TSTP Solution File: SWW328+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW328+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n015.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 12:23:17 EDT 2023
% Result : Theorem 56.97s 14.36s
% Output : Refutation 58.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 1464
% Syntax : Number of formulae : 2791 ( 817 unt; 194 typ; 0 def)
% Number of atoms : 6874 (2528 equ; 0 cnn)
% Maximal formula atoms : 26 ( 2 avg)
% Number of connectives : 64004 ( 750 ~; 219 |; 822 &;58989 @)
% ( 271 <=>;2953 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 433 ( 433 >; 0 *; 0 +; 0 <<)
% Number of symbols : 196 ( 194 usr; 26 con; 0-7 aty)
% Number of variables : 9129 ( 0 ^;8956 !; 173 ?;9129 :)
% Comments :
%------------------------------------------------------------------------------
thf(v_ba_type,type,
v_ba: $i ).
thf(v_b_type,type,
v_b: $i ).
thf(v_ca_type,type,
v_ca: $i ).
thf(v_c_type,type,
v_c: $i ).
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_na_type,type,
v_na: $i ).
thf(v_P_type,type,
v_P: $i > $i > $o ).
thf(v_s0_type,type,
v_s0: $i ).
thf(v_s2_type,type,
v_s2: $i ).
thf(c_List_Odrop_type,type,
c_List_Odrop: $i > $i ).
thf(c_List_Oappend_type,type,
c_List_Oappend: $i > $i ).
thf(c_Groups_Ominus__class_Ominus_type,type,
c_Groups_Ominus__class_Ominus: $i > $i ).
thf(tc_Nat_Onat_type,type,
tc_Nat_Onat: $i ).
thf(c_Nat_Osize__class_Osize_type,type,
c_Nat_Osize__class_Osize: $i > $i ).
thf(tc_List_Olist_type,type,
tc_List_Olist: $i > $i ).
thf(tc_prod_type,type,
tc_prod: $i > $i > $i ).
thf(c_Product__Type_OPair_type,type,
c_Product__Type_OPair: $i > $i > $i ).
thf(c_List_Olistrel_type,type,
c_List_Olistrel: $i > $i > $i ).
thf(c_Product__Type_Ofst_type,type,
c_Product__Type_Ofst: $i > $i > $i ).
thf(c_Product__Type_Oprod_Oprod__case_type,type,
c_Product__Type_Oprod_Oprod__case: $i > $i > $i > $i ).
thf(c_COMBK_type,type,
c_COMBK: $i > $i > $i ).
thf(c_Map_Omap__upds_type,type,
c_Map_Omap__upds: $i > $i > $i > $i > $i > $i ).
thf(c_List_Ofoldl_type,type,
c_List_Ofoldl: $i > $i > $i > $i > $i ).
thf(c_List_Olist_ONil_type,type,
c_List_Olist_ONil: $i > $i ).
thf(c_Orderings_Oord__class_Oless_type,type,
c_Orderings_Oord__class_Oless: $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_Divides_Odiv__class_Odiv_type,type,
c_Divides_Odiv__class_Odiv: $i > $i ).
thf(c_Groups_Otimes__class_Otimes_type,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
thf(c_Nat_OSuc_type,type,
c_Nat_OSuc: $i ).
thf(c_Groups_Oplus__class_Oplus_type,type,
c_Groups_Oplus__class_Oplus: $i > $i ).
thf(c_List_Omap_type,type,
c_List_Omap: $i > $i > $i ).
thf(c_Product__Type_Osnd_type,type,
c_Product__Type_Osnd: $i > $i > $i ).
thf(c_List_Ozip_type,type,
c_List_Ozip: $i > $i > $i ).
thf(c_Orderings_Oord__class_Oless__eq_type,type,
c_Orderings_Oord__class_Oless__eq: $i > $i ).
thf(c_Groups_Oone__class_Oone_type,type,
c_Groups_Oone__class_Oone: $i > $i ).
thf(c_List_OtakeWhile_type,type,
c_List_OtakeWhile: $i > $i > $i > $i ).
thf(c_List_Otake_type,type,
c_List_Otake: $i > $i ).
thf(c_List_Onth_type,type,
c_List_Onth: $i > $i ).
thf(c_List_Olist_OCons_type,type,
c_List_Olist_OCons: $i > $i ).
thf(c_Divides_Odiv__class_Omod_type,type,
c_Divides_Odiv__class_Omod: $i > $i > $i > $i ).
thf(c_Rings_Odvd__class_Odvd_type,type,
c_Rings_Odvd__class_Odvd: $i > $i ).
thf(c_Fun_Ocomp_type,type,
c_Fun_Ocomp: $i > $i > $i > $i > $i ).
thf(c_Product__Type_Omap__pair_type,type,
c_Product__Type_Omap__pair: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Fun_Ofun__upd_type,type,
c_Fun_Ofun__upd: $i > $i > $i ).
thf(tc_Option_Ooption_type,type,
tc_Option_Ooption: $i > $i ).
thf(c_Option_Ooption_OSome_type,type,
c_Option_Ooption_OSome: $i > $i ).
thf(c_Option_Ooption_ONone_type,type,
c_Option_Ooption_ONone: $i > $i ).
thf(c_List_Olexord_type,type,
c_List_Olexord: $i > $i > $i ).
thf(c_List_Olistrel1_type,type,
c_List_Olistrel1: $i > $i > $i ).
thf(c_List_Oset_type,type,
c_List_Oset: $i > $i ).
thf(c_List_Odistinct_type,type,
c_List_Odistinct: $i > $i ).
thf(c_Finite__Set_Ofinite_type,type,
c_Finite__Set_Ofinite: $i > $i ).
thf(c_SetInterval_Oord__class_OatLeastAtMost_type,type,
c_SetInterval_Oord__class_OatLeastAtMost: $i > $i > $i > $i ).
thf(c_Int_Onumber__class_Onumber__of_type,type,
c_Int_Onumber__class_Onumber__of: $i > $i ).
thf(c_Wellfounded_Owf_type,type,
c_Wellfounded_Owf: $i > $i > $o ).
thf(c_Wellfounded_Omeasure_type,type,
c_Wellfounded_Omeasure: $i > $i ).
thf(c_Transitive__Closure_Ortrancl_type,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
thf(c_SetInterval_Oord__class_OatLeastLessThan_type,type,
c_SetInterval_Oord__class_OatLeastLessThan: $i > $i > $i ).
thf(c_SetInterval_Oord__class_OgreaterThanLessThan_type,type,
c_SetInterval_Oord__class_OgreaterThanLessThan: $i > $i > $i > $i ).
thf(c_Finite__Set_Ocard_type,type,
c_Finite__Set_Ocard: $i > $i ).
thf(c_Map_Omap__comp_type,type,
c_Map_Omap__comp: $i > $i > $i > $i > $i > $i > $i ).
thf(c_COMBS_type,type,
c_COMBS: $i > $i > $i > $i ).
thf(c_List_Obutlast_type,type,
c_List_Obutlast: $i > $i > $i ).
thf(c_Map_Omap__add_type,type,
c_Map_Omap__add: $i > $i > $i > $i > $i ).
thf(c_List_Oupt_type,type,
c_List_Oupt: $i > $i > $i ).
thf(c_Set_Oimage_type,type,
c_Set_Oimage: $i > $i > $i > $i ).
thf(c_Relation_ORange_type,type,
c_Relation_ORange: $i > $i > $i ).
thf(c_Map_Omap__of_type,type,
c_Map_Omap__of: $i > $i > $i > $i ).
thf(c_List_Ofilter_type,type,
c_List_Ofilter: $i > $i > $i ).
thf(c_List_Oremdups_type,type,
c_List_Oremdups: $i > $i > $i ).
thf(c_Map_Orestrict__map_type,type,
c_Map_Orestrict__map: $i > $i > $i > $i > $i ).
thf(c_Hoare__Mirabelle_Otriple_Otriple_type,type,
c_Hoare__Mirabelle_Otriple_Otriple: $i > $i ).
thf(c_Divides_Odivmod__nat_type,type,
c_Divides_Odivmod__nat: $i > $i > $i ).
thf(c_SetInterval_Oord__class_OgreaterThanAtMost_type,type,
c_SetInterval_Oord__class_OgreaterThanAtMost: $i > $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_Sum__Type_Osum_Osum__case_type,type,
c_Sum__Type_Osum_Osum__case: $i > $i > $i > $i > $i > $i ).
thf(c_Relation_Orel__comp_type,type,
c_Relation_Orel__comp: $i > $i > $i > $i ).
thf(c_Relation_Orefl__on_type,type,
c_Relation_Orefl__on: $i > $i > $i > $o ).
thf(c_Relation_Oconverse_type,type,
c_Relation_Oconverse: $i > $i > $i ).
thf(c_Finite__Set_Ofold1_type,type,
c_Finite__Set_Ofold1: $i > $i > $i ).
thf(c_HOL_OThe_type,type,
c_HOL_OThe: $i > $i > $i ).
thf(c_Finite__Set_Ofold1Set_type,type,
c_Finite__Set_Ofold1Set: $i > $i > $i > $i ).
thf(c_Set_Oinsert_type,type,
c_Set_Oinsert: $i > $i ).
thf(c_Relation_Ototal__on_type,type,
c_Relation_Ototal__on: $i > $i > $i > $o ).
thf(c_Transitive__Closure_Otrancl_type,type,
c_Transitive__Closure_Otrancl: $i > $i > $i ).
thf(c_Relation_Oinv__image_type,type,
c_Relation_Oinv__image: $i > $i > $i ).
thf(c_Relation_OId__on_type,type,
c_Relation_OId__on: $i > $i > $i ).
thf(c_Finite__Set_Ofolding__image__simple_type,type,
c_Finite__Set_Ofolding__image__simple: $i > $i > $i > $i > $i > $i > $o ).
thf(c_Finite__Set_Ofold__image_type,type,
c_Finite__Set_Ofold__image: $i > $i > $i > $i ).
thf(c_Relation_ODomain_type,type,
c_Relation_ODomain: $i > $i > $i ).
thf(c_Map_Odom_type,type,
c_Map_Odom: $i > $i > $i > $i ).
thf(c_Finite__Set_Ofun__left__comm_type,type,
c_Finite__Set_Ofun__left__comm: $i > $i > $i > $o ).
thf(c_Finite__Set_Ofold_type,type,
c_Finite__Set_Ofold: $i > $i > $i > $i ).
thf(c_SetInterval_Oord__class_OatMost_type,type,
c_SetInterval_Oord__class_OatMost: $i > $i ).
thf(c_Wellfounded_Opred__nat_type,type,
c_Wellfounded_Opred__nat: $i ).
thf(c_Fun_Oinj__on_type,type,
c_Fun_Oinj__on: $i > $i > $i > $i > $o ).
thf(c_Relation_OId_type,type,
c_Relation_OId: $i > $i ).
thf(c_SetInterval_Oord__class_OlessThan_type,type,
c_SetInterval_Oord__class_OlessThan: $i > $i ).
thf(c_Finite__Set_Ofold__graph_type,type,
c_Finite__Set_Ofold__graph: $i > $i > $i > $i > $i > $i ).
thf(c_Wellfounded_Oacyclic_type,type,
c_Wellfounded_Oacyclic: $i > $i > $o ).
thf(c_Equiv__Relations_Oequiv_type,type,
c_Equiv__Relations_Oequiv: $i > $i > $i > $o ).
thf(c_List_Osublist_type,type,
c_List_Osublist: $i > $i > $i > $i ).
thf(c_FunDef_Opair__less_type,type,
c_FunDef_Opair__less: $i ).
thf(c_Finite__Set_Ofolding__one_type,type,
c_Finite__Set_Ofolding__one: $i > $i > $i > $o ).
thf(c_Wellfounded_Oacc_type,type,
c_Wellfounded_Oacc: $i > $i > $i ).
thf(c_Wellfounded_Olex__prod_type,type,
c_Wellfounded_Olex__prod: $i > $i > $i > $i > $i ).
thf(c_Map_Oran_type,type,
c_Map_Oran: $i > $i > $i > $i ).
thf(c_Relation_OField_type,type,
c_Relation_OField: $i > $i ).
thf(c_List_Olistrelp_type,type,
c_List_Olistrelp: $i > $i > $i > $i > $o ).
thf(c_List_Oremove1_type,type,
c_List_Oremove1: $i > $i > $i > $i ).
thf(c_fequal_type,type,
c_fequal: $i ).
thf(c_Wellfounded_Oaccp_type,type,
c_Wellfounded_Oaccp: $i > $i > $i ).
thf(c_Nitpick_Onat__gcd__rel_type,type,
c_Nitpick_Onat__gcd__rel: $i ).
thf(c_Set_Ovimage_type,type,
c_Set_Ovimage: $i > $i > $i > $i ).
thf(c_Relation_Osingle__valued_type,type,
c_Relation_Osingle__valued: $i > $i > $i > $o ).
thf(c_Nitpick_Opair__box_Opair__box__size_type,type,
c_Nitpick_Opair__box_Opair__box__size: $i > $i > $i > $i > $i > $i ).
thf(c_Nitpick_Opair__box_OPairBox_type,type,
c_Nitpick_Opair__box_OPairBox: $i > $i > $i > $i > $i ).
thf(c_Relation_OImage_type,type,
c_Relation_OImage: $i > $i > $i > $i ).
thf(c_Equiv__Relations_Ocongruent2_type,type,
c_Equiv__Relations_Ocongruent2: $i > $i > $i > $i > $i > $i > $o ).
thf(c_Natural_Oevaln_type,type,
c_Natural_Oevaln: $i > $i > $i > $i > $o ).
thf(c_Finite__Set_Ofolding__image__simple__idem_type,type,
c_Finite__Set_Ofolding__image__simple__idem: $i > $i > $i > $i > $i > $i > $o ).
thf(c_Sum__Type_OInl_type,type,
c_Sum__Type_OInl: $i > $i > $i ).
thf(c_Com_Ocom_OWhile_type,type,
c_Com_Ocom_OWhile: $i > $i > $i ).
thf(c_Product__Type_OSigma_type,type,
c_Product__Type_OSigma: $i > $i > $i ).
thf(c_Natural_Oevalc_type,type,
c_Natural_Oevalc: $i > $i ).
thf(c_Sum__Type_OInr_type,type,
c_Sum__Type_OInr: $i > $i > $i ).
thf(c_Fun_Othe__inv__into_type,type,
c_Fun_Othe__inv__into: $i > $i > $i > $i > $i ).
thf(c_Wellfounded_OwfP_type,type,
c_Wellfounded_OwfP: $i > $i > $o ).
thf(c_FunDef_Oin__rel_type,type,
c_FunDef_Oin__rel: $i > $i > $i > $i ).
thf(c_Recdef_Osame__fst_type,type,
c_Recdef_Osame__fst: $i > $i > $i > $i > $i ).
thf(c_Equiv__Relations_Ocongruent_type,type,
c_Equiv__Relations_Ocongruent: $i > $i > $i > $i > $o ).
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_Set_OCollect_type,type,
c_Set_OCollect: $i > $i ).
thf(c_Big__Operators_Ocomm__monoid__big_type,type,
c_Big__Operators_Ocomm__monoid__big: $i > $i > $i > $i > $i > $o ).
thf(c_Finite__Set_Ofolding__one__idem_type,type,
c_Finite__Set_Ofolding__one__idem: $i > $i > $i > $o ).
thf(c_Hilbert__Choice_OEps_type,type,
c_Hilbert__Choice_OEps: $i > $i > $i ).
thf(c_Equiv__Relations_Oequivp_type,type,
c_Equiv__Relations_Oequivp: $i > $i > $o ).
thf(v_s1_type,type,
v_s1: $i ).
thf(c_Predicate_ORangeP_type,type,
c_Predicate_ORangeP: $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OatLeast_type,type,
c_SetInterval_Oord_OatLeast: $i > $i > $i > $i ).
thf(c_Hoare__Mirabelle_Ohoare__valids_type,type,
c_Hoare__Mirabelle_Ohoare__valids: $i > $i > $i > $o ).
thf(c_Typedef_Otype__definition_type,type,
c_Typedef_Otype__definition: $i > $i > $i > $i > $i > $o ).
thf(c_SetInterval_Oord_OatLeastLessThan_type,type,
c_SetInterval_Oord_OatLeastLessThan: $i > $i > $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OlessThan_type,type,
c_SetInterval_Oord_OlessThan: $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OatMost_type,type,
c_SetInterval_Oord_OatMost: $i > $i > $i > $i ).
thf(c_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_fdisj_type,type,
c_fdisj: $i ).
thf(c_SetInterval_Oord_OatLeastAtMost_type,type,
c_SetInterval_Oord_OatLeastAtMost: $i > $i > $i > $i > $i ).
thf(c_Predicate_OPowp_type,type,
c_Predicate_OPowp: $i > $i > $i ).
thf(c_Sum__Type_OProjr_type,type,
c_Sum__Type_OProjr: $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_SetInterval_Oord_OgreaterThanLessThan_type,type,
c_SetInterval_Oord_OgreaterThanLessThan: $i > $i > $i > $i > $i ).
thf(c_Predicate_Opred__comp_type,type,
c_Predicate_Opred__comp: $i > $i > $i > $i > $i > $i > $i > $o ).
thf(c_FunDef_Oreduction__pair_type,type,
c_FunDef_Oreduction__pair: $i > $i > $o ).
thf(c_FunDef_Orp__inv__image_type,type,
c_FunDef_Orp__inv__image: $i > $i > $i ).
thf(c_Lazy__Sequence_Ohb__single_type,type,
c_Lazy__Sequence_Ohb__single: $i > $i > $i ).
thf(c_Fun_Ooverride__on_type,type,
c_Fun_Ooverride__on: $i > $i > $i > $i > $i > $i ).
thf(c_Option_Oset_type,type,
c_Option_Oset: $i > $i > $i ).
thf(c_Hoare__Mirabelle_Otriple_Otriple__rec_type,type,
c_Hoare__Mirabelle_Otriple_Otriple__rec: $i > $i > $i > $i > $i ).
thf(c_fimplies_type,type,
c_fimplies: $i ).
thf(c_fconj_type,type,
c_fconj: $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_Sum__Type_OProjl_type,type,
c_Sum__Type_OProjl: $i > $i > $i > $i ).
thf(c_fTrue_type,type,
c_fTrue: $i ).
thf(c_fNot_type,type,
c_fNot: $i ).
thf(c_SetInterval_Oord_OgreaterThanAtMost_type,type,
c_SetInterval_Oord_OgreaterThanAtMost: $i > $i > $i > $i > $i > $i ).
thf(c_fFalse_type,type,
c_fFalse: $i ).
thf(c_Hoare__Mirabelle_Opeek__and_type,type,
c_Hoare__Mirabelle_Opeek__and: $i > $i > $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_New__Random__Sequence_Opos__single_type,type,
c_New__Random__Sequence_Opos__single: $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 > $i ).
thf(c_Relation_Oirrefl_type,type,
c_Relation_Oirrefl: $i > $i > $o ).
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_SetInterval_Oord_OgreaterThan_type,type,
c_SetInterval_Oord_OgreaterThan: $i > $i > $i > $i ).
thf(c_Predicate_ODomainP_type,type,
c_Predicate_ODomainP: $i > $i > $i > $i ).
thf(c_Lazy__Sequence_Oempty_type,type,
c_Lazy__Sequence_Oempty: $i > $i ).
thf(c_Big__Operators_Osemilattice__big_type,type,
c_Big__Operators_Osemilattice__big: $i > $i > $i > $o ).
thf(c_Int_ORep__Integ_type,type,
c_Int_ORep__Integ: $i ).
thf(c_Hoare__Mirabelle_Otriple_Otriple__case_type,type,
c_Hoare__Mirabelle_Otriple_Otriple__case: $i > $i > $i > $i > $i ).
thf(c_Nitpick_Orefl_H_type,type,
c_Nitpick_Orefl_H: $i > $i > $o ).
thf(c_Predicate_Oreflp_type,type,
c_Predicate_Oreflp: $i > $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(398,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(3021,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)],[398]) ).
thf(1014,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(5509,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)],[1014]) ).
thf(66,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(1586,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)],[66]) ).
thf(1025,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(5561,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)],[1025]) ).
thf(655,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ B ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ A ) ) )
=> ( ( c_List_Oupt @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ tc_Nat_Onat ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ B ) ) @ ( c_List_Oupt @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ B ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ A ) ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ B ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ A ) ) )
=> ( ( c_List_Oupt @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ A ) )
= ( c_List_Olist_ONil @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__rec__number__of) ).
thf(4094,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ B ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ A ) ) )
=> ( ( c_List_Oupt @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ tc_Nat_Onat ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ B ) ) @ ( c_List_Oupt @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ B ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ A ) ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ B ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ A ) ) )
=> ( ( c_List_Oupt @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ A ) )
= ( c_List_Olist_ONil @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(191,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(2072,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)],[191]) ).
thf(865,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(4899,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)],[865]) ).
thf(435,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(3167,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)],[435]) ).
thf(371,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(2921,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)],[371]) ).
thf(168,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(1982,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)],[168]) ).
thf(1069,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(5733,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)],[1069]) ).
thf(1262,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(6527,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)],[1262]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult2__eq) ).
thf(1554,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(778,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ F ) @ ( hAPP @ ( c_List_Oset @ G ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ G ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ D ) ) @ C ) ) ) )
=> ( ( c_Map_Omap__upds @ G @ E @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ G @ ( tc_Option_Ooption @ E ) ) @ B ) @ F ) @ ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) ) @ C @ D )
= ( c_Map_Omap__upds @ G @ E @ B @ C @ D ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ F ) @ ( hAPP @ ( c_List_Oset @ G ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ G ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ D ) ) @ C ) ) ) )
=> ( ( c_Map_Omap__upds @ G @ E @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ G @ ( tc_Option_Ooption @ E ) ) @ B ) @ F ) @ ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) ) @ C @ D )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ G @ ( tc_Option_Ooption @ E ) ) @ ( c_Map_Omap__upds @ G @ E @ B @ C @ D ) ) @ F ) @ ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__upd__upds__conv__if) ).
thf(4560,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ F ) @ ( hAPP @ ( c_List_Oset @ G ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ G ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ D ) ) @ C ) ) ) )
=> ( ( c_Map_Omap__upds @ G @ E @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ G @ ( tc_Option_Ooption @ E ) ) @ B ) @ F ) @ ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) ) @ C @ D )
= ( c_Map_Omap__upds @ G @ E @ B @ C @ D ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ F ) @ ( hAPP @ ( c_List_Oset @ G ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ G ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ D ) ) @ C ) ) ) )
=> ( ( c_Map_Omap__upds @ G @ E @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ G @ ( tc_Option_Ooption @ E ) ) @ B ) @ F ) @ ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) ) @ C @ D )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ G @ ( tc_Option_Ooption @ E ) ) @ ( c_Map_Omap__upds @ G @ E @ B @ C @ D ) ) @ F ) @ ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(752,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Map_Omap__of @ D @ C @ ( hAPP @ ( hAPP @ ( c_List_Omap @ D @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ C @ ( tc_prod @ D @ C ) ) @ ( c_Product__Type_OPair @ D @ C ) ) @ B ) ) @ A ) )
= ( c_Map_Orestrict__map @ D @ C @ ( hAPP @ ( c_Fun_Ocomp @ C @ ( tc_Option_Ooption @ C ) @ D @ ( c_Option_Ooption_OSome @ C ) ) @ B ) @ ( hAPP @ ( c_List_Oset @ D ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__map__restrict) ).
thf(4447,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Map_Omap__of @ D @ C @ ( hAPP @ ( hAPP @ ( c_List_Omap @ D @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ C @ ( tc_prod @ D @ C ) ) @ ( c_Product__Type_OPair @ D @ C ) ) @ B ) ) @ A ) )
= ( c_Map_Orestrict__map @ D @ C @ ( hAPP @ ( c_Fun_Ocomp @ C @ ( tc_Option_Ooption @ C ) @ D @ ( c_Option_Ooption_OSome @ C ) ) @ B ) @ ( hAPP @ ( c_List_Oset @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(629,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Nitpick_Onat__gcd__rel ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ C ) @ B ) ) )
=> ( ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Nitpick_Onat__gcd__rel ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ D ) @ E ) ) )
=> ( ( ( E
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ D @ E ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ D ) @ E ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__gcd_Opinduct) ).
thf(3962,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Nitpick_Onat__gcd__rel ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ C ) @ B ) ) )
=> ( ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_Nitpick_Onat__gcd__rel ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ D ) @ E ) ) )
=> ( ( ( E
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ D @ E ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ D ) @ E ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(989,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(5422,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)],[989]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ C @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__eq__dvd__iff) ).
thf(1337,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ C @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ C ) @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ C ) @ A ) ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ C @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(102,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__mult__div__cancel) ).
thf(1718,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(665,axiom,
( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_One__nat__def) ).
thf(4134,plain,
( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(4135,plain,
( ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ),
inference(lifteq,[status(thm)],[4134]) ).
thf(1176,axiom,
hBOOL @ ( hAPP @ v_ba @ v_s0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(6180,plain,
hBOOL @ ( hAPP @ v_ba @ v_s0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176]) ).
