, fact_image__compose, fact_set__remove1__subset, fact_inf2D1, fact_self__quotient__aux1, fact_Nil__eq__concat__conv, fact_rel__pow__add, fact_fold__graph_OemptyI, fact_rel__comp__mono, fact_setsum__reindex__nonzero, fact_snd__eq__Range, arity_Int__Oint__Groups_Ocomm__monoid__add, fact_setsum_OF__eq, fact_converse__Int, fact_bij__betw__subset, fact_vimage__subset__eq, fact_list__ex__iff, fact_finite__atLeastLessThan, fact_SUPR__apply, fact_concat__eq__concat__iff, fact_single__valued__Id, fact_type__definition_ORep__range, fact_set__diff__eq, fact_finite__vimage__iff, fact_Nil__is__rev__conv, fact_gr0I, fact_predicate2D, fact_fold__graph__imp__finite, fact_add__eq__if, fact_pigeonhole__infinite, fact_bij__betw__id, fact_o__inv__o__cancel, fact_bot__empty__eq, fact_zip__obtain__same__length, fact_conversep_Ointros, fact_folding__one__idem_Oin__idem, fact_fun__left__comm__idem__inf, fact_listrel_ONil, fact_fun__left__comm_Ofold__graph__fold, fact_finite__UnI, fact_list__ex__append, fact_single__valued__rel__comp, fact_singleton__inject, fact_setsum__Un__Int, fact_le__funD, fact_emptyE, fact_le__fun__def, fact_acc__subset, fact_minus, fact_DiffD2, fact_finite__Prod__UNIV, fact_set__takeWhileD, fact_Int__empty__left, fact_UN__simps_I1_J, fact_setsum_Ounion__inter__neutral, fact_folding__one_Oinsert, fact_list_Osize_I4_J, fact_remove1__idem, fact_divmod__nat__rel__def, fact_reduction__pairI, fact_the__elem__def, fact_lists__accI, fact_finite__nat__set__iff__bounded__le, fact_Diff__idemp, fact_setsum_Oinfinite, fact_Collect__split, fact_sym__inv__image, fact_inj__on__inv__into, fact_nat__0, arity_Nat__Onat__Rings_Osemiring__0, fact_diff__le__self, fact_listrel_OCons, fact_UN__equiv__class__inject, fact_upt__Suc, fact_mult__eq__1__iff, fact_set__empty, fact_takeWhile__nth, fact_o__id, help_c__COMBS__1, help_c__COMBI__1, fact_max__extp_Ointros, fact_ord__less__eq__trans, fact_vimage__INT, fact_set__sublist, fact_Domain__Un__eq, fact_Inter__eq, fact_le__iff__add, fact_wf__measure, fact_diff__commute, fact_surj__iff, fact_order__fun_I1_J, fact_neq__if__length__neq, fact_nat__diff__distrib, fact_partition__filter1, fact_diff__Suc__eq__diff__pred, fact_Compl__Diff__eq, fact_UN__Un__distrib, fact_split__twice, fact_listrel1__subset__listrel, fact_Int__absorb2, fact_r__comp__rtrancl__eq, fact_xt1_I9_J, fact_Diff__subset__conv, fact_less__add__eq__less, fact_nat__mult__1__right, fact_singleton__conv, fact_wf__irrefl, fact_le__SUPI, fact_finite__trancl, fact_Image__Un, fact_INT__anti__mono, fact_setsum__head__upt__Suc, fact_Union__quotient, fact_takeWhile__dropWhile__id, fact_length__remdups__card__conv, fact_lists__mono, fact_fold1Set_Oequations, fact_fun__upd__same, fact_bex__reg__eqv, fact_map__pair_Oidentity, fact_folding__image__simple__idem_Oinsert__idem, fact_add__lessD1, fact_add__le__mono1, fact_UN__extend__simps_I1_J, fact_Int__Diff, fact_Eps__split__eq, fact_less__eq__nat_Osimps_I1_J, fact_DiffE, fact_quotient__is__empty, fact_lexord__transI, fact_inf__Int__eq, fact_folding__one__idem_Ounion__idem, fact_Domain__empty__iff, fact_INF__INT__eq, fact_bij__betw__comp__iff2, fact_lessI, fact_finite__Un, fact_setsum__cartesian__product, fact_someI__ex, fact_mem__splitE, fact_partition__filter__conv, fact_in__mono, fact_image__eq__fold__image, fact_list__ex1__iff__raw, arity_HOL__Obool__Enum_Oenum, fact_termination__basic__simps_I4_J, fact_wf__lex__prod, fact_trans__Int, fact_equiv__class__subset, fact_rtrancl__subset, fact_mult__less__mono1, fact_inj__on__iff__card__le, fact_nth__list__update__neq, fact_card__image, fact_nat_Oinject, fact_max__ext_Osimps, fact_fun__left__comm__idem_Ofun__comp__idem, 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help_c__fdisj__3, fact_ivl__disj__int_I11_J, fact_less__bin__lemma, fact_inj__on__iff__surj, fact_BIJ, fact_splitD_H, fact_Image__Id, fact_lexord__trans, fact_zdiv__mono2__neg__lemma, fact_Compl__empty__eq, fact_SUP__subset, fact_gfp__upperbound, fact_image__inv__f__f, fact_Rep__Integ__cases, fact_list__ex1__simps_I1_J, fact_bot__nat__def, fact_trancl__domain, fact_lexord__append__rightI, fact_le, fact_Un__assoc, fact_rtrancl__power, fact_lexord__irreflexive, fact_INF2__iff, fact_listrelp_ONil, fact_single__valuedD, fact_Sigma__empty2, fact_ord_OatLeast__iff, fact_max__extp__max__ext__eq, fact_quotient__empty, fact_imageI, fact_disjoint__iff__not__equal
% 91.70/31.10 % No. of inferences in proof: 5388
% 91.70/31.10 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 30547 ms resp. 29639 ms w/o parsing
% 95.60/32.59 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 95.82/32.61 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------