thf(1188,axiom,
~ ( hBOOL @ c_fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fFalse__1) ).
thf(6215,plain,
~ ( hBOOL @ c_fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188]) ).
thf(6216,plain,
~ ( hBOOL @ c_fFalse ),
inference(polarity_switch,[status(thm)],[6215]) ).
thf(6571,plain,
( ( hBOOL @ ( hAPP @ v_ba @ v_s0 ) )
!= ( hBOOL @ c_fFalse ) ),
inference(paramod_ordered,[status(thm)],[6180,6216]) ).
thf(6573,plain,
( ( hAPP @ v_ba @ v_s0 )
!= c_fFalse ),
inference(simp,[status(thm)],[6571]) ).
thf(6627,plain,
( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
!= c_fFalse )
| ( ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
!= ( hAPP @ v_ba @ v_s0 ) ) ),
inference(paramod_ordered,[status(thm)],[4135,6573]) ).
thf(6669,plain,
( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
!= c_fFalse )
| ( c_Nat_OSuc != v_ba )
| ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= v_s0 ) ),
inference(simp,[status(thm)],[6627]) ).
thf(124,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ A )
= ( c_SetInterval_Oord__class_OgreaterThanLessThan @ tc_Int_Oint @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastPlusOneLessThan__greaterThanLessThan__int) ).
thf(1823,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ A )
= ( c_SetInterval_Oord__class_OgreaterThanLessThan @ tc_Int_Oint @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(656,axiom,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ A )
= ( hAPP @ ( c_List_Oset @ tc_Nat_Onat ) @ ( c_List_Oupt @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast__upt) ).
thf(4101,plain,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ A )
= ( hAPP @ ( c_List_Oset @ tc_Nat_Onat ) @ ( c_List_Oupt @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(753,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(4450,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)],[753]) ).
thf(1035,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ D @ C )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__eq) ).
thf(5593,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ D @ C )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(200,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(2109,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)],[200]) ).
thf(845,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(4824,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)],[845]) ).
thf(925,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(5136,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)],[925]) ).
thf(1113,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G = F )
=> ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ E @ D @ C @ B @ A ) @ G )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ E @ D @ C @ B @ A ) @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__case__weak__cong) ).
thf(5896,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G = F )
=> ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ E @ D @ C @ B @ A ) @ G )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ E @ D @ C @ B @ A ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).
thf(80,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(1633,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)],[80]) ).
thf(171,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ B )
= A )
<=> ( ( C
= ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) @ A ) )
& ( B
= ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__eq__conv__conj) ).
thf(1995,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ B )
= A )
=> ( ( C
= ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) @ A ) )
& ( B
= ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) @ A ) ) ) )
& ( ( ( C
= ( hAPP @ ( hAPP @ ( c_List_Otake @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) @ A ) )
& ( B
= ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) @ A ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(1266,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(6544,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)],[1266]) ).
thf(593,axiom,
! [A: $i,B: $i] :
( ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) )
<=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__nat__less) ).
thf(3830,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) ) )
& ( ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(1054,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oord__eq__less__trans) ).
thf(5654,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).
thf(15,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(1315,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)],[15]) ).
thf(602,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(3863,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)],[602]) ).
thf(279,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ C ) ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ C ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zmod__equality) ).
thf(2544,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ C ) ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ C ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(1241,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(6448,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)],[1241]) ).
thf(899,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(5028,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)],[899]) ).
thf(821,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(4728,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)],[821]) ).
thf(122,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__mod__sign) ).
thf(1818,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_List_Ofoldl @ F @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ B ) @ A ) )
= ( hAPP @ ( c_List_Ofoldl @ F @ E @ D @ ( hAPP @ ( c_List_Ofoldl @ F @ E @ D @ C ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__append) ).
thf(1295,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_List_Ofoldl @ F @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ E ) @ B ) @ A ) )
= ( hAPP @ ( c_List_Ofoldl @ F @ E @ D @ ( hAPP @ ( c_List_Ofoldl @ F @ E @ D @ C ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(92,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(1686,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)],[92]) ).
thf(233,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(2250,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)],[233]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ E ) @ D ) )
=> ( ( 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(1750,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)],[108]) ).
thf(1142,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(6022,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)],[1142]) ).
thf(471,axiom,
! [A: $i,B: $i] :
( ( c_SetInterval_Oord__class_OgreaterThanLessThan @ tc_Nat_Onat @ B @ A )
= ( hAPP @ ( c_List_Oset @ tc_Nat_Onat ) @ ( c_List_Oupt @ ( hAPP @ c_Nat_OSuc @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThanLessThan__upt) ).
thf(3317,plain,
! [A: $i,B: $i] :
( ( c_SetInterval_Oord__class_OgreaterThanLessThan @ tc_Nat_Onat @ B @ A )
= ( hAPP @ ( c_List_Oset @ tc_Nat_Onat ) @ ( c_List_Oupt @ ( hAPP @ c_Nat_OSuc @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(521,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(3549,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)],[521]) ).
thf(494,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(3417,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)],[494]) ).
thf(75,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(1618,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)],[75]) ).
thf(1184,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_Map_Odom @ E @ C @ B ) ) )
=> ( ( hAPP @ ( c_Map_Omap__add @ E @ C @ A @ B ) @ D )
= ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__dom__app__simps_I3_J) ).
thf(6199,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_Map_Odom @ E @ C @ B ) ) )
=> ( ( hAPP @ ( c_Map_Omap__add @ E @ C @ A @ B ) @ D )
= ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).
thf(419,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Map_Omap__of @ D @ C @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ ( tc_prod @ D @ C ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ D @ ( tc_Option_Ooption @ C ) ) @ ( c_Map_Omap__of @ D @ C @ A ) ) @ ( hAPP @ ( c_Product__Type_Ofst @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ ( hAPP @ ( c_Product__Type_Osnd @ D @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of_Osimps_I2_J) ).
thf(3108,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Map_Omap__of @ D @ C @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ ( tc_prod @ D @ C ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ D @ ( tc_Option_Ooption @ C ) ) @ ( c_Map_Omap__of @ D @ C @ A ) ) @ ( hAPP @ ( c_Product__Type_Ofst @ D @ C ) @ B ) ) @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ ( hAPP @ ( c_Product__Type_Osnd @ D @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(817,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ F @ E @ D @ C @ B ) @ ( hAPP @ ( c_Sum__Type_OInl @ F @ D ) @ A ) )
= ( hAPP @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Osimps_I5_J) ).
thf(4711,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ F @ E @ D @ C @ B ) @ ( hAPP @ ( c_Sum__Type_OInl @ F @ D ) @ A ) )
= ( hAPP @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(239,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(2282,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)],[239]) ).
thf(718,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(4326,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)],[718]) ).
thf(970,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(5348,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)],[970]) ).
thf(1042,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(5614,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)],[1042]) ).
thf(786,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(4592,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)],[786]) ).
thf(1011,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(5501,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)],[1011]) ).
thf(818,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__asym) ).
thf(4714,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(643,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(4037,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)],[643]) ).
thf(204,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__div__cancel__disj) ).
thf(2117,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(926,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(5141,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)],[926]) ).
thf(198,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(2104,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)],[198]) ).
thf(227,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__neg__pos__less0) ).
thf(2231,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(298,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__reduce) ).
thf(2622,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(1170,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(6162,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)],[1170]) ).
thf(600,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__mod__geq) ).
thf(3858,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(714,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(4311,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)],[714]) ).
thf(345,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(2808,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)],[345]) ).
thf(766,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( c_List_Oset @ tc_Nat_Onat ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( c_List_Ofoldl @ tc_Nat_Onat @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_elem__le__sum) ).
thf(4515,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( c_List_Oset @ tc_Nat_Onat ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( c_List_Ofoldl @ tc_Nat_Onat @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(587,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(3813,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)],[587]) ).
thf(269,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ B ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) @ B )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__times__mod__eq) ).
thf(2495,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ B ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) @ B )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(1245,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(6458,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1245]) ).
thf(960,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(5297,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)],[960]) ).
thf(156,axiom,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Omod__div__equality_H) ).
thf(1939,plain,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(838,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(4807,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)],[838]) ).
thf(1240,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(6441,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)],[1240]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_List_Ofoldl @ tc_Nat_Onat @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_start__le__sum) ).
thf(1544,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_List_Ofoldl @ tc_Nat_Onat @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(617,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(3910,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)],[617]) ).
thf(202,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(2114,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)],[202]) ).
thf(351,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ C @ A ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__add1__eq) ).
thf(2837,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ C @ A ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(795,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ C ) )
=> ! [E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ G ) @ B ) )
=> ( E
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ G ) @ F ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ E ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ E ) @ C ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bset_I9_J) ).
thf(4623,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ C ) )
=> ! [E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ G ) @ B ) )
=> ( E
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ G ) @ F ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ E ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ E ) @ C ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(880,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(4973,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)],[880]) ).
thf(742,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(4408,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)],[742]) ).
thf(1144,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( 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(6031,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( 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 ) ) )
=> ( c_Predicate_Opred__comp @ G @ F @ E @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).
thf(760,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hAPP @ G @ F )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ D ) )
=> ( ( c_Map_Omap__comp @ E @ C @ B @ A @ G @ F )
= ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__comp__simps_I2_J) ).
thf(4479,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hAPP @ G @ F )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ D ) )
=> ( ( c_Map_Omap__comp @ E @ C @ B @ A @ G @ F )
= ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(1182,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(6194,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)],[1182]) ).
thf(922,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Oinject) ).
thf(5120,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(1094,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(5814,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)],[1094]) ).
thf(746,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(4418,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)],[746]) ).
thf(406,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(3044,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)],[406]) ).
thf(659,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(4110,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)],[659]) ).
thf(249,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(2316,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)],[249]) ).
thf(853,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__imp__neq) ).
thf(4856,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(698,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(4247,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)],[698]) ).
thf(883,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(4980,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)],[883]) ).
thf(830,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(4762,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)],[830]) ).
thf(596,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(3848,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)],[596]) ).
thf(218,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(2195,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)],[218]) ).
thf(423,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Map_Omap__of @ D @ C @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ ( tc_prod @ D @ C ) ) @ B ) @ A ) )
= ( c_Map_Omap__add @ D @ C @ ( c_Map_Omap__of @ D @ C @ A ) @ ( c_Map_Omap__of @ D @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__append) ).
thf(3120,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Map_Omap__of @ D @ C @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ ( tc_prod @ D @ C ) ) @ B ) @ A ) )
= ( c_Map_Omap__add @ D @ C @ ( c_Map_Omap__of @ D @ C @ A ) @ ( c_Map_Omap__of @ D @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(1027,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(5565,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)],[1027]) ).
thf(110,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(1756,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)],[110]) ).
thf(782,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ B )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__div__geq) ).
thf(4575,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ B )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(476,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(3332,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)],[476]) ).
thf(1077,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_List_Oset @ E ) @ C ) ) )
=> ( ( hAPP @ ( c_Map_Omap__of @ E @ B @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ E @ B ) @ A ) @ C ) ) ) @ D )
= ( hAPP @ ( c_Option_Ooption_OSome @ B ) @ ( hAPP @ A @ D ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_List_Oset @ E ) @ C ) ) )
=> ( ( hAPP @ ( c_Map_Omap__of @ E @ B @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ E @ B ) @ A ) @ C ) ) ) @ D )
= ( c_Option_Ooption_ONone @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__zip__map) ).
thf(5755,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_List_Oset @ E ) @ C ) ) )
=> ( ( hAPP @ ( c_Map_Omap__of @ E @ B @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ E @ B ) @ A ) @ C ) ) ) @ D )
= ( hAPP @ ( c_Option_Ooption_OSome @ B ) @ ( hAPP @ A @ D ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_List_Oset @ E ) @ C ) ) )
=> ( ( hAPP @ ( c_Map_Omap__of @ E @ B @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ E @ B ) @ A ) @ C ) ) ) @ D )
= ( c_Option_Ooption_ONone @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).
thf(857,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(4870,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)],[857]) ).
thf(1,conjecture,
( ( ( v_ba = v_b )
& ( v_ca = v_c ) )
=> ( ! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ A ) @ v_G ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ v_na @ A ) )
=> ! [A: $i] :
( ( v_P @ A @ v_s0 )
=> ( ( v_P @ A @ v_s2 )
& ~ ( hBOOL @ ( hAPP @ v_b @ v_s2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_6) ).
thf(2,negated_conjecture,
~ ( ( ( v_ba = v_b )
& ( v_ca = v_c ) )
=> ( ! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ A ) @ v_G ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ v_na @ A ) )
=> ! [A: $i] :
( ( v_P @ A @ v_s0 )
=> ( ( v_P @ A @ v_s2 )
& ~ ( hBOOL @ ( hAPP @ v_b @ v_s2 ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(1272,plain,
~ ( ( ( v_ba = v_b )
& ( v_ca = v_c ) )
=> ( ! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ A ) @ v_G ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ v_na @ A ) )
=> ! [A: $i] :
( ( v_P @ A @ v_s0 )
=> ( ( v_P @ A @ v_s2 )
& ~ ( hBOOL @ ( hAPP @ v_b @ v_s2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1277,plain,
v_P @ sk1 @ v_s0,
inference(cnf,[status(esa)],[1272]) ).
thf(1275,plain,
( ~ ( v_P @ sk1 @ v_s2 )
| ( hBOOL @ ( hAPP @ v_b @ v_s2 ) ) ),
inference(cnf,[status(esa)],[1272]) ).
thf(1276,plain,
v_ba = v_b,
inference(cnf,[status(esa)],[1272]) ).
thf(1279,plain,
v_b = v_ba,
inference(lifteq,[status(thm)],[1276]) ).
thf(6560,plain,
( ~ ( v_P @ sk1 @ v_s2 )
| ( hBOOL @ ( hAPP @ v_ba @ v_s2 ) ) ),
inference(rewrite,[status(thm)],[1275,1279]) ).
thf(6561,plain,
( ( hBOOL @ ( hAPP @ v_ba @ v_s2 ) )
| ( ( v_P @ sk1 @ v_s2 )
!= ( v_P @ sk1 @ v_s0 ) ) ),
inference(paramod_ordered,[status(thm)],[1277,6560]) ).
thf(6562,plain,
( ( hBOOL @ ( hAPP @ v_ba @ v_s2 ) )
| ( sk1 != sk1 )
| ( v_s2 != v_s0 ) ),
inference(simp,[status(thm)],[6561]) ).
thf(6563,plain,
( ( hBOOL @ ( hAPP @ v_ba @ v_s2 ) )
| ( v_s2 != v_s0 ) ),
inference(simp,[status(thm)],[6562]) ).
thf(6631,plain,
( ( hBOOL @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( v_s2 != v_s0 )
| ( ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
!= ( hAPP @ v_ba @ v_s2 ) ) ),
inference(paramod_ordered,[status(thm)],[4135,6563]) ).
thf(6665,plain,
( ( hBOOL @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( v_s2 != v_s0 )
| ( c_Nat_OSuc != v_ba )
| ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= v_s2 ) ),
inference(simp,[status(thm)],[6631]) ).
thf(949,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(5257,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)],[949]) ).
thf(1233,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(6416,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)],[1233]) ).
thf(536,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(3616,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)],[536]) ).
thf(706,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( hAPP @ c_Nat_OSuc @ B ) ) ) ) )
<=> ( B
= ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__div__lemma) ).
thf(4279,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( hAPP @ c_Nat_OSuc @ B ) ) ) ) )
=> ( B
= ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ C ) ) )
& ( ( B
= ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( hAPP @ c_Nat_OSuc @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(299,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(2627,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)],[299]) ).
thf(648,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(4058,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)],[648]) ).
thf(457,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(3253,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)],[457]) ).
thf(170,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ A ) ) )
<=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ A ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ B ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__iff__zmod__eq__0__number__of) ).
thf(1988,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ A ) ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ A ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ B ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ A ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ B ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(591,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(3826,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)],[591]) ).
thf(493,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(3414,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)],[493]) ).
thf(512,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(3481,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)],[512]) ).
thf(161,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(1954,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)],[161]) ).
thf(354,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(2844,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)],[354]) ).
thf(526,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Omap @ F @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ F ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ E ) @ ( hAPP @ ( c_Fun_Ocomp @ F @ E @ C @ D ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_List_Omap_Ocompositionality) ).
thf(3577,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Omap @ F @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ F ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Omap @ C @ E ) @ ( hAPP @ ( c_Fun_Ocomp @ F @ E @ C @ D ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(181,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ A ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonneg1__imp__zdiv__pos__iff) ).
thf(2042,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ A ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ A ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(612,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(3895,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)],[612]) ).
thf(563,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ H ) ) @ G )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ F ) ) @ E ) )
=> ( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ H ) ) @ D )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ F ) ) @ E ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ C ) @ ( hAPP @ ( c_List_Oset @ F ) @ E ) ) )
=> ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ ( tc_Option_Ooption @ H ) ) @ ( c_Map_Omap__of @ F @ H @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ F @ H ) @ E ) @ G ) ) ) @ C ) @ ( hAPP @ ( c_Option_Ooption_OSome @ H ) @ B ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ ( tc_Option_Ooption @ H ) ) @ ( c_Map_Omap__of @ F @ H @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ F @ H ) @ E ) @ D ) ) ) @ C ) @ ( hAPP @ ( c_Option_Ooption_OSome @ H ) @ A ) ) )
=> ( ( c_Map_Omap__of @ F @ H @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ F @ H ) @ E ) @ G ) )
= ( c_Map_Omap__of @ F @ H @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ F @ H ) @ E ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__zip__upd) ).
thf(3717,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ H ) ) @ G )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ F ) ) @ E ) )
=> ( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ H ) ) @ D )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ F ) ) @ E ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ C ) @ ( hAPP @ ( c_List_Oset @ F ) @ E ) ) )
=> ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ ( tc_Option_Ooption @ H ) ) @ ( c_Map_Omap__of @ F @ H @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ F @ H ) @ E ) @ G ) ) ) @ C ) @ ( hAPP @ ( c_Option_Ooption_OSome @ H ) @ B ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ ( tc_Option_Ooption @ H ) ) @ ( c_Map_Omap__of @ F @ H @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ F @ H ) @ E ) @ D ) ) ) @ C ) @ ( hAPP @ ( c_Option_Ooption_OSome @ H ) @ A ) ) )
=> ( ( c_Map_Omap__of @ F @ H @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ F @ H ) @ E ) @ G ) )
= ( c_Map_Omap__of @ F @ H @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ F @ H ) @ E ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(937,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(5192,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)],[937]) ).
thf(645,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(4047,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)],[645]) ).
thf(451,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(3236,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)],[451]) ).
thf(519,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__less__eq__dividend) ).
thf(3545,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(516,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(3502,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)],[516]) ).
thf(1224,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(6381,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)],[1224]) ).
thf(662,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(4124,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)],[662]) ).
thf(567,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(3730,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)],[567]) ).
thf(1106,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(5874,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)],[1106]) ).
thf(877,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(4963,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)],[877]) ).
thf(804,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(4665,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)],[804]) ).
thf(791,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(4610,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)],[791]) ).
thf(42,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(1482,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)],[42]) ).
thf(873,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(4941,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)],[873]) ).
thf(483,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(3370,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)],[483]) ).
thf(383,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) )
<=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__nat__less) ).
thf(2972,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) )
=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) )
& ( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) )
=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(182,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(2046,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)],[182]) ).
thf(1132,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(5977,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)],[1132]) ).
thf(577,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F = E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ D @ C ) @ B ) @ E ) @ A ) @ F )
= A ) )
& ( ( F != E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( 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(3766,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F = E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ D @ C ) @ B ) @ E ) @ A ) @ F )
= A ) )
& ( ( F != E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ D @ C ) @ B ) @ E ) @ A ) @ F )
= ( hAPP @ B @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(149,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(1914,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)],[149]) ).
thf(981,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(5393,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)],[981]) ).
thf(335,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Map_Omap__comp @ E @ D @ C @ B @ ( hAPP @ ( c_COMBK @ ( tc_Option_Ooption @ E ) @ C ) @ ( c_Option_Ooption_ONone @ E ) ) @ A )
= ( c_Option_Ooption_ONone @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__comp__empty_I1_J) ).
thf(2763,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Map_Omap__comp @ E @ D @ C @ B @ ( hAPP @ ( c_COMBK @ ( tc_Option_Ooption @ E ) @ C ) @ ( c_Option_Ooption_ONone @ E ) ) @ A )
= ( c_Option_Ooption_ONone @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(1200,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(6268,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)],[1200]) ).
thf(281,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__mod__conj) ).
thf(2548,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(764,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(4496,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)],[764]) ).
thf(62,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(1576,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)],[62]) ).
thf(174,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(2020,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)],[174]) ).
thf(938,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(5195,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)],[938]) ).
thf(214,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(2173,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)],[214]) ).
thf(790,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(4607,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)],[790]) ).
thf(1178,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(6182,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)],[1178]) ).
thf(255,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(2405,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)],[255]) ).
thf(832,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(4775,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)],[832]) ).
thf(359,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(2869,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)],[359]) ).
thf(1087,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(5797,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)],[1087]) ).
thf(968,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(5342,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)],[968]) ).
thf(140,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(1887,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)],[140]) ).
thf(735,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(4386,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)],[735]) ).
thf(378,axiom,
! [A: $i,B: $i] :
( ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ B @ A )
= ( hAPP @ ( c_List_Oset @ tc_Nat_Onat ) @ ( c_List_Oupt @ B @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastAtMost__upt) ).
thf(2957,plain,
! [A: $i,B: $i] :
( ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ B @ A )
= ( hAPP @ ( c_List_Oset @ tc_Nat_Onat ) @ ( c_List_Oupt @ B @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(252,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(2397,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)],[252]) ).
thf(2398,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(lifteq,[status(thm)],[2397]) ).
thf(6684,plain,
( ( hBOOL @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( v_s2 != v_s0 )
| ( ( hAPP @ ( c_Nat_Osize__class_Osize @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
!= ( hAPP @ v_ba @ v_s2 ) ) ),
inference(paramod_ordered,[status(thm)],[2398,6563]) ).
thf(6707,plain,
( ( hBOOL @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( v_s2 != v_s0 )
| ( ( c_Nat_Osize__class_Osize @ tc_Nat_Onat )
!= v_ba )
| ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= v_s2 ) ),
inference(simp,[status(thm)],[6684]) ).
thf(589,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(3820,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)],[589]) ).
thf(369,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(2916,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)],[369]) ).
thf(745,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(4415,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)],[745]) ).
thf(137,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ C ) )
<=> ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ D ) @ B ) ) ) ) )
=> ( ? [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) )
<=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ C ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_periodic__finite__ex) ).
thf(1871,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ! [C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ A @ C ) )
=> ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ D ) @ B ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ D ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) )
=> ( ( ? [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ C ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) ) )
& ( ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ C ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) )
=> ? [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(936,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(5188,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)],[936]) ).
thf(546,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(3653,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)],[546]) ).
thf(1049,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__lessThan) ).
thf(5640,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).
thf(885,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(4984,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)],[885]) ).
thf(262,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(2466,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)],[262]) ).
thf(287,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ C ) @ B ) @ A ) ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult2__eq) ).
thf(2571,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ C ) @ B ) @ A ) ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(1079,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(5765,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)],[1079]) ).
thf(446,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(3221,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)],[446]) ).
thf(625,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ G @ F @ E @ D ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ E @ G ) @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( 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(3938,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ G @ F @ E @ D ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ E @ G ) @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( 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)],[625]) ).
thf(725,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ F ) @ ( hAPP @ ( c_List_Oset @ G ) @ E ) ) )
=> ( ( c_Map_Omap__upds @ G @ D @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ G @ ( tc_Option_Ooption @ D ) ) @ C ) @ F ) @ ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ B ) ) @ E @ A )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ G @ ( tc_Option_Ooption @ D ) ) @ ( c_Map_Omap__upds @ G @ D @ C @ E @ A ) ) @ F ) @ ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__upds__twist) ).
thf(4348,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ F ) @ ( hAPP @ ( c_List_Oset @ G ) @ E ) ) )
=> ( ( c_Map_Omap__upds @ G @ D @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ G @ ( tc_Option_Ooption @ D ) ) @ C ) @ F ) @ ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ B ) ) @ E @ A )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ G @ ( tc_Option_Ooption @ D ) ) @ ( c_Map_Omap__upds @ G @ D @ C @ E @ A ) ) @ F ) @ ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(497,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(3425,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)],[497]) ).
thf(864,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ F @ E )
= ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ C ) )
=> ( ( hAPP @ ( c_Map_Omap__add @ B @ D @ A @ F ) @ E )
= ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__find__right) ).
thf(4896,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ F @ E )
= ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ C ) )
=> ( ( hAPP @ ( c_Map_Omap__add @ B @ D @ A @ F ) @ E )
= ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(1269,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(6552,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)],[1269]) ).
thf(326,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(2735,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)],[326]) ).
thf(169,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mod__equality_H) ).
thf(1985,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(180,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(2039,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)],[180]) ).
thf(1146,axiom,
( ( ( c_Com_Ocom_OWhile @ v_ba @ v_ca )
= ( c_Com_Ocom_OWhile @ v_b @ v_c ) )
=> ( ! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ A ) @ v_G ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ v_na @ A ) )
=> ! [A: $i] :
( ( v_P @ A @ v_s1 )
=> ( ( v_P @ A @ v_s2 )
& ~ ( hBOOL @ ( hAPP @ v_b @ v_s2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_5) ).
thf(6039,plain,
( ( ( c_Com_Ocom_OWhile @ v_ba @ v_ca )
= ( c_Com_Ocom_OWhile @ v_b @ v_c ) )
=> ( ! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ A ) @ v_G ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ v_na @ A ) )
=> ! [A: $i] :
( ( v_P @ A @ v_s1 )
=> ( ( v_P @ A @ v_s2 )
& ~ ( hBOOL @ ( hAPP @ v_b @ v_s2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).
thf(84,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__mod__sign) ).
thf(1660,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__imp__zdiv__neg__iff) ).
thf(1298,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(308,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(2667,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)],[308]) ).
thf(671,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(4151,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(1267,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(6547,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hAPP @ B @ C )
= ( hAPP @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1267]) ).
thf(812,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
<=> ( A
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__1__iff__1) ).
thf(4692,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
=> ( A
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( A
= ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(957,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oantisym__conv) ).
thf(5284,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(555,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(3689,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)],[555]) ).
thf(332,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ E @ D @ C @ ( hAPP @ ( c_COMBK @ D @ E ) @ B ) @ ( hAPP @ ( c_COMBK @ D @ C ) @ B ) ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__case__KK) ).
thf(2755,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ E @ D @ C @ ( hAPP @ ( c_COMBK @ D @ E ) @ B ) @ ( hAPP @ ( c_COMBK @ D @ C ) @ B ) ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(1117,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(5910,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)],[1117]) ).
thf(133,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__mult__cancel) ).
thf(1860,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(721,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(4334,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)],[721]) ).
thf(223,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(2217,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)],[223]) ).
thf(833,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(4778,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)],[833]) ).
thf(579,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(3776,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(125,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(1826,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)],[125]) ).
thf(928,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F = E )
=> ( ( hAPP @ ( c_Map_Omap__of @ D @ C @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ F ) @ B ) ) @ A ) ) @ E )
= ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ B ) ) )
& ( ( F != E )
=> ( ( hAPP @ ( c_Map_Omap__of @ D @ C @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ F ) @ B ) ) @ A ) ) @ E )
= ( hAPP @ ( c_Map_Omap__of @ D @ C @ A ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__Cons__code_I2_J) ).
thf(5150,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F = E )
=> ( ( hAPP @ ( c_Map_Omap__of @ D @ C @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ F ) @ B ) ) @ A ) ) @ E )
= ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ B ) ) )
& ( ( F != E )
=> ( ( hAPP @ ( c_Map_Omap__of @ D @ C @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ ( tc_prod @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ F ) @ B ) ) @ A ) ) @ E )
= ( hAPP @ ( c_Map_Omap__of @ D @ C @ A ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
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 ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).
thf(5130,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)],[924]) ).
thf(930,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(5160,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)],[930]) ).
thf(6564,plain,
( ( v_s2 != v_s0 )
| ( ( hBOOL @ ( hAPP @ v_ba @ v_s2 ) )
!= ( hBOOL @ c_fFalse ) ) ),
inference(paramod_ordered,[status(thm)],[6563,6216]) ).
thf(6565,plain,
( ( v_s2 != v_s0 )
| ( ( hAPP @ v_ba @ v_s2 )
!= c_fFalse ) ),
inference(simp,[status(thm)],[6564]) ).
thf(6634,plain,
( ( v_s2 != v_s0 )
| ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
!= c_fFalse )
| ( ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
!= ( hAPP @ v_ba @ v_s2 ) ) ),
inference(paramod_ordered,[status(thm)],[4135,6565]) ).
thf(6662,plain,
( ( v_s2 != v_s0 )
| ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
!= c_fFalse )
| ( c_Nat_OSuc != v_ba )
| ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= v_s2 ) ),
inference(simp,[status(thm)],[6634]) ).
thf(1215,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(6332,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)],[1215]) ).
thf(955,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(5279,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)],[955]) ).
thf(316,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zmult1__eq) ).
thf(2703,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(1193,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(6240,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)],[1193]) ).
thf(855,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(4862,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)],[855]) ).
thf(1244,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 @ ( c_Map_Omap__upds @ F @ C @ B @ D @ A ) @ E )
= ( hAPP @ B @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__upds__apply__nontin) ).
thf(6455,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 @ ( c_Map_Omap__upds @ F @ C @ B @ D @ A ) @ E )
= ( hAPP @ B @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1244]) ).
thf(793,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(4617,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)],[793]) ).
thf(41,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(1479,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)],[41]) ).
thf(1007,axiom,
! [A: $i,B: $i] :
( ( B
!= ( c_Option_Ooption_ONone @ A ) )
=> ~ ! [C: $i] :
( B
!= ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Oexhaust) ).
thf(5480,plain,
! [A: $i,B: $i] :
( ( B
!= ( c_Option_Ooption_ONone @ A ) )
=> ~ ! [C: $i] :
( B
!= ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ E @ ( tc_Option_Ooption @ D ) ) @ C ) @ B ) @ ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ A ) )
!= ( hAPP @ ( c_COMBK @ ( tc_Option_Ooption @ D ) @ E ) @ ( c_Option_Ooption_ONone @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__upd__nonempty) ).
thf(1398,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ E @ ( tc_Option_Ooption @ D ) ) @ C ) @ B ) @ ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ A ) )
!= ( hAPP @ ( c_COMBK @ ( tc_Option_Ooption @ D ) @ E ) @ ( c_Option_Ooption_ONone @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(373,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__le__dividend) ).
thf(2929,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(628,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(3951,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)],[628]) ).
thf(113,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(1773,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)],[113]) ).
thf(449,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(3231,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ A ) @ ( c_List_Olist_ONil @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(1043,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(5617,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)],[1043]) ).
thf(945,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ D @ C ) ) @ B ) @ A ) )
=> ( ( ( A = B )
=> ( hBOOL @ ( hAPP @ D @ B ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ D @ B ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ B ) @ E ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ D @ C ) ) @ E ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__WHILE__case) ).
thf(5231,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ D @ C ) ) @ B ) @ A ) )
=> ( ( ( A = B )
=> ( hBOOL @ ( hAPP @ D @ B ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ D @ B ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ B ) @ E ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ D @ C ) ) @ E ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(1073,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(5744,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)],[1073]) ).
thf(150,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(1922,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)],[150]) ).
thf(1138,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Sum__Type_OProjr @ C @ B @ ( hAPP @ ( c_Sum__Type_OInr @ B @ C ) @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Projr_Osimps) ).
thf(6010,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Sum__Type_OProjr @ C @ B @ ( hAPP @ ( c_Sum__Type_OInr @ B @ C ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).
thf(416,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ G @ F ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ E ) @ D ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ C @ F ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ F ) )
=> ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ G ) @ C ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ E ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ A ) ) @ F ) ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ A ) @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__rel__add1__eq) ).
thf(3099,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ G @ F ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ E ) @ D ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ C @ F ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ F ) )
=> ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ G ) @ C ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ E ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ A ) ) @ F ) ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ A ) @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(1197,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_New__DSequence_Opos__single @ C @ B ) @ A )
= ( c_Lazy__Sequence_Osingle @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Opos__single__def) ).
thf(6253,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_New__DSequence_Opos__single @ C @ B ) @ A )
= ( c_Lazy__Sequence_Osingle @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197]) ).
thf(142,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(1892,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)],[142]) ).
thf(487,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(3385,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)],[487]) ).
thf(682,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(4194,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)],[682]) ).
thf(728,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(4358,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)],[728]) ).
thf(183,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ D ) ) ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult2__lemma__aux3) ).
thf(2049,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ D ) ) ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(923,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(5127,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)],[923]) ).
thf(1089,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(5802,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)],[1089]) ).
thf(141,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(1890,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)],[141]) ).
thf(679,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(4179,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)],[679]) ).
thf(1038,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_OCollect @ B ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__def) ).
thf(5604,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_OCollect @ B ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(1208,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(6310,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)],[1208]) ).
thf(963,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(5323,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)],[963]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zmult1__eq) ).
thf(1347,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(732,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ B ) @ A ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ A ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( D != B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ D ) @ C )
!= B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bset_I4_J) ).
thf(4368,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ B ) @ A ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ A ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( D != B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ D ) @ C )
!= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(276,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ A ) )
=> ( ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ C ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ) )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ D ) @ C )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__rel__div__eq) ).
thf(2520,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ A ) )
=> ( ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ C ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ) )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ D ) @ C )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(798,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(4632,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)],[798]) ).
thf(81,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(1641,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)],[81]) ).
thf(121,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__imp__zdiv__neg__iff) ).
thf(1815,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(755,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(4460,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)],[755]) ).
thf(912,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(5076,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)],[912]) ).
thf(164,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(1963,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)],[164]) ).
thf(736,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(4390,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)],[736]) ).
thf(917,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(5091,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)],[917]) ).
thf(836,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( c_Sum__Type_Osum_Osum__case @ G @ F @ E @ D @ C )
= ( c_Sum__Type_Osum_Osum__case @ G @ F @ E @ B @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__case__inject) ).
thf(4793,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( c_Sum__Type_Osum_Osum__case @ G @ F @ E @ D @ C )
= ( c_Sum__Type_Osum_Osum__case @ G @ F @ E @ B @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(532,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(3602,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)],[532]) ).
thf(1143,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(6025,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)],[1143]) ).
thf(115,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(1778,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)],[115]) ).
thf(711,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(4302,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)],[711]) ).
thf(603,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(3866,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)],[603]) ).
thf(277,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(2533,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)],[277]) ).
thf(700,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(4253,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)],[700]) ).
thf(460,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__imp__Suc__add) ).
thf(3268,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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(639,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(4008,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)],[639]) ).
thf(458,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(3258,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)],[458]) ).
thf(349,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(2829,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)],[349]) ).
thf(1085,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(5792,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)],[1085]) ).
thf(787,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(4595,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)],[787]) ).
thf(1131,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(5974,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)],[1131]) ).
thf(224,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(2222,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)],[224]) ).
thf(993,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(5433,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)],[993]) ).
thf(296,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(2616,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)],[296]) ).
thf(783,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(4578,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)],[783]) ).
thf(709,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(4297,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)],[709]) ).
thf(1234,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ E @ D @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ E ) @ C ) @ B ) @ A ) )
<=> ! [F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ C @ F ) @ G ) )
=> ! [H: $i] :
( ( c_Natural_Oevaln @ B @ G @ D @ H )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ F ) @ H ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_triple__valid__def2) ).
thf(6419,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( c_Hoare__Mirabelle_Otriple__valid @ E @ D @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ E ) @ C ) @ B ) @ A ) )
=> ! [F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ C @ F ) @ G ) )
=> ! [H: $i] :
( ( c_Natural_Oevaln @ B @ G @ D @ H )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ F ) @ H ) ) ) ) )
& ( ! [F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ C @ F ) @ G ) )
=> ! [H: $i] :
( ( c_Natural_Oevaln @ B @ G @ D @ H )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ F ) @ H ) ) ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ E @ D @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ E ) @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1234]) ).
thf(843,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevaln @ D @ C @ B @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ D ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__evalc) ).
thf(4820,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevaln @ D @ C @ B @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ D ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(850,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(4847,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)],[850]) ).
thf(901,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(5032,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)],[901]) ).
thf(973,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(5360,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)],[973]) ).
thf(1056,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(5663,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)],[1056]) ).
thf(1112,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(5892,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)],[1112]) ).
thf(719,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(4329,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)],[719]) ).
thf(609,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(3887,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)],[609]) ).
thf(489,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(3393,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)],[489]) ).
thf(895,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(5013,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)],[895]) ).
thf(148,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(1911,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)],[148]) ).
thf(339,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(2782,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)],[339]) ).
thf(1261,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(6523,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)],[1261]) ).
thf(229,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(2236,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)],[229]) ).
thf(19,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(1334,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)],[19]) ).
thf(518,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ G @ ( tc_Option_Ooption @ F ) ) @ E ) @ D ) @ ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ C ) ) @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ A ) )
<=> ( ( ( B = D )
& ( C = A ) )
| ( ( B != D )
& ( ( hAPP @ E @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__upd__Some__unfold) ).
thf(3527,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ G @ ( tc_Option_Ooption @ F ) ) @ E ) @ D ) @ ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ C ) ) @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ A ) )
=> ( ( ( B = D )
& ( C = A ) )
| ( ( B != D )
& ( ( hAPP @ E @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ A ) ) ) ) )
& ( ( ( ( B = D )
& ( C = A ) )
| ( ( B != D )
& ( ( hAPP @ E @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ A ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ G @ ( tc_Option_Ooption @ F ) ) @ E ) @ D ) @ ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ C ) ) @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(1231,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(6410,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)],[1231]) ).
thf(635,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(3983,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)],[635]) ).
thf(1180,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(6189,plain,
! [A: $i,B: $i] :
( ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1180]) ).
thf(1124,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(5946,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)],[1124]) ).
thf(646,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ D @ C ) @ D ) @ ( c_Product__Type_Ofst @ D @ C ) ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ D @ C ) @ D ) @ ( c_Product__Type_Ofst @ D @ C ) ) @ A ) ) )
=> ( ( ( c_Map_Omap__of @ D @ C @ B )
= ( c_Map_Omap__of @ D @ C @ A ) )
<=> ( ( hAPP @ ( c_List_Oset @ ( tc_prod @ D @ C ) ) @ B )
= ( hAPP @ ( c_List_Oset @ ( tc_prod @ D @ C ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__inject__set) ).
thf(4050,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ D @ C ) @ D ) @ ( c_Product__Type_Ofst @ D @ C ) ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ D @ C ) @ D ) @ ( c_Product__Type_Ofst @ D @ C ) ) @ A ) ) )
=> ( ( ( ( c_Map_Omap__of @ D @ C @ B )
= ( c_Map_Omap__of @ D @ C @ A ) )
=> ( ( hAPP @ ( c_List_Oset @ ( tc_prod @ D @ C ) ) @ B )
= ( hAPP @ ( c_List_Oset @ ( tc_prod @ D @ C ) ) @ A ) ) )
& ( ( ( hAPP @ ( c_List_Oset @ ( tc_prod @ D @ C ) ) @ B )
= ( hAPP @ ( c_List_Oset @ ( tc_prod @ D @ C ) ) @ A ) )
=> ( ( c_Map_Omap__of @ D @ C @ B )
= ( c_Map_Omap__of @ D @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(841,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(4815,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)],[841]) ).
thf(1175,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(6176,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)],[1175]) ).
thf(538,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(3621,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)],[538]) ).
thf(632,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ B ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ D ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_aset_I7_J) ).
thf(3973,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ B ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ D ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(1090,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(5804,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)],[1090]) ).
thf(90,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(1677,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)],[90]) ).
thf(962,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Map_Omap__comp @ F @ E @ D @ C @ B @ A )
= ( c_Option_Ooption_ONone @ E ) )
<=> ( ( ( hAPP @ B @ A )
= ( c_Option_Ooption_ONone @ F ) )
| ? [G: $i] :
( ( ( hAPP @ B @ A )
= ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ G ) )
& ( ( hAPP @ C @ G )
= ( c_Option_Ooption_ONone @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__comp__None__iff) ).
thf(5311,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( c_Map_Omap__comp @ F @ E @ D @ C @ B @ A )
= ( c_Option_Ooption_ONone @ E ) )
=> ( ( ( hAPP @ B @ A )
= ( c_Option_Ooption_ONone @ F ) )
| ? [G: $i] :
( ( ( hAPP @ B @ A )
= ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ G ) )
& ( ( hAPP @ C @ G )
= ( c_Option_Ooption_ONone @ E ) ) ) ) )
& ( ( ( ( hAPP @ B @ A )
= ( c_Option_Ooption_ONone @ F ) )
| ? [G: $i] :
( ( ( hAPP @ B @ A )
= ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ G ) )
& ( ( hAPP @ C @ G )
= ( c_Option_Ooption_ONone @ E ) ) ) )
=> ( ( c_Map_Omap__comp @ F @ E @ D @ C @ B @ A )
= ( c_Option_Ooption_ONone @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(1177,axiom,
hBOOL @ c_fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fTrue__1) ).
thf(6181,plain,
hBOOL @ c_fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).
thf(6558,plain,
( ( hBOOL @ c_fFalse )
!= ( hBOOL @ c_fTrue ) ),
inference(paramod_ordered,[status(thm)],[6181,6216]) ).
thf(6559,plain,
c_fFalse != c_fTrue,
inference(simp,[status(thm)],[6558]) ).
thf(621,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(3923,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)],[621]) ).
thf(163,axiom,
! [A: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zero) ).
thf(1960,plain,
! [A: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(661,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(4115,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)],[661]) ).
thf(64,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(1581,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)],[64]) ).
thf(1169,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(6157,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)],[1169]) ).
thf(950,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(5259,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)],[950]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ C ) @ B ) ) @ ( c_List_Olistrel @ D @ A ) ) )
=> ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__eq__len) ).
thf(1283,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ C ) @ B ) ) @ ( c_List_Olistrel @ D @ A ) ) )
=> ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(839,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(4810,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)],[839]) ).
thf(1186,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(6204,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)],[1186]) ).
thf(597,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(3851,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)],[597]) ).
thf(636,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(3986,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)],[636]) ).
thf(1071,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Map_Omap__add @ E @ D @ C @ ( c_Map_Omap__add @ E @ D @ B @ A ) )
= ( c_Map_Omap__add @ E @ D @ ( c_Map_Omap__add @ E @ D @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__assoc) ).
thf(5738,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Map_Omap__add @ E @ D @ C @ ( c_Map_Omap__add @ E @ D @ B @ A ) )
= ( c_Map_Omap__add @ E @ D @ ( c_Map_Omap__add @ E @ D @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).
thf(152,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(1928,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)],[152]) ).
thf(438,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(3189,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)],[438]) ).
thf(357,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(2861,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)],[357]) ).
thf(919,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Sum__Type_OInl @ D @ C ) @ B )
!= ( hAPP @ ( c_Sum__Type_OInr @ C @ D ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inl__not__Inr) ).
thf(5101,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Sum__Type_OInl @ D @ C ) @ B )
!= ( hAPP @ ( c_Sum__Type_OInr @ C @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(517,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(3505,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)],[517]) ).
thf(403,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(3036,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)],[403]) ).
thf(1190,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_Map_Orestrict__map @ E @ B @ A @ C ) @ D )
= ( hAPP @ A @ D ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_Map_Orestrict__map @ E @ B @ A @ C ) @ D )
= ( c_Option_Ooption_ONone @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrict__map__def) ).
thf(6221,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_Map_Orestrict__map @ E @ B @ A @ C ) @ D )
= ( hAPP @ A @ D ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_Map_Orestrict__map @ E @ B @ A @ C ) @ D )
= ( c_Option_Ooption_ONone @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190]) ).
thf(36,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(1394,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)],[36]) ).
thf(644,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ A ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ D ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ A ) )
=> ( B
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ E ) @ D ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ C )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bset_I3_J) ).
thf(4040,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ A ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ D ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ A ) )
=> ( B
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ E ) @ D ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ C )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(303,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(2639,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)],[303]) ).
thf(71,axiom,
! [A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
& ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DIVISION__BY__ZERO) ).
thf(1600,plain,
! [A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
& ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(524,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(3559,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)],[524]) ).
thf(514,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(3492,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)],[514]) ).
thf(1062,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(5695,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)],[1062]) ).
thf(1248,axiom,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ c_fNot @ A ) )
| ~ ( hBOOL @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__1) ).
thf(6474,plain,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ c_fNot @ A ) )
| ~ ( hBOOL @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1248]) ).
thf(1030,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ C @ B ) ) @ A ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ C @ A ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ B ) @ A ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ C @ B ) ) @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I7_J) ).
thf(5572,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ C @ B ) ) @ A ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ C @ A ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ B ) @ A ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ C @ B ) ) @ D ) @ A ) ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ C @ A ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ B ) @ A ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ C @ B ) ) @ D ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ C @ B ) ) @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(272,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Int_Oint @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThanPlusOne__atLeastAtMost__int) ).
thf(2508,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Int_Oint @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(908,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(5059,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)],[908]) ).
thf(647,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(4055,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)],[647]) ).
thf(30,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(1377,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)],[30]) ).
thf(1160,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(6110,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)],[1160]) ).
thf(561,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(3712,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)],[561]) ).
thf(444,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(3211,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)],[444]) ).
thf(1159,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Option_Oset @ C @ A ) ) )
<=> ( A
= ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_elem__set) ).
thf(6103,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Option_Oset @ C @ A ) ) )
=> ( A
= ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ B ) ) )
& ( ( A
= ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Option_Oset @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).
thf(965,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__le__trans) ).
thf(5328,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(796,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(4628,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)],[796]) ).
thf(1187,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(6210,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)],[1187]) ).
thf(94,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(1696,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)],[94]) ).
thf(134,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(1863,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)],[134]) ).
thf(377,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(2954,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)],[377]) ).
thf(614,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ C ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ C @ A ) ) ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__rel__mult2__eq) ).
thf(3899,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ C ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ C @ A ) ) ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(984,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(5406,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)],[984]) ).
thf(459,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(3265,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)],[459]) ).
thf(1063,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(5697,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)],[1063]) ).
thf(910,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(5070,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)],[910]) ).
thf(1226,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(6388,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)],[1226]) ).
thf(98,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(1708,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)],[98]) ).
thf(1009,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(5487,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)],[1009]) ).
thf(1018,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(5540,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)],[1018]) ).
thf(869,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ B ) @ A ) )
=> ? [D: $i] : ( c_Natural_Oevaln @ C @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__evaln) ).
thf(4925,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ B ) @ A ) )
=> ? [D: $i] : ( c_Natural_Oevaln @ C @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(105,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(1730,plain,
! [A: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ tc_Nat_Onat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(933,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(5174,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)],[933]) ).
thf(1128,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ B ) @ ( c_SetInterval_Oord_OatMost @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatMost__iff) ).
thf(5961,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ B ) @ ( c_SetInterval_Oord_OatMost @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ B ) @ ( c_SetInterval_Oord_OatMost @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).
thf(789,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(4604,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)],[789]) ).
thf(1263,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(6529,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)],[1263]) ).
thf(689,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(4216,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)],[689]) ).
thf(863,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(4893,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)],[863]) ).
thf(717,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(4323,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)],[717]) ).
thf(467,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(3301,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)],[467]) ).
thf(219,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ D ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ B ) ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ E ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ E ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unique__quotient__lemma__neg) ).
thf(2204,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ D ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ B ) ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ E ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ E ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(468,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__less) ).
thf(3303,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(827,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInl @ D @ C ) @ B )
= ( hAPP @ ( c_Sum__Type_OInl @ D @ C ) @ A ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inl__inject) ).
thf(4753,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInl @ D @ C ) @ B )
= ( hAPP @ ( c_Sum__Type_OInl @ D @ C ) @ A ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(785,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(4589,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)],[785]) ).
thf(1141,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(6020,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)],[1141]) ).
thf(1075,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(5751,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)],[1075]) ).
thf(1140,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(6015,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)],[1140]) ).
thf(288,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ A ) )
= ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times__numeral__code_I5_J) ).
thf(2574,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ A ) )
= ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(564,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(3720,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)],[564]) ).
thf(542,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ B ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ D ) @ C ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bset_I6_J) ).
thf(3635,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ B ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ D ) @ C ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(209,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(2162,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)],[209]) ).
thf(2163,plain,
( ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint )
!= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ),
inference(polarity_switch,[status(thm)],[2162]) ).
thf(2164,plain,
( ( c_Groups_Oone__class_Oone @ tc_Int_Oint )
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(lifteq,[status(thm)],[2163]) ).
thf(931,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__imp__not__eq) ).
thf(5167,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(1149,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(6058,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)],[1149]) ).
thf(1196,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(6250,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)],[1196]) ).
thf(777,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(4557,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)],[777]) ).
thf(112,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(1768,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)],[112]) ).
thf(136,axiom,
! [A: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__self) ).
thf(1868,plain,
! [A: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(188,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(2061,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)],[188]) ).
thf(956,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(5281,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)],[956]) ).
thf(905,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(5049,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)],[905]) ).
thf(1218,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(6343,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)],[1218]) ).
thf(260,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(2428,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)],[260]) ).
thf(1268,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(6550,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)],[1268]) ).
thf(278,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(2541,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)],[278]) ).
thf(887,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(4989,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)],[887]) ).
thf(1127,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(5956,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)],[1127]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ A ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__div__cancel) ).
thf(1487,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ A ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(553,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(3682,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)],[553]) ).
thf(1274,plain,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ A ) @ v_G ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ v_na @ A ) ),
inference(cnf,[status(esa)],[1272]) ).
thf(309,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(2673,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)],[309]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__not__zless) ).
thf(1387,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(144,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__imp__zdiv__nonneg__iff) ).
thf(1900,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(1046,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(5630,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)],[1046]) ).
thf(344,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(2805,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)],[344]) ).
thf(292,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__function__closures_I1_J) ).
thf(2596,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(739,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= B ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__if) ).
thf(4397,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= B ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(382,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Map_Omap__add @ F @ E @ D @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ ( tc_Option_Ooption @ E ) ) @ C ) @ B ) @ ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ ( tc_Option_Ooption @ E ) ) @ ( c_Map_Omap__add @ F @ E @ D @ C ) ) @ B ) @ ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__upd) ).
thf(2969,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Map_Omap__add @ F @ E @ D @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ ( tc_Option_Ooption @ E ) ) @ C ) @ B ) @ ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ ( tc_Option_Ooption @ E ) ) @ ( c_Map_Omap__add @ F @ E @ D @ C ) ) @ B ) @ ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(654,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(4091,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)],[654]) ).
thf(572,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(3752,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)],[572]) ).
thf(637,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(3989,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)],[637]) ).
thf(412,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(3069,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)],[412]) ).
thf(450,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(3233,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)],[450]) ).
thf(608,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ E @ D )
= ( c_Option_Ooption_ONone @ C ) )
=> ( ( c_Map_Oran @ B @ C @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ B @ ( tc_Option_Ooption @ C ) ) @ E ) @ D ) @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Map_Oran @ B @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ran__map__upd) ).
thf(3884,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ E @ D )
= ( c_Option_Ooption_ONone @ C ) )
=> ( ( c_Map_Oran @ B @ C @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ B @ ( tc_Option_Ooption @ C ) ) @ E ) @ D ) @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ ( c_Map_Oran @ B @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(1004,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(5470,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)],[1004]) ).
thf(765,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(4499,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)],[765]) ).
thf(294,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(2606,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)],[294]) ).
thf(427,axiom,
! [A: $i,B: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) )
= A )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( ( hAPP @ c_Nat_OSuc @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) )
!= A )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__Suc) ).
thf(3134,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) )
= A )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( ( hAPP @ c_Nat_OSuc @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) )
!= A )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(915,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(5085,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)],[915]) ).
thf(1255,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(6496,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)],[1255]) ).
thf(1013,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ F @ E ) )
=> ( ( c_Natural_Oevaln @ D @ E @ C @ B )
=> ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ F @ D ) @ B @ C @ A )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ F @ D ) @ E @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OWhileTrue) ).
thf(5507,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ F @ E ) )
=> ( ( c_Natural_Oevaln @ D @ E @ C @ B )
=> ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ F @ D ) @ B @ C @ A )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ F @ D ) @ E @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(982,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInr @ D @ C ) @ B )
= ( hAPP @ ( c_Sum__Type_OInr @ D @ C ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Osimps_I2_J) ).
thf(5396,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( c_Sum__Type_OInr @ D @ C ) @ B )
= ( hAPP @ ( c_Sum__Type_OInr @ D @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( c_Sum__Type_OInr @ D @ C ) @ B )
= ( hAPP @ ( c_Sum__Type_OInr @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(363,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(2890,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)],[363]) ).
thf(256,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ C @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ C ) )
=> ? [D: $i] :
( C
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mod__eq__lemma) ).
thf(2414,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ C @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ C ) )
=> ? [D: $i] :
( C
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(456,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(3250,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)],[456]) ).
thf(173,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(2015,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)],[173]) ).
thf(610,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(3889,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)],[610]) ).
thf(510,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(3471,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)],[510]) ).
thf(464,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Map_Odom @ C @ B @ ( c_Map_Omap__of @ C @ B @ A ) )
= ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ C @ B ) @ C @ ( c_Product__Type_Ofst @ C @ B ) ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ C @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dom__map__of__conv__image__fst) ).
thf(3286,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Map_Odom @ C @ B @ ( c_Map_Omap__of @ C @ B @ A ) )
= ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ C @ B ) @ C @ ( c_Product__Type_Ofst @ C @ B ) ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ C @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(59,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(1560,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)],[59]) ).
thf(627,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(3948,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)],[627]) ).
thf(537,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(3618,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)],[537]) ).
thf(1016,axiom,
! [A: $i,B: $i] :
( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oeq__refl) ).
thf(5534,plain,
! [A: $i,B: $i] :
( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(681,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olist_ONil @ C ) ) @ B ) ) @ ( c_List_Olexord @ C @ A ) ) )
<=> ? [D: $i,E: $i] :
( B
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ D ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__Nil__left) ).
thf(4187,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olist_ONil @ C ) ) @ B ) ) @ ( c_List_Olexord @ C @ A ) ) )
=> ? [D: $i,E: $i] :
( B
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ D ) @ E ) ) )
& ( ? [D: $i,E: $i] :
( B
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ D ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olist_ONil @ C ) ) @ B ) ) @ ( c_List_Olexord @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(1150,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(6060,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)],[1150]) ).
thf(1172,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(6168,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ~ ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).
thf(222,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(2211,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)],[222]) ).
thf(1081,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(5769,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)],[1081]) ).
thf(461,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(3271,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)],[461]) ).
thf(708,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(4295,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)],[708]) ).
thf(1207,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(6303,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)],[1207]) ).
thf(1097,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(5826,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)],[1097]) ).
thf(261,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(2464,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)],[261]) ).
thf(333,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__mod__bound) ).
thf(2758,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(980,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(5391,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)],[980]) ).
thf(1135,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(5983,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)],[1135]) ).
thf(668,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(4140,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)],[668]) ).
thf(851,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ D @ C ) )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ D @ B ) @ C @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OWhileFalse) ).
thf(4849,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ D @ C ) )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ D @ B ) @ C @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(27,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(1365,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)],[27]) ).
thf(586,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_Divides_Odivmod__nat @ A @ B )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ) @ B ) ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__step) ).
thf(3810,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_Divides_Odivmod__nat @ A @ B )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ) @ B ) ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(672,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(4155,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)],[672]) ).
thf(470,axiom,
! [A: $i,B: $i] :
( ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) @ A )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastSucAtMost__greaterThanAtMost) ).
thf(3314,plain,
! [A: $i,B: $i] :
( ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) @ A )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(828,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(4757,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)],[828]) ).
thf(515,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(3499,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)],[515]) ).
thf(523,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(3556,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)],[523]) ).
thf(1060,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(5690,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)],[1060]) ).
thf(1271,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(6556,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)],[1271]) ).
thf(160,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(1951,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)],[160]) ).
thf(1000,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(5460,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)],[1000]) ).
thf(1084,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ E @ D ) @ C @ B @ A )
<=> ( ( ( A = C )
& ~ ( hBOOL @ ( hAPP @ E @ C ) ) )
| ( ( hBOOL @ ( hAPP @ E @ C ) )
& ? [F: $i] :
( ( c_Natural_Oevaln @ D @ C @ B @ F )
& ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ E @ D ) @ F @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I8_J) ).
thf(5779,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ E @ D ) @ C @ B @ A )
=> ( ( ( A = C )
& ~ ( hBOOL @ ( hAPP @ E @ C ) ) )
| ( ( hBOOL @ ( hAPP @ E @ C ) )
& ? [F: $i] :
( ( c_Natural_Oevaln @ D @ C @ B @ F )
& ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ E @ D ) @ F @ B @ A ) ) ) ) )
& ( ( ( ( A = C )
& ~ ( hBOOL @ ( hAPP @ E @ C ) ) )
| ( ( hBOOL @ ( hAPP @ E @ C ) )
& ? [F: $i] :
( ( c_Natural_Oevaln @ D @ C @ B @ F )
& ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ E @ D ) @ F @ B @ A ) ) ) )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ E @ D ) @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).
thf(77,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(1624,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)],[77]) ).
thf(1165,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ E @ D )
= ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ D ) @ ( c_Map_Odom @ A @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_domI) ).
thf(6143,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ E @ D )
= ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ D ) @ ( c_Map_Odom @ A @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).
thf(295,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(2609,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)],[295]) ).
thf(1022,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(5551,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)],[1022]) ).
thf(429,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(3144,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)],[429]) ).
thf(824,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(4746,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(127,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(1836,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)],[127]) ).
thf(921,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_Map_Omap__of @ D @ C @ B ) @ A )
= ( c_Option_Ooption_ONone @ C ) )
<=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ D @ C ) @ D @ ( c_Product__Type_Ofst @ D @ C ) ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ D @ C ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__eq__None__iff) ).
thf(5113,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( c_Map_Omap__of @ D @ C @ B ) @ A )
= ( c_Option_Ooption_ONone @ C ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ D @ C ) @ D @ ( c_Product__Type_Ofst @ D @ C ) ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ D @ C ) ) @ B ) ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ D @ C ) @ D @ ( c_Product__Type_Ofst @ D @ C ) ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ D @ C ) ) @ B ) ) ) )
=> ( ( hAPP @ ( c_Map_Omap__of @ D @ C @ B ) @ A )
= ( c_Option_Ooption_ONone @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(1227,axiom,
c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ v_ba @ v_ca ) @ v_s1 @ v_na @ v_s2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
thf(6392,plain,
c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ v_ba @ v_ca ) @ v_s1 @ v_na @ v_s2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1227]) ).
thf(280,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(2547,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)],[280]) ).
thf(576,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(3763,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)],[576]) ).
thf(657,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Map_Omap__upds @ D @ C @ B @ A @ ( c_List_Olist_ONil @ C ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__upds__Nil2) ).
thf(4104,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Map_Omap__upds @ D @ C @ B @ A @ ( c_List_Olist_ONil @ C ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(566,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(3727,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)],[566]) ).
thf(328,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(2741,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)],[328]) ).
thf(35,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(1392,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)],[35]) ).
thf(226,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__pos__pos__trivial) ).
thf(2228,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(544,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ E ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ E ) @ D ) @ C ) @ B ) ) @ C ) @ A )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ E ) @ D ) @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__upd) ).
thf(3647,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ E ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ E ) @ D ) @ C ) @ B ) ) @ C ) @ A )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ E ) @ D ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(201,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__zmod) ).
thf(2112,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(624,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(3931,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)],[624]) ).
thf(491,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(3408,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)],[491]) ).
thf(809,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(4680,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)],[809]) ).
thf(583,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(3799,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)],[583]) ).
thf(1212,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(6324,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)],[1212]) ).
thf(17,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(1328,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)],[17]) ).
thf(318,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono1) ).
thf(2709,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(313,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__imp__zdiv__nonneg__iff) ).
thf(2694,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(974,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ E ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ E @ D ) @ E ) @ ( c_Product__Type_Ofst @ E @ D ) ) @ C ) ) )
=> ( ( ( hAPP @ ( c_Map_Omap__of @ E @ D @ C ) @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ E @ D ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__eq__Some__iff) ).
thf(5362,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ E ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ E @ D ) @ E ) @ ( c_Product__Type_Ofst @ E @ D ) ) @ C ) ) )
=> ( ( ( ( hAPP @ ( c_Map_Omap__of @ E @ D @ C ) @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ E @ D ) ) @ C ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ E @ D ) ) @ C ) ) )
=> ( ( hAPP @ ( c_Map_Omap__of @ E @ D @ C ) @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(322,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(2724,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)],[322]) ).
thf(848,axiom,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatMost @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatMost @ tc_Nat_Onat ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atMost__Suc) ).
thf(4840,plain,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatMost @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatMost @ tc_Nat_Onat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(545,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(3650,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)],[545]) ).
thf(626,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(3941,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)],[626]) ).
thf(1162,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(6128,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)],[1162]) ).
thf(1006,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(5475,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)],[1006]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) )
<=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( hBOOL @ ( hAPP @ C @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ! [D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ E ) @ A ) )
& ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ C @ E ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ! [D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ E ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ C @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__zmod) ).
thf(1402,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( hBOOL @ ( hAPP @ C @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ! [D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ E ) @ A ) )
& ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ C @ E ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ! [D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ E ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ C @ E ) ) ) ) ) )
& ( ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( hBOOL @ ( hAPP @ C @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ! [D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ E ) @ A ) )
& ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ C @ E ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ! [D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ E ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ C @ E ) ) ) ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(1154,axiom,
( ( v_ca
= ( c_Com_Ocom_OWhile @ v_b @ v_c ) )
=> ( ! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ A ) @ v_G ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ v_na @ A ) )
=> ! [A: $i] :
( ( v_P @ A @ v_s0 )
=> ( ( v_P @ A @ v_s1 )
& ~ ( hBOOL @ ( hAPP @ v_b @ v_s1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
thf(6075,plain,
( ( v_ca
= ( c_Com_Ocom_OWhile @ v_b @ v_c ) )
=> ( ! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ A ) @ v_G ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ v_na @ A ) )
=> ! [A: $i] :
( ( v_P @ A @ v_s0 )
=> ( ( v_P @ A @ v_s1 )
& ~ ( hBOOL @ ( hAPP @ v_b @ v_s1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).
thf(231,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__mod__bound) ).
thf(2245,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zmult__distrib2) ).
thf(1350,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(155,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(1936,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)],[155]) ).
thf(68,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(1592,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)],[68]) ).
thf(582,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(3784,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)],[582]) ).
thf(270,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(2498,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)],[270]) ).
thf(1232,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(6413,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)],[1232]) ).
thf(581,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(3782,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)],[581]) ).
thf(51,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(1541,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)],[51]) ).
thf(207,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(2157,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)],[207]) ).
thf(352,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__le__divisor) ).
thf(2840,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(1040,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(5609,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)],[1040]) ).
thf(203,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(2115,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)],[203]) ).
thf(130,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(1851,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)],[130]) ).
thf(387,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(2990,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)],[387]) ).
thf(952,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(5270,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)],[952]) ).
thf(805,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ tc_Nat_Onat @ c_Nat_OSuc ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ B @ A ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Suc__atLeastAtMost) ).
thf(4668,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ tc_Nat_Onat @ c_Nat_OSuc ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ B @ A ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(969,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(5345,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)],[969]) ).
thf(364,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(2895,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)],[364]) ).
thf(289,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(2577,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)],[289]) ).
thf(1047,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ D ) @ C )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__eq) ).
thf(5635,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ D ) @ C )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).
thf(445,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ E @ D )
= ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ A @ ( tc_Option_Ooption @ C ) ) @ E ) @ D ) @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ B ) )
= E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__upd__triv) ).
thf(3218,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ E @ D )
= ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ A @ ( tc_Option_Ooption @ C ) ) @ E ) @ D ) @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ B ) )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(750,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(4429,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)],[750]) ).
thf(991,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(5428,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)],[991]) ).
thf(694,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(4233,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)],[694]) ).
thf(88,axiom,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__self) ).
thf(1672,plain,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(558,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__1) ).
thf(3704,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(541,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__geq) ).
thf(3632,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(1111,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(5889,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)],[1111]) ).
thf(978,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ B ) @ A ) )
<=> ? [D: $i] : ( c_Natural_Oevaln @ C @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eval__eq) ).
thf(5373,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ B ) @ A ) )
=> ? [D: $i] : ( c_Natural_Oevaln @ C @ B @ D @ A ) )
& ( ? [D: $i] : ( c_Natural_Oevaln @ C @ B @ D @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(571,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(3746,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)],[571]) ).
thf(442,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(3205,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)],[442]) ).
thf(690,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(4219,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)],[690]) ).
thf(236,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(2268,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)],[236]) ).
thf(501,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(3440,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)],[501]) ).
thf(409,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(3060,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)],[409]) ).
thf(397,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(3018,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)],[397]) ).
thf(842,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(4817,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)],[842]) ).
thf(803,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__le) ).
thf(4653,plain,
! [A: $i,B: $i] :
( ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ( B != A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ( B != A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(428,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(3141,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)],[428]) ).
thf(854,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevaln @ D @ C @ B @ A )
=> ( c_Natural_Oevaln @ D @ C @ ( hAPP @ c_Nat_OSuc @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__Suc) ).
thf(4860,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevaln @ D @ C @ B @ A )
=> ( c_Natural_Oevaln @ D @ C @ ( hAPP @ c_Nat_OSuc @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(391,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(3000,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)],[391]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_List_Ofoldl @ D @ C @ B @ A ) @ ( c_List_Olist_ONil @ C ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__Nil) ).
thf(1292,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_List_Ofoldl @ D @ C @ B @ A ) @ ( c_List_Olist_ONil @ C ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1053,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(5651,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)],[1053]) ).
thf(676,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(4167,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)],[676]) ).
thf(562,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(3714,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)],[562]) ).
thf(774,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(4545,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(129,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ C ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ C ) ) )
<=> ! [D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ E ) @ C ) )
& ( A
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__pos__lemma) ).
thf(1842,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ C ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ C ) ) )
=> ! [D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ E ) @ C ) )
& ( A
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ E ) ) ) )
& ( ! [D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ E ) @ C ) )
& ( A
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ C ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(1103,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(5865,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)],[1103]) ).
thf(1256,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(6501,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)],[1256]) ).
thf(466,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(3294,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)],[466]) ).
thf(46,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(1493,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)],[46]) ).
thf(716,axiom,
! [A: $i,B: $i] :
( ( c_Divides_Odivmod__nat @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__div__mod) ).
thf(4320,plain,
! [A: $i,B: $i] :
( ( c_Divides_Odivmod__nat @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(157,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__pos__pos__trivial) ).
thf(1942,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(1235,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(6428,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ B ) @ A ) )
| ( hBOOL @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1235]) ).
thf(1044,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(5620,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)],[1044]) ).
thf(530,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(3596,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)],[530]) ).
thf(747,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(4421,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)],[747]) ).
thf(395,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ B ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ A ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ D ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_aset_I8_J) ).
thf(3010,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ B ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ A ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ D ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(826,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__antisym) ).
thf(4750,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(741,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(4406,plain,
! [A: $i] : ( c_Relation_Osingle__valued @ A @ A @ ( c_Relation_OId @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(65,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(1584,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)],[65]) ).
thf(401,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leI) ).
thf(3032,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(418,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(3104,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(3105,plain,
~ ? [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
= ( hAPP @ c_Nat_OSuc @ A ) ),
inference(miniscope,[status(thm)],[3104]) ).
thf(3106,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
inference(cnf,[status(esa)],[3105]) ).
thf(3107,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(lifteq,[status(thm)],[3106]) ).
thf(6629,plain,
! [A: $i] :
( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
!= ( hAPP @ c_Nat_OSuc @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4135,3107]) ).
thf(6630,plain,
( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(pattern_uni,[status(thm)],[6629:[bind(A,$thf( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ))]]) ).
thf(1121,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(5932,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)],[1121]) ).
thf(1198,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(6256,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198]) ).
thf(119,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(1810,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)],[119]) ).
thf(802,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(4648,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)],[802]) ).
thf(498,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(3428,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)],[498]) ).
thf(282,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__mod__conj) ).
thf(2551,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ B ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(551,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(3671,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)],[551]) ).
thf(194,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(2085,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)],[194]) ).
thf(1115,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(5905,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)],[1115]) ).
thf(82,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(1644,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)],[82]) ).
thf(205,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__nonneg__neg__le0) ).
thf(2125,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(1157,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hAPP @ ( c_Fun_Ooverride__on @ F @ C @ B @ A @ D ) @ E )
= ( hAPP @ B @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_override__on__apply__notin) ).
thf(6097,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hAPP @ ( c_Fun_Ooverride__on @ F @ C @ B @ A @ D ) @ E )
= ( hAPP @ B @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).
thf(425,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(3126,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)],[425]) ).
thf(650,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(4068,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)],[650]) ).
thf(570,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(3743,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)],[570]) ).
thf(1114,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(5900,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)],[1114]) ).
thf(285,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(2566,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)],[285]) ).
thf(1219,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(6346,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)],[1219]) ).
thf(101,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__imp__zdiv__pos__iff) ).
thf(1715,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(976,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(5369,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)],[976]) ).
thf(393,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(3005,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)],[393]) ).
thf(1220,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(6349,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)],[1220]) ).
thf(240,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(2285,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)],[240]) ).
thf(114,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(1776,plain,
! [A: $i,B: $i] : ( c_Wellfounded_Owf @ B @ ( hAPP @ ( c_Wellfounded_Omeasure @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(535,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ B ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ D ) @ C ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bset_I5_J) ).
thf(3611,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ B ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ D ) @ C ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(547,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ C @ B ) @ C ) @ ( c_Product__Type_Ofst @ C @ B ) ) @ A ) ) )
=> ( ( c_Map_Oran @ C @ B @ ( c_Map_Omap__of @ C @ B @ A ) )
= ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ C @ B ) @ B @ ( c_Product__Type_Osnd @ C @ B ) ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ C @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ran__distinct) ).
thf(3656,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ C @ B ) @ C ) @ ( c_Product__Type_Ofst @ C @ B ) ) @ A ) ) )
=> ( ( c_Map_Oran @ C @ B @ ( c_Map_Omap__of @ C @ B @ A ) )
= ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ C @ B ) @ B @ ( c_Product__Type_Osnd @ C @ B ) ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ C @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(1164,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(6134,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)],[1164]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__imp__le) ).
thf(1539,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(31,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(1382,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)],[31]) ).
thf(266,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(2487,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)],[266]) ).
thf(293,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(2598,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)],[293]) ).
thf(1237,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_Map_Odom @ E @ C @ B ) ) )
=> ( ( hAPP @ ( c_Map_Omap__add @ E @ C @ A @ B ) @ D )
= ( hAPP @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__dom__app__simps_I1_J) ).
thf(6433,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_Map_Odom @ E @ C @ B ) ) )
=> ( ( hAPP @ ( c_Map_Omap__add @ E @ C @ A @ B ) @ D )
= ( hAPP @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1237]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono1__neg) ).
thf(1552,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(1010,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(5498,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)],[1010]) ).
thf(761,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(4482,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)],[761]) ).
thf(872,axiom,
! [A: $i,B: $i] :
( ( B
!= ( c_Option_Ooption_ONone @ A ) )
<=> ? [C: $i] :
( B
= ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__None__eq) ).
thf(4934,plain,
! [A: $i,B: $i] :
( ( ( B
!= ( c_Option_Ooption_ONone @ A ) )
=> ? [C: $i] :
( B
= ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ C ) ) )
& ( ? [C: $i] :
( B
= ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ C ) )
=> ( B
!= ( c_Option_Ooption_ONone @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(772,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__diffD1) ).
thf(4540,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(172,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(2006,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)],[172]) ).
thf(539,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(3628,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)],[539]) ).
thf(1242,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(6450,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)],[1242]) ).
thf(575,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(3760,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)],[575]) ).
thf(630,axiom,
! [A: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__lessThan) ).
thf(3967,plain,
! [A: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(455,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(3247,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)],[455]) ).
thf(336,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(2766,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)],[336]) ).
thf(314,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(2697,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)],[314]) ).
thf(620,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThanSuc__atLeastAtMost) ).
thf(3920,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(1179,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(6186,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)],[1179]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__zmod__right) ).
thf(1627,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(947,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(5245,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)],[947]) ).
thf(1259,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(6514,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)],[1259]) ).
thf(707,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(4288,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)],[707]) ).
thf(437,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(3173,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)],[437]) ).
thf(599,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(3856,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)],[599]) ).
thf(469,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(3306,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)],[469]) ).
thf(1152,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(6070,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)],[1152]) ).
thf(254,axiom,
! [A: $i,B: $i] :
( ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ tc_Int_Oint @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastPlusOneAtMost__greaterThanAtMost__int) ).
thf(2402,plain,
! [A: $i,B: $i] :
( ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ tc_Int_Oint @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(143,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(1895,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)],[143]) ).
thf(595,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(3841,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)],[595]) ).
thf(306,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Int_Oint ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ tc_Int_Oint @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__greaterThanAtMost__int) ).
thf(2662,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Int_Oint ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(713,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 @ ( tc_Option_Ooption @ C ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ ( tc_Option_Ooption @ C ) ) @ B ) @ E ) @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ A ) ) ) @ D )
= ( hAPP @ ( c_Set_Oimage @ F @ ( tc_Option_Ooption @ C ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__map__upd) ).
thf(4308,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 @ ( tc_Option_Ooption @ C ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ ( tc_Option_Ooption @ C ) ) @ B ) @ E ) @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ A ) ) ) @ D )
= ( hAPP @ ( c_Set_Oimage @ F @ ( tc_Option_Ooption @ C ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(781,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(4572,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)],[781]) ).
thf(430,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(3147,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)],[430]) ).
thf(504,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(3454,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)],[504]) ).
thf(670,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(4148,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)],[670]) ).
thf(301,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(2634,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)],[301]) ).
thf(331,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) @ B ) )
<=> ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__cancel1) ).
thf(2749,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) @ B ) )
=> ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
& ( ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(616,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(3903,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)],[616]) ).
thf(132,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Map_Omap__comp @ E @ D @ C @ ( hAPP @ ( c_COMBK @ ( tc_Option_Ooption @ D ) @ E ) @ ( c_Option_Ooption_ONone @ D ) ) @ B @ A )
= ( c_Option_Ooption_ONone @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__comp__empty_I2_J) ).
thf(1857,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Map_Omap__comp @ E @ D @ C @ ( hAPP @ ( c_COMBK @ ( tc_Option_Ooption @ D ) @ E ) @ ( c_Option_Ooption_ONone @ D ) ) @ B @ A )
= ( c_Option_Ooption_ONone @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(800,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(4644,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)],[800]) ).
thf(447,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(3225,plain,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_Oacyclic @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(779,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__le__mono2) ).
thf(4567,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(221,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(2208,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)],[221]) ).
thf(653,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ B ) @ A ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ A ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( D != B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ D ) @ C )
!= B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_aset_I4_J) ).
thf(4081,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ B ) @ A ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ A ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( D != B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ D ) @ C )
!= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(687,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(4212,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)],[687]) ).
thf(861,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ E @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ D ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ E @ C ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ E @ C ) ) @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OWhileTrue) ).
thf(4889,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ E @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ D ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ E @ C ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ E @ C ) ) @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(1252,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_Map_Odom @ E @ C @ B ) ) )
=> ( ( hAPP @ ( c_Map_Omap__add @ E @ C @ B @ A ) @ D )
= ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__dom__app__simps_I2_J) ).
thf(6486,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_Map_Odom @ E @ C @ B ) ) )
=> ( ( hAPP @ ( c_Map_Omap__add @ E @ C @ B @ A ) @ D )
= ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1252]) ).
thf(878,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(4966,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)],[878]) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__simps_I3_J) ).
thf(1563,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(987,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 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( 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(5415,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 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( 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)],[987]) ).
thf(380,axiom,
! [A: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__1) ).
thf(2963,plain,
! [A: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(5,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(1286,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)],[5]) ).
thf(940,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oorder__trans) ).
thf(5209,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(195,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(2089,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)],[195]) ).
thf(304,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ A ) )
=> ( ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ C ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ) )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ D @ C )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__rel__mod__eq) ).
thf(2645,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ A ) )
=> ( ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ C ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ) )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ D @ C )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(496,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(3422,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)],[496]) ).
thf(939,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Com_Ocom_OWhile @ D @ C )
= ( c_Com_Ocom_OWhile @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I5_J) ).
thf(5198,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( c_Com_Ocom_OWhile @ D @ C )
= ( c_Com_Ocom_OWhile @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( c_Com_Ocom_OWhile @ D @ C )
= ( c_Com_Ocom_OWhile @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(367,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(2909,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)],[367]) ).
thf(585,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(3807,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)],[585]) ).
thf(868,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(4919,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)],[868]) ).
thf(1015,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(5524,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)],[1015]) ).
thf(758,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(4470,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(321,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(2717,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)],[321]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__div__less__self) ).
thf(1548,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(554,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(3686,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)],[554]) ).
thf(1254,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(6492,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)],[1254]) ).
thf(29,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(1374,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)],[29]) ).
thf(754,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(4453,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)],[754]) ).
thf(946,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Sum__Type_OInr @ D @ C ) @ B )
!= ( hAPP @ ( c_Sum__Type_OInl @ C @ D ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Osimps_I4_J) ).
thf(5241,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Sum__Type_OInr @ D @ C ) @ B )
!= ( hAPP @ ( c_Sum__Type_OInl @ C @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(1273,plain,
v_ca = v_c,
inference(cnf,[status(esa)],[1272]) ).
thf(1278,plain,
v_c = v_ca,
inference(lifteq,[status(thm)],[1273]) ).
thf(146,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(1906,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)],[146]) ).
thf(1058,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ F @ E @ D @ C ) @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) )
=> ( ( ( hAPP @ C @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) )
| ( ( ( hAPP @ C @ B )
= ( c_Option_Ooption_ONone @ E ) )
& ( ( hAPP @ D @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__SomeD) ).
thf(5679,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ F @ E @ D @ C ) @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) )
=> ( ( ( hAPP @ C @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) )
| ( ( ( hAPP @ C @ B )
= ( c_Option_Ooption_ONone @ E ) )
& ( ( hAPP @ D @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(324,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self1__is__m) ).
thf(2729,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(559,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(3707,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)],[559]) ).
thf(104,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zmult2__eq) ).
thf(1727,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(1092,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Sum__Type_OInr @ D @ C ) @ B )
!= ( hAPP @ ( c_Sum__Type_OInl @ C @ D ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inr__not__Inl) ).
thf(5808,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Sum__Type_OInr @ D @ C ) @ B )
!= ( hAPP @ ( c_Sum__Type_OInl @ C @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(284,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(2556,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)],[284]) ).
thf(178,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(2033,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)],[178]) ).
thf(1078,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(5762,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)],[1078]) ).
thf(792,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(4613,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(234,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( c_List_Ofoldl @ tc_Nat_Onat @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_List_Oset @ tc_Nat_Onat ) @ A ) ) )
=> ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__eq__0__conv) ).
thf(2253,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( c_List_Ofoldl @ tc_Nat_Onat @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_List_Oset @ tc_Nat_Onat ) @ A ) ) )
=> ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_List_Oset @ tc_Nat_Onat ) @ A ) ) )
=> ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
=> ( ( hAPP @ ( c_List_Ofoldl @ tc_Nat_Onat @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(1102,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(5855,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)],[1102]) ).
thf(1155,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(6084,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)],[1155]) ).
thf(751,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( c_Map_Omap__comp @ G @ F @ E @ D @ C @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ A ) )
<=> ? [H: $i] :
( ( ( hAPP @ C @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ G ) @ H ) )
& ( ( hAPP @ D @ H )
= ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__comp__Some__iff) ).
thf(4438,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( ( c_Map_Omap__comp @ G @ F @ E @ D @ C @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ A ) )
=> ? [H: $i] :
( ( ( hAPP @ C @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ G ) @ H ) )
& ( ( hAPP @ D @ H )
= ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ A ) ) ) )
& ( ? [H: $i] :
( ( ( hAPP @ C @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ G ) @ H ) )
& ( ( hAPP @ D @ H )
= ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ A ) ) )
=> ( ( c_Map_Omap__comp @ G @ F @ E @ D @ C @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(107,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self__is__m) ).
thf(1747,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(737,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__rel) ).
thf(4393,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(465,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ C ) )
=> ! [E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ G ) @ B ) )
=> ( E
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ G ) @ F ) ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ E ) @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ E ) @ C ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bset_I10_J) ).
thf(3289,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ C ) )
=> ! [E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ G ) @ B ) )
=> ( E
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ G ) @ F ) ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ E ) @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ E ) @ C ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(10,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(1301,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)],[10]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ C @ B ) ) @ A ) @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ C ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__zmod__left) ).
thf(1595,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ C @ B ) ) @ A ) @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ C ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(1108,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(5882,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)],[1108]) ).
thf(1191,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ E @ D @ C ) @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_peek__and__def) ).
thf(6228,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ E @ D @ C ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ C @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ C @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ E @ D @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191]) ).
thf(1133,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(5979,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ B ) @ A ) )
| ( hBOOL @ B )
| ( hBOOL @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).
thf(420,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(3111,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)],[420]) ).
thf(462,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(3274,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)],[462]) ).
thf(480,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(3343,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)],[480]) ).
thf(432,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(3158,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)],[432]) ).
thf(890,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(4998,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)],[890]) ).
thf(323,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Int_Oint ) @ ( c_SetInterval_Oord__class_OgreaterThanLessThan @ tc_Int_Oint @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__greaterThanLessThan__int) ).
thf(2727,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Int_Oint ) @ ( c_SetInterval_Oord__class_OgreaterThanLessThan @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(622,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(3925,plain,
! [A: $i,B: $i] :
( ( c_HOL_OThe @ B @ ( hAPP @ c_fequal @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(909,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(5065,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)],[909]) ).
thf(837,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(4801,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)],[837]) ).
thf(1098,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(5831,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)],[1098]) ).
thf(506,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(3458,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)],[506]) ).
thf(881,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(4975,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)],[881]) ).
thf(531,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(3599,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)],[531]) ).
thf(1067,axiom,
! [A: $i,B: $i] :
( ( B = A )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oeq__iff) ).
thf(5720,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).
thf(1192,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(6234,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)],[1192]) ).
thf(520,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(3547,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)],[520]) ).
thf(126,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(1833,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)],[126]) ).
thf(225,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Map_Orestrict__map @ D @ C @ ( hAPP @ ( c_COMBK @ ( tc_Option_Ooption @ C ) @ D ) @ ( c_Option_Ooption_ONone @ C ) ) @ B ) @ A )
= ( c_Option_Ooption_ONone @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrict__map__empty) ).
thf(2225,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Map_Orestrict__map @ D @ C @ ( hAPP @ ( c_COMBK @ ( tc_Option_Ooption @ C ) @ D ) @ ( c_Option_Ooption_ONone @ C ) ) @ B ) @ A )
= ( c_Option_Ooption_ONone @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(139,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zero) ).
thf(1884,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(74,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(1615,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)],[74]) ).
thf(34,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(1389,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)],[34]) ).
thf(569,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(3736,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)],[569]) ).
thf(1122,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(5940,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)],[1122]) ).
thf(463,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Map_Omap__of @ C @ B @ ( c_List_Olist_ONil @ ( tc_prod @ C @ B ) ) ) @ A )
= ( c_Option_Ooption_ONone @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of_Osimps_I1_J) ).
thf(3283,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Map_Omap__of @ C @ B @ ( c_List_Olist_ONil @ ( tc_prod @ C @ B ) ) ) @ A )
= ( c_Option_Ooption_ONone @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(274,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ D ) ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__period) ).
thf(2514,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ E ) @ D ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ D ) ) ) @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ D ) ) ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(1041,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__diff__nat) ).
thf(5612,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(816,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(4709,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)],[816]) ).
thf(96,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(1701,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)],[96]) ).
thf(734,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(4381,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)],[734]) ).
thf(971,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(5350,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)],[971]) ).
thf(1088,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(5799,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)],[1088]) ).
thf(875,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(4946,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)],[875]) ).
thf(762,axiom,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatMost @ tc_Nat_Onat ) @ A )
= ( hAPP @ ( c_List_Oset @ tc_Nat_Onat ) @ ( c_List_Oupt @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atMost__upto) ).
thf(4485,plain,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatMost @ tc_Nat_Onat ) @ A )
= ( hAPP @ ( c_List_Oset @ tc_Nat_Onat ) @ ( c_List_Oupt @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(882,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(4978,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)],[882]) ).
thf(663,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__diffD) ).
thf(4127,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(744,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(4413,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)],[744]) ).
thf(479,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(3340,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)],[479]) ).
thf(500,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ B @ D ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ D ) @ C ) ) ) ) )
=> ( ( hBOOL @ ( hAPP @ B @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__induct__0) ).
thf(3436,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ B @ D ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ D ) @ C ) ) ) ) )
=> ( ( hBOOL @ ( hAPP @ B @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(317,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ D @ ( tc_Option_Ooption @ C ) ) @ ( hAPP @ ( c_COMBK @ ( tc_Option_Ooption @ C ) @ D ) @ ( c_Option_Ooption_ONone @ C ) ) ) @ B ) @ ( c_Option_Ooption_ONone @ C ) ) @ A )
= ( c_Option_Ooption_ONone @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__upd__none) ).
thf(2706,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ D @ ( tc_Option_Ooption @ C ) ) @ ( hAPP @ ( c_COMBK @ ( tc_Option_Ooption @ C ) @ D ) @ ( c_Option_Ooption_ONone @ C ) ) ) @ B ) @ ( c_Option_Ooption_ONone @ C ) ) @ A )
= ( c_Option_Ooption_ONone @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(111,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(1765,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)],[111]) ).
thf(1161,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ B ) @ ( c_SetInterval_Oord_OatLeast @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeast__iff) ).
thf(6123,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ B ) @ ( c_SetInterval_Oord_OatLeast @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ B ) @ ( c_SetInterval_Oord_OatLeast @ tc_Nat_Onat @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).
thf(1136,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(5997,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)],[1136]) ).
thf(264,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(2474,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)],[264]) ).
thf(1222,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(6372,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)],[1222]) ).
thf(436,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(3170,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)],[436]) ).
thf(1147,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(6048,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)],[1147]) ).
thf(771,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(4537,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)],[771]) ).
thf(48,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(1503,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)],[48]) ).
thf(935,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_List_Osublist @ C @ B @ ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__upt__eq__take) ).
thf(5185,plain,
! [A: $i,B: $i,C: $i] :
( ( c_List_Osublist @ C @ B @ ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(117,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
<=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) ) )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__eq__0__iff) ).
thf(1786,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) ) )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ B ) ) ) ) )
& ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) ) )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ B ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(903,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(5039,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)],[903]) ).
thf(1229,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(6403,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)],[1229]) ).
thf(242,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) @ B ) )
<=> ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__cancel2) ).
thf(2293,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) @ B ) )
=> ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
& ( ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(246,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(2308,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)],[246]) ).
thf(28,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(1371,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)],[28]) ).
thf(14,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(1312,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)],[14]) ).
thf(660,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(4112,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)],[660]) ).
thf(557,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(3695,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)],[557]) ).
thf(327,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(2738,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)],[327]) ).
thf(966,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__imp__not__eq2) ).
thf(5331,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(695,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(4236,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)],[695]) ).
thf(375,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(2935,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)],[375]) ).
thf(844,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(4822,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)],[844]) ).
thf(106,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(1733,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)],[106]) ).
thf(927,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(5148,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)],[927]) ).
thf(424,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ E @ D ) @ C ) @ B ) @ A ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__same) ).
thf(3123,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ E @ D ) @ C ) @ B ) @ A ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(1070,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(5735,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)],[1070]) ).
thf(259,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(2425,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)],[259]) ).
thf(1195,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(6248,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)],[1195]) ).
thf(929,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__greaterThanAtMost) ).
thf(5158,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(250,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(2319,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)],[250]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2__neg) ).
thf(1356,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(89,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Int_Oint ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__atLeastAtMost__int) ).
thf(1675,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Int_Oint ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(1023,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ C ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__trans) ).
thf(5556,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ C ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(1031,axiom,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
thf(5580,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).
thf(819,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ E @ D ) @ C @ B @ A )
=> ( ( ( A = C )
=> ( hBOOL @ ( hAPP @ E @ C ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ E @ C ) )
=> ! [F: $i] :
( ( c_Natural_Oevaln @ D @ C @ B @ F )
=> ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ E @ D ) @ F @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__WHILE__case) ).
thf(4716,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ E @ D ) @ C @ B @ A )
=> ( ( ( A = C )
=> ( hBOOL @ ( hAPP @ E @ C ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ E @ C ) )
=> ! [F: $i] :
( ( c_Natural_Oevaln @ D @ C @ B @ F )
=> ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ E @ D ) @ F @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(247,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_Option_Ooption @ B ) ) @ ( hAPP @ ( c_Option_Ooption_OSome @ B ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Osize_I4_J) ).
thf(2311,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_Option_Ooption @ B ) ) @ ( hAPP @ ( c_Option_Ooption_OSome @ B ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(417,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(3101,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)],[417]) ).
thf(481,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(3352,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)],[481]) ).
thf(722,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ C ) )
=> ! [E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ G ) @ B ) )
=> ( E
!= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ G ) @ F ) ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ E ) @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ E ) @ C ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_aset_I10_J) ).
thf(4337,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ C ) )
=> ! [E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ G ) @ B ) )
=> ( E
!= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ G ) @ F ) ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ E ) @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ E ) @ C ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(6570,plain,
! [A: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ v_na @ A )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ A ) @ v_G ) )
!= ( hBOOL @ ( hAPP @ v_ba @ v_s0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[6180,1274]) ).
thf(6572,plain,
! [A: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ v_na @ A )
| ( ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ A ) @ v_G )
!= ( hAPP @ v_ba @ v_s0 ) ) ),
inference(simp,[status(thm)],[6570]) ).
thf(693,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ B ) @ A ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ A ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ D ) @ C ) ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_aset_I5_J) ).
thf(4228,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ B ) @ A ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ A ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ D ) @ C ) ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ B ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__append) ).
thf(1280,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ B ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1281,plain,
! [D: $i,C: $i,B: $i,A: $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(cnf,[status(esa)],[1280]) ).
thf(1282,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( 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 ) )
= ( hAPP @ ( hAPP @ ( c_List_Odrop @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ B ) @ A ) ) ),
inference(lifteq,[status(thm)],[1281]) ).
thf(452,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(3238,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)],[452]) ).
thf(794,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(4620,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)],[794]) ).
thf(1189,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(6217,plain,
! [A: $i,B: $i] :
( ( B != A )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189]) ).
thf(813,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ E @ D )
= ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ ( c_Map_Odom @ A @ C @ E ) )
= ( c_Map_Odom @ A @ C @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__dom) ).
thf(4699,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ E @ D )
= ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ ( c_Map_Odom @ A @ C @ E ) )
= ( c_Map_Odom @ A @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(509,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(3468,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)],[509]) ).
thf(1217,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ D ) @ C ) @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com__det) ).
thf(6340,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ D ) @ C ) @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1217]) ).
thf(943,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(5222,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)],[943]) ).
thf(784,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(4586,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)],[784]) ).
thf(560,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(3710,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)],[560]) ).
thf(710,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(4300,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)],[710]) ).
thf(360,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(2871,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)],[360]) ).
thf(268,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(2493,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)],[268]) ).
thf(386,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(2987,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)],[386]) ).
thf(404,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(3038,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)],[404]) ).
thf(522,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(3551,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)],[522]) ).
thf(258,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(2422,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)],[258]) ).
thf(712,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( 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(4305,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ D @ C ) @ B ) @ E ) @ A ) @ F )
= ( hAPP @ B @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(366,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(2906,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)],[366]) ).
thf(1183,axiom,
! [A: $i] :
( ~ ~ ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ c_fNot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__2) ).
thf(6197,plain,
! [A: $i] :
( ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ c_fNot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183]) ).
thf(67,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__neg__neg__trivial) ).
thf(1589,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(154,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Map_Omap__add @ C @ B @ ( hAPP @ ( c_COMBK @ ( tc_Option_Ooption @ B ) @ C ) @ ( c_Option_Ooption_ONone @ B ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__map__add) ).
thf(1933,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Map_Omap__add @ C @ B @ ( hAPP @ ( c_COMBK @ ( tc_Option_Ooption @ B ) @ C ) @ ( c_Option_Ooption_ONone @ B ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(1211,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ E @ D )
= ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Map_Oran @ A @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ranI) ).
thf(6321,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ E @ D )
= ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Map_Oran @ A @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1211]) ).
thf(243,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Map_Omap__add @ C @ B @ A @ ( hAPP @ ( c_COMBK @ ( tc_Option_Ooption @ B ) @ C ) @ ( c_Option_Ooption_ONone @ B ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__empty) ).
thf(2299,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Map_Omap__add @ C @ B @ A @ ( hAPP @ ( c_COMBK @ ( tc_Option_Ooption @ B ) @ C ) @ ( c_Option_Ooption_ONone @ B ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(1205,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(6289,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)],[1205]) ).
thf(343,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(2802,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)],[343]) ).
thf(1168,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple__rec @ F @ E @ D @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ F ) @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ D @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_triple_Orecs) ).
thf(6154,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple__rec @ F @ E @ D @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ F ) @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ D @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).
thf(1086,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(5795,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)],[1086]) ).
thf(529,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(3586,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)],[529]) ).
thf(1130,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(5972,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)],[1130]) ).
thf(831,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(4773,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)],[831]) ).
thf(1246,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(6460,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)],[1246]) ).
thf(658,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(4107,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)],[658]) ).
thf(166,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ C @ A ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zadd1__eq) ).
thf(1969,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ C @ A ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(951,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(5267,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)],[951]) ).
thf(12,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(1307,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)],[12]) ).
thf(902,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oord__le__eq__trans) ).
thf(5035,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(176,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(2025,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)],[176]) ).
thf(400,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(3027,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)],[400]) ).
thf(780,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__atLeastAtMost) ).
thf(4569,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(867,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ D @ C ) @ B @ A @ B )
<=> ( ( hBOOL @ ( hAPP @ D @ B ) )
=> ? [E: $i] :
( ( c_Natural_Oevaln @ C @ B @ A @ E )
& ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ D @ C ) @ E @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I7_J) ).
thf(4911,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ D @ C ) @ B @ A @ B )
=> ( ( hBOOL @ ( hAPP @ D @ B ) )
=> ? [E: $i] :
( ( c_Natural_Oevaln @ C @ B @ A @ E )
& ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ D @ C ) @ E @ A @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ D @ B ) )
=> ? [E: $i] :
( ( c_Natural_Oevaln @ C @ B @ A @ E )
& ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ D @ C ) @ E @ A @ B ) ) )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ D @ C ) @ B @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult1__eq) ).
thf(1630,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(967,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(5335,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)],[967]) ).
thf(705,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(4277,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)],[705]) ).
thf(1002,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(5466,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)],[1002]) ).
thf(889,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(4993,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)],[889]) ).
thf(6566,plain,
! [A: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ v_na @ A )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ A ) @ v_G ) )
!= ( hBOOL @ c_fTrue ) ) ),
inference(paramod_ordered,[status(thm)],[6181,1274]) ).
thf(6568,plain,
! [A: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ v_na @ A )
| ( ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ A ) @ v_G )
!= c_fTrue ) ),
inference(simp,[status(thm)],[6566]) ).
thf(985,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(5410,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)],[985]) ).
thf(123,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(1820,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)],[123]) ).
thf(1223,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(6376,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)],[1223]) ).
thf(505,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__imp__le) ).
thf(3456,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(86,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(1667,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)],[86]) ).
thf(1026,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(5563,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)],[1026]) ).
thf(348,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(2824,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)],[348]) ).
thf(216,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(2182,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)],[216]) ).
thf(975,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(5367,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)],[975]) ).
thf(1156,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(6087,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)],[1156]) ).
thf(1095,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(5816,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)],[1095]) ).
thf(1032,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(5584,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)],[1032]) ).
thf(859,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(4882,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)],[859]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ F ) ) @ E ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) )
=> ( ( c_Map_Omap__upds @ F @ D @ B @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ F ) @ E ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ A ) @ ( c_List_Olist_ONil @ F ) ) ) @ C )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ ( tc_Option_Ooption @ D ) ) @ ( c_Map_Omap__upds @ F @ D @ B @ E @ C ) ) @ A ) @ ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ C ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ F ) ) @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__upds__append1) ).
thf(1557,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ F ) ) @ E ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C ) ) )
=> ( ( c_Map_Omap__upds @ F @ D @ B @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ F ) @ E ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ A ) @ ( c_List_Olist_ONil @ F ) ) ) @ C )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ ( tc_Option_Ooption @ D ) ) @ ( c_Map_Omap__upds @ F @ D @ B @ E @ C ) ) @ A ) @ ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ ( hAPP @ ( hAPP @ ( c_List_Onth @ D ) @ C ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ F ) ) @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(248,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ C ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2) ).
thf(2314,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(550,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Map_Orestrict__map @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ E @ ( tc_Option_Ooption @ D ) ) @ ( c_Map_Orestrict__map @ E @ D @ C @ A ) ) @ B ) @ ( hAPP @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrict__map__insert) ).
thf(3668,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Map_Orestrict__map @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ E @ ( tc_Option_Ooption @ D ) ) @ ( c_Map_Orestrict__map @ E @ D @ C @ A ) ) @ B ) @ ( hAPP @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(847,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(4833,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(995,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(5439,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)],[995]) ).
thf(702,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).
thf(4264,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(147,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(1909,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)],[147]) ).
thf(1037,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(5599,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)],[1037]) ).
thf(402,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__le__mono) ).
thf(3034,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_List_OtakeWhile @ C @ B @ A )
= ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( c_List_OtakeWhile @ C @ B @ A ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile__eq__take) ).
thf(1325,plain,
! [A: $i,B: $i,C: $i] :
( ( c_List_OtakeWhile @ C @ B @ A )
= ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( c_List_OtakeWhile @ C @ B @ A ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(340,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(2785,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)],[340]) ).
thf(291,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(2593,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)],[291]) ).
thf(503,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(3451,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)],[503]) ).
thf(1109,axiom,
c_Natural_Oevaln @ v_ca @ v_s0 @ v_na @ v_s1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
thf(5885,plain,
c_Natural_Oevaln @ v_ca @ v_s0 @ v_na @ v_s1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).
thf(528,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ ( c_Product__Type_Ofst @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Divides_Odivmod__nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__nat__def) ).
thf(3583,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ ( c_Product__Type_Ofst @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Divides_Odivmod__nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__pos__neg__trivial) ).
thf(1344,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(820,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(4726,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)],[820]) ).
thf(307,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__div__cancel) ).
thf(2664,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(601,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(3861,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)],[601]) ).
thf(353,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(2842,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)],[353]) ).
thf(1099,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ G ) @ F ) @ E ) @ D )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ G ) @ C ) @ B ) @ A ) )
<=> ( ( F = C )
& ( E = B )
& ( D = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_triple_Oinject) ).
thf(5838,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ G ) @ F ) @ E ) @ D )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ G ) @ C ) @ B ) @ A ) )
=> ( ( F = C )
& ( E = B )
& ( D = A ) ) )
& ( ( ( F = C )
& ( E = B )
& ( D = A ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ G ) @ F ) @ E ) @ D )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ G ) @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).
thf(192,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(2075,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)],[192]) ).
thf(37,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(1396,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)],[37]) ).
thf(948,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(5254,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)],[948]) ).
thf(95,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(1699,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)],[95]) ).
thf(213,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(2171,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)],[213]) ).
thf(594,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ A ) ) )
=> ( ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_expand__Suc) ).
thf(3838,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ A ) ) )
=> ( ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ A )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(1167,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(6151,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)],[1167]) ).
thf(552,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(3674,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)],[552]) ).
thf(1257,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hAPP @ ( c_Fun_Ooverride__on @ F @ C @ B @ A @ D ) @ E )
= ( hAPP @ A @ E ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hAPP @ ( c_Fun_Ooverride__on @ F @ C @ B @ A @ D ) @ E )
= ( hAPP @ B @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_override__on__def) ).
thf(6504,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hAPP @ ( c_Fun_Ooverride__on @ F @ C @ B @ A @ D ) @ E )
= ( hAPP @ A @ E ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hAPP @ ( c_Fun_Ooverride__on @ F @ C @ B @ A @ D ) @ E )
= ( hAPP @ B @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1257]) ).
thf(964,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatMost @ tc_Nat_Onat ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__atMost) ).
thf(5326,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatMost @ tc_Nat_Onat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(93,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(1694,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)],[93]) ).
thf(184,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 ) )
=> ( ( c_Map_Omap__upds @ F @ D @ B @ E @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ A ) )
= ( c_Map_Omap__upds @ F @ D @ B @ E @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upds__append2__drop) ).
thf(2051,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 ) )
=> ( ( c_Map_Omap__upds @ F @ D @ B @ E @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ D ) @ C ) @ A ) )
= ( c_Map_Omap__upds @ F @ D @ B @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(918,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(5094,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)],[918]) ).
thf(1201,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(6270,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)],[1201]) ).
thf(619,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ ( c_SetInterval_Oord__class_OgreaterThanLessThan @ tc_Nat_Onat @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__greaterThanLessThan) ).
thf(3917,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ ( c_SetInterval_Oord__class_OgreaterThanLessThan @ tc_Nat_Onat @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(846,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(4827,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)],[846]) ).
thf(374,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ? [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_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__add__positive) ).
thf(2931,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ? [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_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(241,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(2288,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)],[241]) ).
thf(453,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(3241,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)],[453]) ).
thf(342,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(2797,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)],[342]) ).
thf(175,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(2022,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)],[175]) ).
thf(1100,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( c_Map_Omap__of @ E @ D @ C ) @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ E @ D ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__is__SomeD) ).
thf(5849,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( c_Map_Omap__of @ E @ D @ C ) @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ E @ D ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).
thf(40,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(1477,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)],[40]) ).
thf(474,axiom,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__Suc__eq__Suc__mod) ).
thf(3325,plain,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(1158,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_Map_Orestrict__map @ E @ B @ A @ C ) @ D )
= ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrict__in) ).
thf(6100,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_Map_Orestrict__map @ E @ B @ A @ C ) @ D )
= ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).
thf(1057,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ F @ E @ D @ C ) @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) )
<=> ( ( ( hAPP @ C @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) )
| ( ( ( hAPP @ C @ B )
= ( c_Option_Ooption_ONone @ E ) )
& ( ( hAPP @ D @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__Some__iff) ).
thf(5667,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( hAPP @ ( c_Map_Omap__add @ F @ E @ D @ C ) @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) )
=> ( ( ( hAPP @ C @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) )
| ( ( ( hAPP @ C @ B )
= ( c_Option_Ooption_ONone @ E ) )
& ( ( hAPP @ D @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) ) ) ) )
& ( ( ( ( hAPP @ C @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) )
| ( ( ( hAPP @ C @ B )
= ( c_Option_Ooption_ONone @ E ) )
& ( ( hAPP @ D @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) ) ) )
=> ( ( hAPP @ ( c_Map_Omap__add @ F @ E @ D @ C ) @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
<=> ? [C: $i] :
( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__eq__0__iff) ).
thf(1496,plain,
! [A: $i,B: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ? [C: $i] :
( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) ) )
& ( ? [C: $i] :
( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(983,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_List_Oset @ ( tc_prod @ E @ D ) ) @ A ) ) )
=> ? [F: $i] :
( ( hAPP @ ( c_Map_Omap__of @ E @ D @ A ) @ C )
= ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_weak__map__of__SomeI) ).
thf(5403,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_List_Oset @ ( tc_prod @ E @ D ) ) @ A ) ) )
=> ? [F: $i] :
( ( hAPP @ ( c_Map_Omap__of @ E @ D @ A ) @ C )
= ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(686,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(4209,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)],[686]) ).
thf(6683,plain,
! [A: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
!= ( hAPP @ c_Nat_OSuc @ A ) ),
inference(paramod_ordered,[status(thm)],[2398,3107]) ).
thf(6713,plain,
! [A: $i] :
( ( ( c_Nat_Osize__class_Osize @ tc_Nat_Onat )
!= c_Nat_OSuc )
| ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= A ) ),
inference(simp,[status(thm)],[6683]) ).
thf(6736,plain,
( ( c_Nat_Osize__class_Osize @ tc_Nat_Onat )
!= c_Nat_OSuc ),
inference(simp,[status(thm)],[6713]) ).
thf(673,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(4158,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)],[673]) ).
thf(118,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__number__of__int__code) ).
thf(1805,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(190,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(2069,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)],[190]) ).
thf(1249,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple__case @ F @ E @ D @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ F ) @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ D @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_triple_Osimps_I2_J) ).
thf(6476,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple__case @ F @ E @ D @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ F ) @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ D @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1249]) ).
thf(823,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(4741,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)],[823]) ).
thf(990,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Sum__Type_OInl @ D @ C ) @ B )
!= ( hAPP @ ( c_Sum__Type_OInr @ C @ D ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Osimps_I3_J) ).
thf(5424,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Sum__Type_OInl @ D @ C ) @ B )
!= ( hAPP @ ( c_Sum__Type_OInr @ C @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(11,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(1304,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)],[11]) ).
thf(389,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(2994,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)],[389]) ).
thf(433,axiom,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ tc_Nat_Onat @ c_Nat_OSuc ) @ ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessThan__Suc__eq__insert__0) ).
thf(3161,plain,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Set_Oimage @ tc_Nat_Onat @ tc_Nat_Onat @ c_Nat_OSuc ) @ ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(634,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__less__divisor) ).
thf(3981,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) )
<=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ C @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ E ) @ A ) )
=> ( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ D ) ) @ E ) )
=> ( hBOOL @ ( hAPP @ C @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__mod) ).
thf(1509,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ C @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ E ) @ A ) )
=> ( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ D ) ) @ E ) )
=> ( hBOOL @ ( hAPP @ C @ E ) ) ) ) ) ) )
& ( ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ C @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ E ) @ A ) )
=> ( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ D ) ) @ E ) )
=> ( hBOOL @ ( hAPP @ C @ E ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(311,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(2684,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)],[311]) ).
thf(1173,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(6170,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)],[1173]) ).
thf(972,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_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(5358,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)],[972]) ).
thf(1185,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(6202,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)],[1185]) ).
thf(1093,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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ E ) @ D ) @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__fun__updI) ).
thf(5812,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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ E ) @ D ) @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).
thf(1055,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(5661,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)],[1055]) ).
thf(1001,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(5463,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)],[1001]) ).
thf(720,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(4331,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)],[720]) ).
thf(185,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(2054,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)],[185]) ).
thf(749,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__implies__Suc) ).
thf(4426,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ? [B: $i] :
( A
= ( hAPP @ c_Nat_OSuc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(685,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(4207,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)],[685]) ).
thf(159,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(1948,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)],[159]) ).
thf(1017,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(5538,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)],[1017]) ).
thf(368,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(2914,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)],[368]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__mono) ).
thf(1662,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(666,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__trans) ).
thf(4136,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(3932,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 ) ) )
& ! [A: $i] :
( ( 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(miniscope,[status(thm)],[3931]) ).
thf(3933,plain,
! [A: $i] :
( ~ ( 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(cnf,[status(esa)],[3932]) ).
thf(3935,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(lifteq,[status(thm)],[3933]) ).
thf(3936,plain,
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(simp,[status(thm)],[3935]) ).
thf(1265,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(6540,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)],[1265]) ).
thf(1110,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(5886,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ B ) @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).
thf(305,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(2652,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)],[305]) ).
thf(263,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(2471,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)],[263]) ).
thf(1181,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(6191,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ B ) @ A ) )
| ( hBOOL @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1181]) ).
thf(1125,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(5952,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)],[1125]) ).
thf(678,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(4177,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)],[678]) ).
thf(300,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__number__of__int__code) ).
thf(2629,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(811,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(4688,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)],[811]) ).
thf(355,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(2846,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)],[355]) ).
thf(727,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(4355,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)],[727]) ).
thf(1091,axiom,
! [A: $i] : ( c_Equiv__Relations_Oequivp @ A @ c_fequal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_identity__equivp) ).
thf(5806,plain,
! [A: $i] : ( c_Equiv__Relations_Oequivp @ A @ c_fequal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).
thf(5807,plain,
! [A: $i] : ( c_Equiv__Relations_Oequivp @ A @ c_fequal ),
inference(cnf,[status(esa)],[5806]) ).
thf(840,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(4812,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)],[840]) ).
thf(892,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Ole__neq__trans) ).
thf(5003,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(886,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(4986,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)],[886]) ).
thf(1163,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 ) )
=> ( c_Predicate_Opred__comp @ C @ B @ A @ H @ E @ G @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__comp_Ointros) ).
thf(6132,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 ) )
=> ( c_Predicate_Opred__comp @ C @ B @ A @ H @ E @ G @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).
thf(1029,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(5570,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)],[1029]) ).
thf(1039,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(5607,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)],[1039]) ).
thf(856,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(4864,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)],[856]) ).
thf(731,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(4366,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)],[731]) ).
thf(61,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(1566,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)],[61]) ).
thf(426,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ B ) @ A ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ A ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ D ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bset_I7_J) ).
thf(3129,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ B ) @ A ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ A ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ D ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(109,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(1753,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)],[109]) ).
thf(605,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(3872,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)],[605]) ).
thf(797,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(4630,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)],[797]) ).
thf(1166,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(6146,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)],[1166]) ).
thf(485,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ A ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ D ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ A ) )
=> ( B
!= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ E ) @ D ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ C )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_aset_I3_J) ).
thf(3376,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ A ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ D ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ A ) )
=> ( B
!= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ E ) @ D ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ C )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(1096,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Option_Ooption_OSome @ B ) @ A )
!= ( c_Option_Ooption_ONone @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Osimps_I3_J) ).
thf(5822,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Option_Ooption_OSome @ B ) @ A )
!= ( c_Option_Ooption_ONone @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).
thf(543,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= ( c_List_Olist_ONil @ C ) ) )
& ( ( ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__Cons__number__of) ).
thf(3640,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= ( c_List_Olist_ONil @ C ) ) )
& ( ( ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_List_Otake @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(70,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__nonpos__pos__le0) ).
thf(1598,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(959,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(5294,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)],[959]) ).
thf(729,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(4360,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)],[729]) ).
thf(217,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(2192,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)],[217]) ).
thf(807,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(4673,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)],[807]) ).
thf(290,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(2588,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)],[290]) ).
thf(573,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(3754,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)],[573]) ).
thf(932,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(5171,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)],[932]) ).
thf(1123,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(5944,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)],[1123]) ).
thf(548,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(3659,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)],[548]) ).
thf(325,axiom,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zdiv__equality_H) ).
thf(2732,plain,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(1008,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(5484,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)],[1008]) ).
thf(507,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(3462,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)],[507]) ).
thf(684,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(4200,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)],[684]) ).
thf(767,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ B )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__geq) ).
thf(4517,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ B )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(799,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(4641,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)],[799]) ).
thf(215,axiom,
! [A: $i,B: $i] :
( ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ? [C: $i] :
( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__eq__0__iff) ).
thf(2175,plain,
! [A: $i,B: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ? [C: $i] :
( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ C ) ) )
& ( ? [C: $i] :
( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ C ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(116,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(1780,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)],[116]) ).
thf(347,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(2821,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)],[347]) ).
thf(443,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(3209,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)],[443]) ).
thf(534,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(3608,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)],[534]) ).
thf(43,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(1484,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)],[43]) ).
thf(897,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(5018,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)],[897]) ).
thf(1225,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(6384,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)],[1225]) ).
thf(99,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__zmod__imp__zdvd) ).
thf(1711,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(286,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ D ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__lemma) ).
thf(2569,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ D ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(1080,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__imp__le) ).
thf(5767,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).
thf(196,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(2092,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)],[196]) ).
thf(988,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oord__eq__le__trans) ).
thf(5418,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(410,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(3063,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)],[410]) ).
thf(1118,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(5912,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)],[1118]) ).
thf(441,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(3202,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)],[441]) ).
thf(590,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(3823,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)],[590]) ).
thf(900,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(5030,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)],[900]) ).
thf(578,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(3774,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)],[578]) ).
thf(726,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(4351,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)],[726]) ).
thf(834,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(4781,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)],[834]) ).
thf(954,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(5277,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)],[954]) ).
thf(675,axiom,
! [A: $i,B: $i] :
( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ tc_Nat_Onat @ B @ A )
= ( hAPP @ ( c_List_Oset @ tc_Nat_Onat ) @ ( c_List_Oupt @ ( hAPP @ c_Nat_OSuc @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThanAtMost__upt) ).
thf(4164,plain,
! [A: $i,B: $i] :
( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ tc_Nat_Onat @ B @ A )
= ( hAPP @ ( c_List_Oset @ tc_Nat_Onat ) @ ( c_List_Oupt @ ( hAPP @ c_Nat_OSuc @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(1068,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(5731,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)],[1068]) ).
thf(210,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ D ) ) ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult2__lemma__aux1) ).
thf(2165,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ D ) ) ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(588,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ C ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) @ D ) ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__rel__mult1__eq) ).
thf(3818,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ C ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) @ D ) ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(556,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(3691,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(421,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(3114,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)],[421]) ).
thf(477,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(3334,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)],[477]) ).
thf(1145,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(6037,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)],[1145]) ).
thf(315,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__div__cancel1) ).
thf(2700,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(896,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( c_Map_Omap__of @ E @ D @ C ) @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ E @ D ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__SomeD) ).
thf(5015,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( c_Map_Omap__of @ E @ D @ C ) @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ E @ D ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(565,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(3722,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)],[565]) ).
thf(1076,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(5753,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)],[1076]) ).
thf(775,axiom,
! [A: $i] :
( ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
= ( hAPP @ ( c_SetInterval_Oord__class_OatMost @ tc_Nat_Onat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast0AtMost) ).
thf(4549,plain,
! [A: $i] :
( ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
= ( hAPP @ ( c_SetInterval_Oord__class_OatMost @ tc_Nat_Onat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(592,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(3828,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)],[592]) ).
thf(1020,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(5543,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)],[1020]) ).
thf(1209,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_Map_Orestrict__map @ E @ B @ A @ C ) @ D )
= ( c_Option_Ooption_ONone @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrict__out) ).
thf(6313,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_Map_Orestrict__map @ E @ B @ A @ C ) @ D )
= ( c_Option_Ooption_ONone @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1209]) ).
thf(83,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(1658,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)],[83]) ).
thf(251,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) )
<=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ! [D: $i] :
( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ E ) @ A ) )
& ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ! [D: $i] :
( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ E ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__zdiv) ).
thf(2322,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ! [D: $i] :
( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ E ) @ A ) )
& ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ! [D: $i] :
( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ E ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) ) ) )
& ( ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ! [D: $i] :
( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ E ) @ A ) )
& ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ! [D: $i] :
( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ E ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) ) )
=> ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(891,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(5001,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)],[891]) ).
thf(1238,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(6436,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)],[1238]) ).
thf(884,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(4982,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)],[884]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) ) )
& ( ( ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__Cons__number__of) ).
thf(1679,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) ) )
& ( ( ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_List_Odrop @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(1048,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(5638,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)],[1048]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ D ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult2__lemma__aux4) ).
thf(1579,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ D ) ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(1284,plain,
! [D: $i,C: $i,B: $i,A: $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(cnf,[status(esa)],[1283]) ).
thf(1285,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ C )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ D ) ) @ B ) )
| ~ ( 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(lifteq,[status(thm)],[1284]) ).
thf(997,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(5450,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)],[997]) ).
thf(405,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Map_Omap__upds @ G @ F @ E @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ G ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ B ) @ A ) )
= ( c_Map_Omap__upds @ G @ F @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ G @ ( tc_Option_Ooption @ F ) ) @ E ) @ D ) @ ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ B ) ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__upds__Cons) ).
thf(3041,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Map_Omap__upds @ G @ F @ E @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ G ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ F ) @ B ) @ A ) )
= ( c_Map_Omap__upds @ G @ F @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ G @ ( tc_Option_Ooption @ F ) ) @ E ) @ D ) @ ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ B ) ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(415,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(3095,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)],[415]) ).
thf(598,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Map_Omap__of @ D @ C @ B )
= ( c_Map_Omap__of @ D @ C @ A ) )
=> ( ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ D @ C ) @ D @ ( c_Product__Type_Ofst @ D @ C ) ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ D @ C ) ) @ B ) )
= ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ D @ C ) @ D @ ( c_Product__Type_Ofst @ D @ C ) ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ D @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__eq__dom) ).
thf(3853,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Map_Omap__of @ D @ C @ B )
= ( c_Map_Omap__of @ D @ C @ A ) )
=> ( ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ D @ C ) @ D @ ( c_Product__Type_Ofst @ D @ C ) ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ D @ C ) ) @ B ) )
= ( hAPP @ ( c_Set_Oimage @ ( tc_prod @ D @ C ) @ D @ ( c_Product__Type_Ofst @ D @ C ) ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ D @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(271,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(2500,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)],[271]) ).
thf(1216,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(6337,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)],[1216]) ).
thf(876,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(4959,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)],[876]) ).
thf(631,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Map_Omap__upds @ D @ C @ B @ ( c_List_Olist_ONil @ D ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__upds__Nil1) ).
thf(3970,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Map_Omap__upds @ D @ C @ B @ ( c_List_Olist_ONil @ D ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(488,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(3388,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)],[488]) ).
thf(273,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(2511,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)],[273]) ).
thf(422,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(3117,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)],[422]) ).
thf(394,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(3007,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)],[394]) ).
thf(806,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__atLeastAtMost) ).
thf(4671,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(310,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(2675,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)],[310]) ).
thf(186,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) ) @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self4) ).
thf(2056,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) ) @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(26,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(1358,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)],[26]) ).
thf(232,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_Hoare__Mirabelle_Otriple @ D ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ D ) @ C ) @ B ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_triple_Osize_I2_J) ).
thf(2247,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_Hoare__Mirabelle_Otriple @ D ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ D ) @ C ) @ B ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(763,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(4488,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)],[763]) ).
thf(1250,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(6479,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)],[1250]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zdiv__equality) ).
thf(1353,plain,
! [A: $i,B: $i] :
( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(238,axiom,
! [A: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_Option_Ooption @ A ) ) @ ( c_Option_Ooption_ONone @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Osize_I3_J) ).
thf(2279,plain,
! [A: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_Option_Ooption @ A ) ) @ ( c_Option_Ooption_ONone @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(825,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(4748,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)],[825]) ).
thf(1012,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ F @ E @ D @ C @ B ) @ ( hAPP @ ( c_Sum__Type_OInr @ D @ F ) @ A ) )
= ( hAPP @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Osimps_I6_J) ).
thf(5504,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ F @ E @ D @ C @ B ) @ ( hAPP @ ( c_Sum__Type_OInr @ D @ F ) @ A ) )
= ( hAPP @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(167,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(1972,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)],[167]) ).
thf(319,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ C ) @ B ) ) @ B ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ C @ B ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zmod__equality2) ).
thf(2711,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ C ) @ B ) ) @ B ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ C @ B ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(888,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__imp__not__less) ).
thf(4991,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(998,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(5453,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ E @ D @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ B ) ) @ A ) )
=> ~ ! [F: $i,G: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ F ) @ G ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ E @ E @ D @ F @ G ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(871,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__asym_H) ).
thf(4932,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(87,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(1670,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)],[87]) ).
thf(1059,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Ole__imp__less__or__eq) ).
thf(5685,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
| ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).
thf(399,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ D @ C ) @ B ) @ A ) @ ( hAPP @ B @ A ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__triv) ).
thf(3024,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ D @ C ) @ B ) @ A ) @ ( hAPP @ B @ A ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(703,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(4267,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)],[703]) ).
thf(177,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ B ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__neg__neg__trivial) ).
thf(2030,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ A ) @ B ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(692,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(4225,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)],[692]) ).
thf(723,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(4342,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)],[723]) ).
thf(1005,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(5472,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)],[1005]) ).
thf(1247,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Map_Odom @ D @ B @ A ) ) )
<=> ( ( hAPP @ A @ C )
!= ( c_Option_Ooption_ONone @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_domIff) ).
thf(6467,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Map_Odom @ D @ B @ A ) ) )
=> ( ( hAPP @ A @ C )
!= ( c_Option_Ooption_ONone @ B ) ) )
& ( ( ( hAPP @ A @ C )
!= ( c_Option_Ooption_ONone @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Map_Odom @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1247]) ).
thf(914,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(5083,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)],[914]) ).
thf(1194,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(6245,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)],[1194]) ).
thf(138,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(1881,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)],[138]) ).
thf(1258,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(6511,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)],[1258]) ).
thf(431,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(3156,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)],[431]) ).
thf(618,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(3914,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)],[618]) ).
thf(1036,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(5596,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_New__Random__Sequence_Opos__empty @ D @ C @ B @ A )
= ( c_New__DSequence_Opos__empty @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).
thf(356,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) )
<=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
| ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ D ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ D ) ) ) )
& ( hBOOL @ ( hAPP @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__div_H) ).
thf(2848,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
| ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ D ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ D ) ) ) )
& ( hBOOL @ ( hAPP @ C @ D ) ) ) ) )
& ( ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
| ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ D ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( hAPP @ c_Nat_OSuc @ D ) ) ) )
& ( hBOOL @ ( hAPP @ C @ D ) ) ) )
=> ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(334,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(2760,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)],[334]) ).
thf(1119,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(5917,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)],[1119]) ).
thf(362,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ A ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ A ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ D ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bset_I8_J) ).
thf(2885,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ A ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ A ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ D ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(822,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(4738,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)],[822]) ).
thf(623,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(3928,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)],[623]) ).
thf(6,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 ) )
=> ( ( c_Map_Omap__upds @ F @ D @ B @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ F ) @ E ) @ A ) @ C )
= ( c_Map_Omap__upds @ F @ D @ B @ E @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upds__append__drop) ).
thf(1289,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 ) )
=> ( ( c_Map_Omap__upds @ F @ D @ B @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ F ) @ E ) @ A ) @ C )
= ( c_Map_Omap__upds @ F @ D @ B @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(361,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(2875,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)],[361]) ).
thf(1203,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hAPP @ ( c_Fun_Ooverride__on @ F @ C @ B @ A @ D ) @ E )
= ( hAPP @ A @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_override__on__apply__in) ).
thf(6284,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hAPP @ ( c_Fun_Ooverride__on @ F @ C @ B @ A @ D ) @ E )
= ( hAPP @ A @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1203]) ).
thf(372,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(2924,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)],[372]) ).
thf(511,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(3478,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)],[511]) ).
thf(128,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ B ) @ A ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ ( hAPP @ ( c_List_Oset @ B ) @ A ) )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__card) ).
thf(1839,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ B ) @ A ) )
=> ( ( hAPP @ ( c_Finite__Set_Ocard @ B ) @ ( hAPP @ ( c_List_Oset @ B ) @ A ) )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(1134,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(5981,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)],[1134]) ).
thf(748,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(4424,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)],[748]) ).
thf(667,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__less__dividend) ).
thf(4138,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(574,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(3757,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)],[574]) ).
thf(852,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oinj__on @ D @ ( tc_Option_Ooption @ C ) @ ( c_Map_Omap__add @ D @ C @ B @ A ) @ ( c_Map_Odom @ D @ C @ A ) )
<=> ( c_Fun_Oinj__on @ D @ ( tc_Option_Ooption @ C ) @ A @ ( c_Map_Odom @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__map__add__dom) ).
thf(4851,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Fun_Oinj__on @ D @ ( tc_Option_Ooption @ C ) @ ( c_Map_Omap__add @ D @ C @ B @ A ) @ ( c_Map_Odom @ D @ C @ A ) )
=> ( c_Fun_Oinj__on @ D @ ( tc_Option_Ooption @ C ) @ A @ ( c_Map_Odom @ D @ C @ A ) ) )
& ( ( c_Fun_Oinj__on @ D @ ( tc_Option_Ooption @ C ) @ A @ ( c_Map_Odom @ D @ C @ A ) )
=> ( c_Fun_Oinj__on @ D @ ( tc_Option_Ooption @ C ) @ ( c_Map_Omap__add @ D @ C @ B @ A ) @ ( c_Map_Odom @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(414,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(3092,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)],[414]) ).
thf(1074,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(5749,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)],[1074]) ).
thf(934,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(5179,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)],[934]) ).
thf(346,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ B @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastAtMostSuc__conv) ).
thf(2818,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) ) )
=> ( ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ B @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(411,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(3067,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)],[411]) ).
thf(165,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) @ C ) ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zmult2__eq) ).
thf(1966,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ B ) @ A ) @ C ) ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(1230,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(6408,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1230]) ).
thf(1139,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(6013,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)],[1139]) ).
thf(379,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(2960,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(1083,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(5777,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)],[1083]) ).
thf(874,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(4944,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)],[874]) ).
thf(858,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ E @ D @ C @ B ) @ A )
= ( c_Option_Ooption_ONone @ D ) )
<=> ( ( ( hAPP @ B @ A )
= ( c_Option_Ooption_ONone @ D ) )
& ( ( hAPP @ C @ A )
= ( c_Option_Ooption_ONone @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__None) ).
thf(4873,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( hAPP @ ( c_Map_Omap__add @ E @ D @ C @ B ) @ A )
= ( c_Option_Ooption_ONone @ D ) )
=> ( ( ( hAPP @ B @ A )
= ( c_Option_Ooption_ONone @ D ) )
& ( ( hAPP @ C @ A )
= ( c_Option_Ooption_ONone @ D ) ) ) )
& ( ( ( ( hAPP @ B @ A )
= ( c_Option_Ooption_ONone @ D ) )
& ( ( hAPP @ C @ A )
= ( c_Option_Ooption_ONone @ D ) ) )
=> ( ( hAPP @ ( c_Map_Omap__add @ E @ D @ C @ B ) @ A )
= ( c_Option_Ooption_ONone @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(1129,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(5966,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)],[1129]) ).
thf(502,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(3447,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)],[502]) ).
thf(801,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( c_Map_Odom @ C @ B @ ( c_Map_Omap__of @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__dom__map__of) ).
thf(4646,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( c_Map_Odom @ C @ B @ ( c_Map_Omap__of @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(1116,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(5907,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)],[1116]) ).
thf(329,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ C @ B ) ) @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__distrib) ).
thf(2743,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ C @ B ) ) @ A )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(390,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(2997,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)],[390]) ).
thf(267,axiom,
! [A: $i] :
( ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__is__id) ).
thf(2490,plain,
! [A: $i] :
( ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(472,axiom,
! [A: $i,B: $i,C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ B ) @ ( c_List_Olist_ONil @ C ) ) ) @ ( c_List_Olistrel1 @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__listrel1__Nil) ).
thf(3320,plain,
! [A: $i,B: $i,C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ B ) @ ( c_List_Olist_ONil @ C ) ) ) @ ( c_List_Olistrel1 @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(245,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(2305,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)],[245]) ).
thf(370,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(2919,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)],[370]) ).
thf(756,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(4463,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)],[756]) ).
thf(135,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(1866,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)],[135]) ).
thf(338,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(2775,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)],[338]) ).
thf(341,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ B )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__if) ).
thf(2792,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ A ) @ B )
= ( hAPP @ c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(649,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(4061,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)],[649]) ).
thf(549,axiom,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast0LessThan) ).
thf(3665,plain,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(808,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Natural_Oevaln @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( c_Natural_Oevaln @ E @ D @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__nonstrict) ).
thf(4678,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Natural_Oevaln @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( c_Natural_Oevaln @ E @ D @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(103,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(1721,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)],[103]) ).
thf(211,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(2167,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)],[211]) ).
thf(513,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(3484,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)],[513]) ).
thf(699,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(4250,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)],[699]) ).
thf(773,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(4542,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)],[773]) ).
thf(1137,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(6003,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)],[1137]) ).
thf(131,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(1854,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)],[131]) ).
thf(525,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(3561,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)],[525]) ).
thf(916,axiom,
! [A: $i] :
( A
!= ( hAPP @ c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
thf(5087,plain,
! [A: $i] :
( A
!= ( hAPP @ c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(482,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(3368,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)],[482]) ).
thf(508,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(3465,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)],[508]) ).
thf(907,axiom,
! [A: $i,B: $i] :
( ( c_Option_Ooption_ONone @ B )
!= ( hAPP @ ( c_Option_Ooption_OSome @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Osimps_I2_J) ).
thf(5055,plain,
! [A: $i,B: $i] :
( ( c_Option_Ooption_ONone @ B )
!= ( hAPP @ ( c_Option_Ooption_OSome @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(953,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ E ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ E @ D ) @ E ) @ ( c_Product__Type_Ofst @ E @ D ) ) @ C ) ) )
=> ( ( ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ B )
= ( hAPP @ ( c_Map_Omap__of @ E @ D @ C ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ A ) @ B ) ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ E @ D ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Some__eq__map__of__iff) ).
thf(5272,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ E ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ E @ D ) @ E ) @ ( c_Product__Type_Ofst @ E @ D ) ) @ C ) ) )
=> ( ( ( ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ B )
= ( hAPP @ ( c_Map_Omap__of @ E @ D @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ A ) @ B ) ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ E @ D ) ) @ C ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ A ) @ B ) ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ E @ D ) ) @ C ) ) )
=> ( ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ B )
= ( hAPP @ ( c_Map_Omap__of @ E @ D @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(1253,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(6489,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)],[1253]) ).
thf(145,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ A ) @ B ) )
=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__antisym__nonneg) ).
thf(1903,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ A ) @ B ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(893,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__not__sym) ).
thf(5008,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(283,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(2554,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)],[283]) ).
thf(757,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(4468,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( c_List_Oset @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(810,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(4683,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)],[810]) ).
thf(486,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(3383,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)],[486]) ).
thf(944,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(5228,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)],[944]) ).
thf(540,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(3630,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)],[540]) ).
thf(392,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(3003,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)],[392]) ).
thf(894,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(5010,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)],[894]) ).
thf(770,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(4527,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)],[770]) ).
thf(580,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(3780,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)],[580]) ).
thf(701,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(4261,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)],[701]) ).
thf(1120,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(5922,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)],[1120]) ).
thf(1221,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(6354,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)],[1221]) ).
thf(413,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( 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(3085,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ E @ D ) @ C ) @ B ) @ A )
= C )
=> ( ( hAPP @ C @ B )
= A ) )
& ( ( ( hAPP @ C @ B )
= A )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ E @ D ) @ C ) @ B ) @ A )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(680,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(4182,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)],[680]) ).
thf(683,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 ) )
=> ( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ D ) @ C ) )
=> ( ( c_Map_Odom @ D @ B @ ( c_Map_Omap__of @ D @ B @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ D @ B ) @ C ) @ A ) ) )
= ( hAPP @ ( c_List_Oset @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dom__map__of__zip) ).
thf(4197,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 ) )
=> ( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ D ) @ C ) )
=> ( ( c_Map_Odom @ D @ B @ ( c_Map_Omap__of @ D @ B @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ D @ B ) @ C ) @ A ) ) )
= ( hAPP @ ( c_List_Oset @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(1236,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(6430,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)],[1236]) ).
thf(1061,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(5692,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)],[1061]) ).
thf(898,axiom,
! [A: $i,B: $i] :
( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oneq__le__trans) ).
thf(5023,plain,
! [A: $i,B: $i] :
( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(189,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 @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ A )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ B ) )
=> ( ( ( c_Map_Omap__of @ C @ E @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ C @ E ) @ B ) @ D ) )
= ( c_Map_Omap__of @ C @ E @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ C @ E ) @ B ) @ A ) ) )
=> ( D = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__zip__inject) ).
thf(2066,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 @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ E ) ) @ A )
= ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ C ) @ B ) )
=> ( ( ( c_Map_Omap__of @ C @ E @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ C @ E ) @ B ) @ D ) )
= ( c_Map_Omap__of @ C @ E @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ C @ E ) @ B ) @ A ) ) )
=> ( D = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(941,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(5211,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)],[941]) ).
thf(495,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__dvd__not__less) ).
thf(3420,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(633,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(3978,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)],[633]) ).
thf(961,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInl @ D @ C ) @ B )
= ( hAPP @ ( c_Sum__Type_OInl @ D @ C ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Osimps_I1_J) ).
thf(5304,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( c_Sum__Type_OInl @ D @ C ) @ B )
= ( hAPP @ ( c_Sum__Type_OInl @ D @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( c_Sum__Type_OInl @ D @ C ) @ B )
= ( hAPP @ ( c_Sum__Type_OInl @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(193,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(2081,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)],[193]) ).
thf(253,axiom,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= ( hAPP @ ( c_Product__Type_Osnd @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Divides_Odivmod__nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__nat__def) ).
thf(2399,plain,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= ( hAPP @ ( c_Product__Type_Osnd @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Divides_Odivmod__nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(1251,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( c_List_Oset @ D ) @ ( hAPP @ ( hAPP @ ( c_List_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(6484,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)],[1251]) ).
thf(606,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(3879,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)],[606]) ).
thf(688,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(4214,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)],[688]) ).
thf(829,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(4759,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)],[829]) ).
thf(1270,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(6554,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)],[1270]) ).
thf(97,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__function__closures_I2_J) ).
thf(1706,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(1260,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(6521,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)],[1260]) ).
thf(1202,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Typedef_Otype__definition @ G @ F @ E @ D @ C )
=> ( ( ( hAPP @ E @ B )
= ( hAPP @ E @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_ORep__inject) ).
thf(6277,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Typedef_Otype__definition @ G @ F @ E @ D @ C )
=> ( ( ( ( hAPP @ E @ B )
= ( hAPP @ E @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ E @ B )
= ( hAPP @ E @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1202]) ).
thf(1021,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( c_SetInterval_Oord__class_OgreaterThanLessThan @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__greaterThanLessThan) ).
thf(5549,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( c_SetInterval_Oord__class_OgreaterThanLessThan @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(1028,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(5568,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)],[1028]) ).
thf(72,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(1607,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)],[72]) ).
thf(740,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(4404,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)],[740]) ).
thf(1171,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(6166,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ B ) @ A ) )
| ~ ( hBOOL @ B )
| ( hBOOL @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).
thf(1105,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(5869,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)],[1105]) ).
thf(638,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(3993,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)],[638]) ).
thf(197,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ C ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ C ) ) )
<=> ! [D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ E ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( A
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__neg__lemma) ).
thf(2095,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ C ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ C ) ) )
=> ! [D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ E ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( A
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ E ) ) ) )
& ( ! [D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ E ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( A
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ D ) ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ A ) @ C ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(652,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(4074,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)],[652]) ).
thf(179,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(2036,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)],[179]) ).
thf(13,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(1309,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)],[13]) ).
thf(1064,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(5704,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)],[1064]) ).
thf(870,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(4927,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)],[870]) ).
thf(906,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(5051,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)],[906]) ).
thf(1101,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(5852,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)],[1101]) ).
thf(1148,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(6055,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)],[1148]) ).
thf(815,axiom,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessThan__Suc) ).
thf(4706,plain,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(733,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(4378,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)],[733]) ).
thf(1239,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(6439,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)],[1239]) ).
thf(385,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ G @ ( tc_Option_Ooption @ F ) ) @ E ) @ D ) @ ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ C ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ G @ ( tc_Option_Ooption @ F ) ) @ B ) @ D ) @ ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ A ) ) )
=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__upd__eqD1) ).
thf(2983,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ G @ ( tc_Option_Ooption @ F ) ) @ E ) @ D ) @ ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ C ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ G @ ( tc_Option_Ooption @ F ) ) @ B ) @ D ) @ ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ A ) ) )
=> ( C = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(568,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(3733,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)],[568]) ).
thf(611,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ tc_Nat_Onat @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__greaterThanAtMost) ).
thf(3892,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ tc_Nat_Onat @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__le__nonneg__dividend) ).
thf(1546,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(992,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Map_Omap__add @ F @ E @ D @ ( c_Map_Omap__upds @ F @ E @ C @ B @ A ) )
= ( c_Map_Omap__upds @ F @ E @ ( c_Map_Omap__add @ F @ E @ D @ C ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__upds) ).
thf(5430,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Map_Omap__add @ F @ E @ D @ ( c_Map_Omap__upds @ F @ E @ C @ B @ A ) )
= ( c_Map_Omap__upds @ F @ E @ ( c_Map_Omap__add @ F @ E @ D @ C ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(484,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(3373,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)],[484]) ).
thf(849,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInr @ D @ C ) @ B )
= ( hAPP @ ( c_Sum__Type_OInr @ D @ C ) @ A ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inr__inject) ).
thf(4843,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInr @ D @ C ) @ B )
= ( hAPP @ ( c_Sum__Type_OInr @ D @ C ) @ A ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(478,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(3337,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)],[478]) ).
thf(977,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(5371,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)],[977]) ).
thf(788,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(4597,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)],[788]) ).
thf(434,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(3164,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)],[434]) ).
thf(244,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(2302,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)],[244]) ).
thf(275,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(2517,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)],[275]) ).
thf(1213,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(6326,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)],[1213]) ).
thf(162,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(1957,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)],[162]) ).
thf(759,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(4472,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ B ) @ A )
= B )
=> ( A
= ( c_List_Olist_ONil @ C ) ) )
& ( ( A
= ( c_List_Olist_ONil @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ C ) @ B ) @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(228,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(2233,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)],[228]) ).
thf(607,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(3882,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)],[607]) ).
thf(1126,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(5954,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)],[1126]) ).
thf(376,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( c_Map_Odom @ F @ D @ C ) ) )
=> ( ( c_Map_Omap__add @ F @ D @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ ( tc_Option_Ooption @ D ) ) @ B ) @ E ) @ ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ A ) ) @ C )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ ( tc_Option_Ooption @ D ) ) @ ( c_Map_Omap__add @ F @ D @ B @ C ) ) @ E ) @ ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__upd__left) ).
thf(2951,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( c_Map_Odom @ F @ D @ C ) ) )
=> ( ( c_Map_Omap__add @ F @ D @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ ( tc_Option_Ooption @ D ) ) @ B ) @ E ) @ ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ A ) ) @ C )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ F @ ( tc_Option_Ooption @ D ) ) @ ( c_Map_Omap__add @ F @ D @ B @ C ) ) @ E ) @ ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(913,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(5078,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)],[913]) ).
thf(769,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(4523,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)],[769]) ).
thf(860,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_Map_Oran @ C @ E @ ( c_Map_Orestrict__map @ C @ E @ B @ A ) ) ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ A ) )
& ( ( hAPP @ B @ F )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ran__restrictD) ).
thf(4885,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_Map_Oran @ C @ E @ ( c_Map_Orestrict__map @ C @ E @ B @ A ) ) ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ A ) )
& ( ( hAPP @ B @ F )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(337,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D ) )
= B ) )
& ( ( ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__Cons__number__of) ).
thf(2768,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D ) )
= B ) )
& ( ( ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_List_Onth @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat ) @ D ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(396,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(3015,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)],[396]) ).
thf(613,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(3897,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)],[613]) ).
thf(1206,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(6294,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)],[1206]) ).
thf(1066,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Ole__less) ).
thf(5709,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
| ( B = A ) ) )
& ( ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
| ( B = A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).
thf(958,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(5290,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)],[958]) ).
thf(584,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(3804,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)],[584]) ).
thf(640,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ A ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ A ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ D ) @ C ) ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_aset_I6_J) ).
thf(4024,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ A ) )
=> ! [D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ E ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ A ) )
=> ( D
!= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ F ) @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ D ) @ C ) ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(986,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(5413,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)],[986]) ).
thf(996,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(5441,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)],[996]) ).
thf(1204,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(6287,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ B ) @ ( c_List_Oremdups @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1204]) ).
thf(942,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( B
!= ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ C ) )
<=> ( B
= ( c_Option_Ooption_ONone @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__Some__eq) ).
thf(5215,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( B
!= ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ C ) )
=> ( B
= ( c_Option_Ooption_ONone @ A ) ) )
& ( ( B
= ( c_Option_Ooption_ONone @ A ) )
=> ! [C: $i] :
( B
!= ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(73,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(1610,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)],[73]) ).
thf(715,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(4318,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)],[715]) ).
thf(1024,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(5559,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)],[1024]) ).
thf(302,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_List_Ofoldl @ F @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ B ) @ A ) )
= ( hAPP @ ( c_List_Ofoldl @ F @ E @ D @ ( hAPP @ ( hAPP @ D @ C ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__Cons) ).
thf(2636,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_List_Ofoldl @ F @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ E ) @ B ) @ A ) )
= ( hAPP @ ( c_List_Ofoldl @ F @ E @ D @ ( hAPP @ ( hAPP @ D @ C ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(1264,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(6535,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)],[1264]) ).
thf(669,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(4146,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)],[669]) ).
thf(641,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ C ) )
=> ! [E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ G ) @ B ) )
=> ( E
!= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ G ) @ F ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ E ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ E ) @ C ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_aset_I9_J) ).
thf(4029,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ C ) )
=> ! [E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ F ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ C ) ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Int_Oint ) @ G ) @ B ) )
=> ( E
!= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ G ) @ F ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ E ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ E ) @ C ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(475,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(3328,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)],[475]) ).
thf(879,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(4968,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)],[879]) ).
thf(920,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(5105,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)],[920]) ).
thf(330,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self3) ).
thf(2746,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) @ B )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(1072,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ E ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ E @ D ) @ E ) @ ( c_Product__Type_Ofst @ E @ D ) ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ E @ D ) ) @ C ) ) )
=> ( ( hAPP @ ( c_Map_Omap__of @ E @ D @ C ) @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__is__SomeI) ).
thf(5741,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_List_Odistinct @ E ) @ ( hAPP @ ( hAPP @ ( c_List_Omap @ ( tc_prod @ E @ D ) @ E ) @ ( c_Product__Type_Ofst @ E @ D ) ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) @ ( hAPP @ ( c_List_Oset @ ( tc_prod @ E @ D ) ) @ C ) ) )
=> ( ( hAPP @ ( c_Map_Omap__of @ E @ D @ C ) @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
thf(257,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(2417,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)],[257]) ).
thf(1199,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(6258,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)],[1199]) ).
thf(1287,plain,
! [C: $i,B: $i,A: $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(cnf,[status(esa)],[1286]) ).
thf(1288,plain,
! [C: $i,B: $i,A: $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(lifteq,[status(thm)],[1287]) ).
thf(1033,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(5586,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)],[1033]) ).
thf(473,axiom,
! [A: $i,B: $i] : ( c_Fun_Oinj__on @ B @ ( tc_Option_Ooption @ B ) @ ( c_Option_Ooption_OSome @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__Some) ).
thf(3323,plain,
! [A: $i,B: $i] : ( c_Fun_Oinj__on @ B @ ( tc_Option_Ooption @ B ) @ ( c_Option_Ooption_OSome @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(1104,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(5867,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)],[1104]) ).
thf(320,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osize_I4_J) ).
thf(2714,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Nat_Osize__class_Osize @ ( tc_List_Olist @ C ) ) @ A ) ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(439,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(3196,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)],[439]) ).
thf(979,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ D @ C ) ) @ B ) @ A ) )
<=> ( ( ( A = B )
& ~ ( hBOOL @ ( hAPP @ D @ B ) ) )
| ( ( hBOOL @ ( hAPP @ D @ B ) )
& ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ B ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ D @ C ) ) @ E ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I8_J) ).
thf(5378,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ D @ C ) ) @ B ) @ A ) )
=> ( ( ( A = B )
& ~ ( hBOOL @ ( hAPP @ D @ B ) ) )
| ( ( hBOOL @ ( hAPP @ D @ B ) )
& ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ B ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ D @ C ) ) @ E ) @ A ) ) ) ) ) )
& ( ( ( ( A = B )
& ~ ( hBOOL @ ( hAPP @ D @ B ) ) )
| ( ( hBOOL @ ( hAPP @ D @ B ) )
& ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ B ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ D @ C ) ) @ E ) @ A ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ D @ C ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(642,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Map_Omap__of @ C @ B @ ( c_List_Olist_ONil @ ( tc_prod @ C @ B ) ) ) @ A )
= ( c_Option_Ooption_ONone @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__Cons__code_I1_J) ).
thf(4034,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Map_Omap__of @ C @ B @ ( c_List_Olist_ONil @ ( tc_prod @ C @ B ) ) ) @ A )
= ( c_Option_Ooption_ONone @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(1050,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(5642,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)],[1050]) ).
thf(297,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(2619,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)],[297]) ).
thf(1228,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(6393,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)],[1228]) ).
thf(153,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(1930,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)],[153]) ).
thf(454,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(3244,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)],[454]) ).
thf(206,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) )
<=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ E ) @ A ) )
=> ( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ D ) ) @ E ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__div) ).
thf(2127,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ E ) @ A ) )
=> ( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ D ) ) @ E ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) ) ) ) )
& ( ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ E ) @ A ) )
=> ( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ D ) ) @ E ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(208,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(2159,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)],[208]) ).
thf(664,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__conv) ).
thf(4129,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ D ) ) ) @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult2__lemma__aux2) ).
thf(1550,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ A @ D ) ) ) @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(743,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(4410,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)],[743]) ).
thf(696,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(4239,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)],[696]) ).
thf(1045,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ C ) ) )
=> ( ( B = A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oord__less__eq__trans) ).
thf(5623,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ C ) ) )
=> ( ( B = A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(1243,axiom,
! [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,C: $i] :
( ( ( v_P @ B @ C )
& ( hBOOL @ ( hAPP @ v_b @ C ) ) )
=> ! [D: $i] :
( ( c_Natural_Oevaln @ v_c @ C @ A @ D )
=> ( v_P @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(6452,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,C: $i] :
( ( ( v_P @ B @ C )
& ( hBOOL @ ( hAPP @ v_b @ C ) ) )
=> ! [D: $i] :
( ( c_Natural_Oevaln @ v_c @ C @ A @ D )
=> ( v_P @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1243]) ).
thf(738,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(4395,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)],[738]) ).
thf(651,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ F @ E )
= ( c_Option_Ooption_ONone @ D ) )
=> ( ( c_Map_Omap__comp @ D @ C @ B @ A @ F @ E )
= ( c_Option_Ooption_ONone @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__comp__simps_I1_J) ).
thf(4071,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ F @ E )
= ( c_Option_Ooption_ONone @ D ) )
=> ( ( c_Map_Omap__comp @ D @ C @ B @ A @ F @ E )
= ( c_Option_Ooption_ONone @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(381,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(2966,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)],[381]) ).
thf(1210,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(6316,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)],[1210]) ).
thf(697,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 @ ( c_Map_Omap__of @ E @ C @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ C ) @ D ) @ B ) ) @ A )
= ( c_Option_Ooption_ONone @ C ) )
<=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ ( hAPP @ ( c_List_Oset @ E ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__zip__is__None) ).
thf(4242,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 @ ( c_Map_Omap__of @ E @ C @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ C ) @ D ) @ B ) ) @ A )
= ( c_Option_Ooption_ONone @ C ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ ( hAPP @ ( c_List_Oset @ E ) @ D ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ ( hAPP @ ( c_List_Oset @ E ) @ D ) ) )
=> ( ( hAPP @ ( c_Map_Omap__of @ E @ C @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ C ) @ D ) @ B ) ) @ A )
= ( c_Option_Ooption_ONone @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(1214,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(6329,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)],[1214]) ).
thf(365,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(2898,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)],[365]) ).
thf(492,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(3411,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(265,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(2485,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)],[265]) ).
thf(32,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(1384,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)],[32]) ).
thf(533,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(3605,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)],[533]) ).
thf(235,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ A ) )
= ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__numeral__code_I9_J) ).
thf(2265,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ A ) )
= ( hAPP @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(604,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__less) ).
thf(3869,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(904,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oantisym) ).
thf(5046,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(1082,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(5774,plain,
! [A: $i,B: $i] :
( ( c_Hilbert__Choice_OEps @ B @ ( hAPP @ c_fequal @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).
thf(151,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(1925,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)],[151]) ).
thf(1003,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(5468,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)],[1003]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__zdiffD) ).
thf(1713,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(312,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(2687,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)],[312]) ).
thf(358,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(2864,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)],[358]) ).
thf(1051,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(5645,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)],[1051]) ).
thf(724,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A )
= ( c_SetInterval_Oord__class_OgreaterThanLessThan @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastSucLessThan__greaterThanLessThan) ).
thf(4345,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A )
= ( c_SetInterval_Oord__class_OgreaterThanLessThan @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(237,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(2270,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)],[237]) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zdiv__trivial) ).
thf(1621,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Omod @ tc_Int_Oint @ B @ A ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(691,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(4221,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)],[691]) ).
thf(730,axiom,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ? [B: $i] :
( A
= ( hAPP @ c_Nat_OSuc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not0__implies__Suc) ).
thf(4363,plain,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ? [B: $i] :
( A
= ( hAPP @ c_Nat_OSuc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(615,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(3901,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)],[615]) ).
thf(18,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(1331,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)],[18]) ).
thf(490,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G != F )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ E @ D ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ E @ D ) @ C ) @ G ) @ B ) ) @ F ) @ A )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ E @ D ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ E @ D ) @ C ) @ F ) @ A ) ) @ G ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__twist) ).
thf(3405,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G != F )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ E @ D ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ E @ D ) @ C ) @ G ) @ B ) ) @ F ) @ A )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ E @ D ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ E @ D ) @ C ) @ F ) @ A ) ) @ G ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(994,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(5436,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)],[994]) ).
thf(187,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(2059,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)],[187]) ).
thf(1153,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(6072,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)],[1153]) ).
thf(499,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ E @ D )
= C )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ B @ A ) @ E ) @ D ) @ C )
= E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__idem) ).
thf(3432,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ E @ D )
= C )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ B @ A ) @ E ) @ D ) @ C )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(866,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(4908,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)],[866]) ).
thf(408,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F = E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ D @ C ) @ B ) @ E ) @ A ) @ F )
= A ) )
& ( ( F != E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( 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(3052,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F = E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ D @ C ) @ B ) @ E ) @ A ) @ F )
= A ) )
& ( ( F != E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ D @ C ) @ B ) @ E ) @ A ) @ F )
= ( hAPP @ B @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(212,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(2170,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)],[212]) ).
thf(199,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(2106,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)],[199]) ).
thf(407,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(3047,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)],[407]) ).
thf(677,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(4174,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)],[677]) ).
thf(6687,plain,
( ( v_s2 != v_s0 )
| ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= c_fFalse )
| ( ( hAPP @ ( c_Nat_Osize__class_Osize @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
!= ( hAPP @ v_ba @ v_s2 ) ) ),
inference(paramod_ordered,[status(thm)],[2398,6565]) ).
thf(6722,plain,
( ( v_s2 != v_s0 )
| ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= c_fFalse )
| ( ( c_Nat_Osize__class_Osize @ tc_Nat_Onat )
!= v_ba )
| ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= v_s2 ) ),
inference(simp,[status(thm)],[6687]) ).
thf(384,axiom,
! [A: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatMost @ tc_Nat_Onat ) @ A ) )
= ( hAPP @ c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__atMost) ).
thf(2980,plain,
! [A: $i] :
( ( hAPP @ ( c_Finite__Set_Ocard @ tc_Nat_Onat ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatMost @ tc_Nat_Onat ) @ A ) )
= ( hAPP @ c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(776,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 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ ( hAPP @ ( c_List_Oset @ E ) @ D ) ) )
<=> ? [F: $i] :
( ( hAPP @ ( c_Map_Omap__of @ E @ C @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ C ) @ D ) @ B ) ) @ A )
= ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__zip__is__Some) ).
thf(4552,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 ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ ( hAPP @ ( c_List_Oset @ E ) @ D ) ) )
=> ? [F: $i] :
( ( hAPP @ ( c_Map_Omap__of @ E @ C @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ C ) @ D ) @ B ) ) @ A )
= ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ F ) ) )
& ( ? [F: $i] :
( ( hAPP @ ( c_Map_Omap__of @ E @ C @ ( hAPP @ ( hAPP @ ( c_List_Ozip @ E @ C ) @ D ) @ B ) ) @ A )
= ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ F ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ ( hAPP @ ( c_List_Oset @ E ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(1151,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(6067,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)],[1151]) ).
thf(527,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(3580,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)],[527]) ).
thf(1107,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__reduce) ).
thf(5877,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).
thf(1034,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(5591,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)],[1034]) ).
thf(1174,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Sum__Type_OProjl @ C @ B @ ( hAPP @ ( c_Sum__Type_OInl @ C @ B ) @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Projl_Osimps) ).
thf(6173,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Sum__Type_OProjl @ C @ B @ ( hAPP @ ( c_Sum__Type_OInl @ C @ B ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).
thf(911,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Ole__less__trans) ).
thf(5073,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ C ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(768,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(4520,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)],[768]) ).
thf(704,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Nitpick_Opair__box_Opair__box__size @ F @ E @ D @ C @ ( c_Nitpick_Opair__box_OPairBox @ F @ E @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ D @ B ) ) @ ( hAPP @ C @ A ) ) ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__box_Osize_I1_J) ).
thf(4274,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Nitpick_Opair__box_Opair__box__size @ F @ E @ D @ C @ ( c_Nitpick_Opair__box_OPairBox @ F @ E @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ D @ B ) ) @ ( hAPP @ C @ A ) ) ) @ ( hAPP @ c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(448,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(3227,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)],[448]) ).
thf(814,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(4702,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)],[814]) ).
thf(1019,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(5542,plain,
c_Wellfounded_Owf @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_FunDef_Opair__less,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).
thf(862,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(4891,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)],[862]) ).
thf(1065,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(5707,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)],[1065]) ).
thf(158,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(1945,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)],[158]) ).
thf(1052,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(5649,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)],[1052]) ).
thf(999,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ C @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ C @ A ) ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OWhileFalse) ).
thf(5458,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ C @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ C @ A ) ) @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(220,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(2206,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)],[220]) ).
thf(835,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(4784,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)],[835]) ).
thf(674,axiom,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( c_SetInterval_Oord__class_OatMost @ tc_Nat_Onat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessThan__Suc__atMost) ).
thf(4161,plain,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( c_SetInterval_Oord__class_OatMost @ tc_Nat_Onat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(350,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(2832,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)],[350]) ).
thf(230,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(2238,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)],[230]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__distrib2) ).
thf(1490,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) )
= ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(388,axiom,
c_Wellfounded_Owf @ tc_Nat_Onat @ c_Wellfounded_Opred__nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__pred__nat) ).
thf(2993,plain,
c_Wellfounded_Owf @ tc_Nat_Onat @ c_Wellfounded_Opred__nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(440,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(3200,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)],[440]) ).
thf(120,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(1812,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)],[120]) ).
thf(12995,plain,
$false,
inference(cvc4,[status(thm)],[3021,5509,1586,5561,4094,2072,4899,3167,2921,1982,5733,6527,1554,4560,4447,3962,5422,1337,1718,6669,1823,4101,4450,5593,2109,4824,5136,5896,1633,1995,6544,3830,5654,1315,3863,2544,6448,5028,4728,1818,1295,1686,2250,1750,6022,3317,3549,3417,1618,6199,3108,4711,2282,4326,5348,5614,4592,5501,4714,4037,2117,5141,2104,2231,2622,6162,3858,4311,2808,4515,3813,2495,6458,5297,1939,4807,6441,1544,3910,2114,2837,4623,4973,4408,6031,4479,6194,5120,5814,4418,3044,4110,2316,4856,4247,4980,4762,3848,2195,3120,5565,1756,4575,3332,5755,4870,6665,5257,6416,3616,4279,2627,4058,3253,1988,3826,3414,3481,1954,2844,3577,2042,3895,3717,5192,4047,3236,3545,3502,6381,4124,3730,5874,4963,4665,4610,1482,4941,3370,2972,2046,5977,3766,1914,5393,2763,6268,2548,4496,1576,2020,5195,2173,4607,6182,2405,4775,2869,5797,5342,1887,4386,2957,6707,3820,2916,4415,1871,5188,3653,1279,5640,4984,2466,2571,5765,3221,3938,4348,3425,4896,6552,2735,1985,2039,6039,1660,1298,2667,4151,6547,4692,5284,3689,2755,5910,1860,4334,2217,4778,3776,1826,5150,5130,5160,6662,6332,5279,2703,6240,4862,6455,4617,1479,5480,1398,2929,3951,1773,3231,5617,5231,5744,1922,6010,3099,6253,1892,3385,4194,4358,2049,5127,5802,1890,4179,5604,6310,5323,1347,4368,2520,4632,1641,1815,4460,5076,1963,4390,5091,4793,3602,6025,1778,4302,3866,2533,4253,3268,4008,3258,2829,5792,4595,5974,2222,5433,2616,4578,4297,6419,4820,4847,5032,4134,5360,5663,5892,4329,3887,3393,5013,1911,2782,6523,2236,1334,3527,6410,3983,6189,5946,4050,4815,6176,3621,3973,5804,1677,5311,6559,3923,1960,4115,1581,6157,5259,1283,4810,6204,3851,3986,5738,1928,3189,2861,5101,3505,3036,6221,1394,4040,2639,1600,3559,3492,5695,6474,5572,2508,5059,4055,1377,6110,3712,3211,6103,5328,4628,6210,1696,1863,2954,3899,5406,3265,5697,5070,6388,1708,5487,5540,4925,1730,5174,5961,4604,6529,6560,4216,4893,4323,3301,2204,3303,4753,4589,6020,5751,6015,2574,3720,3635,2164,5167,6058,6250,4557,1768,1868,2061,5281,5049,6343,2428,6550,2541,4989,5956,1487,3682,1274,2673,1387,1900,5630,2805,2596,4397,6565,2969,4091,3752,3989,3069,3233,3884,5470,4499,2606,3134,5085,6496,5507,5396,2890,2414,3250,2015,3889,3471,3286,1560,3948,3618,5534,4187,6060,6168,2211,5769,3271,4295,6303,5826,2464,2758,5391,5983,4140,4849,1365,3810,4155,3314,4757,3499,3556,5690,6556,1951,5460,5779,1624,6143,2609,5551,3144,4746,1836,5113,6392,2547,3763,4104,3727,2741,1392,2228,3647,2112,3931,3408,4680,3799,6324,1328,2709,2694,5362,2724,4840,3650,3941,6128,5475,1402,6215,6075,2245,1350,1936,1592,3784,2498,6413,3782,1541,2157,2840,5609,2115,1851,2990,5270,4668,5345,2895,2577,5635,3218,4429,5428,4233,1672,3704,3632,5889,5373,3746,3205,4219,2268,3440,3060,3018,4817,4653,3141,4860,3000,1292,5651,4167,3714,4545,1842,5865,6501,3294,1493,4320,1942,6428,5620,3596,4421,3010,4750,4406,1584,3032,6630,5932,6573,6256,1810,4648,3428,2551,3671,2085,5905,1644,2125,6097,3126,4068,3743,5900,2566,6346,1715,5369,3005,6349,2285,1776,3611,3656,6134,1539,1382,2487,2598,6433,1552,5498,4482,4934,4540,2006,3628,6450,3760,3967,3247,4135,2766,2697,3920,6186,1627,5245,6514,4288,3173,3856,3306,6070,2402,1895,3841,2662,4308,4572,3147,3454,4148,2634,2749,3903,1857,4644,3225,4567,2208,4081,4212,4889,6486,4966,1563,5415,2963,1286,5209,2089,2645,3422,5198,2909,3807,4919,5524,4470,2717,1548,3686,6492,1374,4453,5241,1278,1906,5679,2729,3707,1727,5808,2556,2033,5762,4613,2253,5855,6084,4438,1747,4393,3289,1301,1595,5882,6228,5979,3111,3274,3343,3158,4998,2727,3925,5065,4801,5831,3458,4975,3599,5720,6234,3547,1833,2225,1884,1615,1389,3736,5940,3283,2514,5612,4709,1701,2398,4381,5350,5799,4946,4485,4978,4127,4413,3340,3436,2706,1765,6123,5997,2474,6372,3170,6048,4537,1503,5185,1786,5039,6403,2293,2308,1371,1312,4112,3695,2738,5331,4236,2935,4822,1733,5148,3123,5735,2425,6248,5158,2319,1356,1675,5556,5580,4716,2311,3101,3352,4337,6572,4228,1282,3238,4620,6217,4699,3468,6340,5222,4586,3710,4300,2871,6216,2493,2987,3038,3551,2422,4305,2906,6197,1589,1933,6321,2299,6289,2802,6154,5795,3586,5972,4773,6460,4107,1969,5267,1307,5035,2025,3027,4569,4911,1630,5335,4277,5466,4993,6568,5410,1820,6376,3456,1667,5563,2824,2182,5367,6087,5816,5584,4882,1557,2314,3668,4833,5439,4264,1909,5599,3034,1325,2785,2593,3451,5885,3583,1344,4726,2664,3861,2842,5838,2075,1396,5254,1699,2171,3838,6151,3674,6504,5326,1694,2051,5094,6270,3917,4827,2931,2288,3241,2797,2022,5849,1477,3325,6100,5667,1496,6180,5403,4209,6736,4158,1805,2069,6476,4741,5424,1304,2994,3161,3981,1509,2684,6170,5358,6202,5812,5661,5463,4331,2054,4426,4207,1948,5538,2914,1662,4136,3936,6540,5886,2652,2471,1277,6191,5952,4177,2629,4688,2846,4355,5807,4812,5003,4986,6132,5570,5607,4864,4366,1566,3129,1753,3872,4630,6146,3376,5822,3640,1598,5294,4360,2397,2192,4673,2588,3754,5171,5944,3659,2732,5484,3462,4200,4517,4641,2175,1780,2821,3209,3608,1484,5018,6384,1711,2569,5767,2092,5418,3063,5912,3202,3823,5030,3774,4351,4781,5277,4164,5731,2165,3818,3691,3114,3334,6037,2700,5015,3722,5753,4549,3828,5543,6313,1658,2322,5001,6436,4982,1679,5638,1579,1285,5450,3041,3095,3853,2500,3107,6337,4959,3970,3388,2511,3117,3007,4671,2675,2056,1358,2247,4488,6479,1353,2279,4748,5504,1972,2711,4991,5453,4932,1670,5685,3024,4267,2030,4225,4342,5472,6467,5083,6245,1881,6511,1272,3156,3914,5596,2848,2760,5917,2885,4738,3928,1289,2875,6284,2924,3478,1839,5981,4424,4138,3757,4851,3092,5749,5179,2818,3067,1966,6408,6013,2960,5777,4944,4873,5966,3447,4646,5907,2743,2997,2490,3320,2305,2919,4463,1866,2775,2792,4061,3665,4678,1721,2167,3484,4250,4542,3104,6003,1854,3561,5087,3368,3465,5055,5272,6489,1903,5008,2554,4468,4683,3383,5228,3630,3003,5010,4527,3780,4261,5922,6354,3085,4182,4197,6430,5692,5023,2066,5211,3420,3978,5304,2081,2399,6484,6181,3879,4214,4759,6554,1706,6521,6277,2162,5549,5568,1607,4404,6166,5869,3993,2095,4074,2036,1309,5704,4927,5051,5852,6055,1280,4706,4378,6439,2983,3733,3892,1546,5430,3373,4843,3337,5371,4597,3164,2302,2517,6326,1957,4472,6563,2233,3882,5954,2951,5078,4523,4885,2768,3015,3897,6294,5709,5290,3804,4024,5413,5441,6287,5215,1610,4318,5559,2636,6535,4146,4029,3328,4968,5105,2746,5741,2417,6258,1288,5586,3323,5867,2714,3196,5378,4034,5642,2619,6393,1930,3244,2127,2159,4129,1550,4410,4239,5623,6452,4395,4071,2966,6316,4242,6329,2898,5806,3411,2485,1384,3605,2265,3869,5046,5774,1925,5468,1713,2687,2864,5645,4345,2270,1621,4221,4363,3901,1331,3405,5436,2059,6072,3432,4908,3052,2170,2106,3047,4174,6722,2980,4552,6067,3580,5877,5591,6173,5073,4520,4274,3227,4702,5542,4891,5707,1945,5649,5458,2206,4784,4161,2832,2238,1490,2993,3200,1812]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SWW328+1 : TPTP v8.1.2. Released v5.2.0.
% 0.10/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n015.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 22:38:23 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.86/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.70/1.35 % [INFO] Parsing done (508ms).
% 2.70/1.37 % [INFO] Running in sequential loop mode.
% 3.07/1.56 % [INFO] eprover registered as external prover.
% 3.07/1.56 % [INFO] cvc4 registered as external prover.
% 3.07/1.57 % [INFO] Scanning for conjecture ...
% 4.55/1.96 % [INFO] Found a conjecture and 5210 axioms. Running axiom selection ...
% 6.79/2.94 % [INFO] Axiom selection finished. Selected 1269 axioms (removed 3941 axioms).
% 8.87/3.55 % [INFO] Problem is first-order (TPTP FOF).
% 8.87/3.59 % [INFO] Type checking passed.
% 8.87/3.59 % [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 ...
% 56.97/14.35 % External prover 'cvc4' found a proof!
% 56.97/14.35 % [INFO] Killing All external provers ...
% 56.97/14.35 % Time passed: 13827ms (effective reasoning time: 12978ms)
% 56.97/14.35 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 56.97/14.35 % Axioms used in derivation (1269): fact_wf__not__refl, fact_Nat_Oadd__0__right, fact_atLeastLessThan__upt, fact_divmod__nat__zero, fact_insertCI, fact_card__image__le, fact_le__imp__diff__is__add, fact_divmod__nat__rel__mult1__eq, fact_evalc_Oequations_I8_J, fact_wf__not__sym, fact_com__det, fact_refl__onD2, fact_wf__inv__image, fact_drop__butlast, fact_zle__refl, fact_converseI, fact_dvd_Oord__less__eq__trans, fact_sum_Osimps_I5_J, fact_le__SucI, fact_notin__set__remove1, fact_drop__Cons__number__of, fact_finite__greaterThanLessThan__int, fact_single__valued__Id__on, fact_nat__gcd_Opinduct, fact_divmod__nat__rel__divmod__nat, fact_append__Nil2, fact_divmod__nat__base, fact_nth__Cons__0, fact_evalc__evaln, fact_nat_Osimps_I3_J, fact_ImageE, fact_dvd_Oless__trans, fact_length__filter__less, fact_lessThan__Suc__atMost, fact_sequence__trans, fact_converse__converse, fact_card__atLeastAtMost, fact_zdvd__zmod, fact_restrict__map__def, fact_fold1Set_Ointros, fact_incr__mult__lemma, fact_map__upds__twist, fact_map__upd__Some__unfold, fact_diff__0__eq__0, fact_fun__upds__append__drop, fact_q__pos__lemma, fact_length__0__conv, fact_map__fst__zip, fact_finite__greaterThanAtMost, fact_pair__lessI2, fact_map__upds__apply__nontin, fact_image__insert, fact_take__drop, fact_zdvd__antisym__nonneg, fact_le__eq__less__or__eq, fact_termination__basic__simps_I5_J, fact_odd__nonzero, fact_map_Osimps_I1_J, fact_trans__less__add1, fact_folding__image__simple__idem_Oin__idem, fact_comp__inj__on__iff, fact_accp_Oequations, fact_notin__set__sublistI, fact_lexord__append__leftI, fact_list__eq__iff__nth__eq, fact_nat__add__left__commute, fact_dvd_Oeq__iff, fact_nth__upt, fact_zdiv__eq__0__iff, fact_zdvd__not__zless, fact_finite__dom__map__of, fact_listrel1E, fact_map__add__SomeD, fact_insert__iff, fact_zip__append1, fact_atLeast__upt, fact_mod__mult2__eq, fact_diff__add__inverse, fact_inj__Some, fact_ran__restrictD, fact_map__add__dom__app__simps_I3_J, fact_fst__eq__Domain, fact_fst__map__pair, fact_nat__less__cases, fact_drop__upt, fact_one__is__add, fact_diff__le__mono2, fact_listrel__Cons1, fact_zip__Nil, fact_dvd_Oorder__trans, fact_zdiff__zmod__right, fact_rtranclD, fact_pred__nat__trancl__eq__le, fact_le__imp__0__less, fact_add__leD1, fact_dvd_Oless__asym_H, fact_divmod__nat__eq, fact_Inr__not__Inl, fact_List_Omap_Ocompositionality, fact_add__less__mono, fact_zadd__commute, fact_mult__0, fact_in__listrel1__converse, fact_zip__Cons__Cons, fact_pair__box_Oinject, fact_map__add__Some__iff, fact_less__imp__le__nat, fact_drop__eq__Nil, fact_sum__case__weak__cong, fact_n__less__m__mult__n, fact_Transitive__Closure_Otrancl__into__trancl, fact_fun__left__comm_Ofold__equality, fact_Suc__times__mod__eq, fact_prod_Orecs, fact_mod__eq, fact_Suc__mono, fact_distinct__remdups, fact_self__append__conv, fact_O__assoc, fact_less__nat__zero__code, fact_nat_Osize_I4_J, fact_equivp__transp, fact_IdI, fact_List_Omap_Ocomp, fact_map__of_Osimps_I2_J, fact_diff__Suc__less, fact_insertI1, fact_triple_Osize_I2_J, fact_comm__monoid__big_Oinfinite, fact_div__nonpos__pos__le0, fact_folding__image__simple_Oeq__fold__g, fact_option_Osimps_I2_J, fact_rtrancl_Ortrancl__refl, fact_diff__diff__cancel, fact_aset_I3_J, fact_gr0__conv__Suc, fact_o__eq__elim, fact_listrelp_Oequations_I2_J, fact_zdvd__mult__cancel, fact_take__upt, fact_SigmaE2, fact_CollectI, fact_Suc__le__mono, fact_dvd_Oless__imp__not__less, fact_div__mod__equality_H, fact_map__butlast, fact_prod__eqI, fact_zero__less__diff, fact_remove1_Osimps_I1_J, fact_acc_Osimps, fact_zmult2__lemma__aux4, fact_map__of__append, fact_nat__add__right__cancel, fact_Some__eq__map__of__iff, fact_inj__on__the__inv__into, fact_div__le__dividend, fact_takeWhile__eq__all__conv, fact_mod__pos__pos__trivial, fact_dvd_Oord__eq__less__trans, fact_mult__le__mono2, help_c__fconj__3, fact_zmod__zdiv__equality, fact_Suc__diff__diff, fact_filter__empty__conv, fact_option_Oexhaust, fact_zmult__div__cancel, fact_comp__inj__on, fact_aset_I10_J, fact_Cons__acc__listrel1I, fact_nat__add__left__cancel__less, fact_int__0__less__1, fact_nth__Cons__Suc, fact_rtrancl__listrel1__if__listrel, help_c__fFalse__1, fact_mod__mult__distrib2, fact_r__into__trancl_H, fact_mod__less, fact_rel__compI, fact_empty__upd__none, fact_atLeastPlusOneLessThan__greaterThanLessThan__int, help_c__fequal__2, fact_mult__eq__self__implies__10, fact_le__neq__implies__less, fact_tranclD2, fact_Projl_Osimps, fact_distinct__zipI2, conj_3, fact_divmod__nat__rel__unique, fact_expand__Suc, fact_map__add__upd, fact_dvd__diffD, fact_sum_Osimps_I3_J, fact_snd__eqD, fact_zle__linear, fact_append__eq__conv__conj, fact_triple__valid__def2, fact_neg__single__def, fact_evaln__Suc, fact_o__apply, fact_aset_I6_J, fact_nat__mod__eq__lemma, fact_take__Suc__conv__app__nth, fact_prod_Osimps_I2_J, fact_rtrancl__converse, fact_div__if, fact_Divides_Omod__div__equality_H, fact_append__is__Nil__conv, fact_fun__left__comm_Ofun__left__comm, fact_distinct_Osimps_I2_J, fact_acyclic__converse, fact_nth__map, fact_finite__atLeastZeroLessThan__int, fact_inj__on__imageI2, fact_acc_OaccI, fact_append1__eq__conv, fact_mod__if, fact_nth__take, fact_div__1, fact_peek__and__def, fact_finite__SigmaI, fact_type__definition_OAbs__inject, fact_inj__on__fun__updI, fact_exE__realizer, fact_zadd__left__mono, fact_exI__realizer, fact_mod__mult__self4, fact_number__of__is__id, fact_listrel__iff__nth, fact_split__paired__All, fact_restrict__map__insert, fact_upt__eq__Nil__conv, fact_less__eq, fact_aset_I4_J, fact_zdvd__mult__div__cancel, fact_dvd__reduce, fact_list_Osimps_I3_J, fact_split__div_H, fact_rev__ImageI, fact_fun__left__comm_Ofold__graph__insertE, fact_upt__conv__Cons, fact_zdiv__zero, fact_map__add__upds, fact_atMost__upto, fact_split__div__lemma, fact_butlast__take, fact_image__Suc__atLeastLessThan, fact_snd__eq__Range, fact_finite__atLeastLessThan, fact_add__eq__if, fact_image__compose, fact_Divides_Otransfer__nat__int__function__closures_I2_J, fact_set__takeWhileD, fact_map__of__is__SomeD, fact_neg__mod__sign, fact_finite__nat__set__iff__bounded__le, fact_nat__dvd__not__less, fact_diff__le__self, fact_listrel_OCons, fact_takeWhile__nth, fact_zdvd__zmod__imp__zdvd, fact_remove1__filter__not, fact_map__upd__nonempty, fact_self__quotient__aux1, fact_mod__pos__neg__trivial, fact_greaterThanAtMost__upt, fact_single__valued__Id, fact_map__add__dom__app__simps_I2_J, fact_nonneg1__imp__zdiv__pos__iff, fact_fold__graph__imp__finite, fact_gr0I, fact_folding__one__idem_Oin__idem, fact_listrel_ONil, fact_fun__left__comm_Ofold__graph__fold, fact_triple_Oinject, fact_single__valued__rel__comp, fact_take__Cons__number__of, fact_inj__on__map__add__dom, fact_list_Osize_I4_J, fact_remove1__idem, fact_divmod__nat__rel__def, fact_upt__Suc, fact_mult__eq__1__iff, help_c__COMBS__1, fact_nat__mult__1__right, fact_override__on__def, fact_finite__trancl, fact_ran__distinct, fact_folding__image__simple__idem_Oinsert__idem, fact_less__eq__nat_Osimps_I1_J, fact_lessI, fact_someI__ex, fact_lessThan__Suc__eq__insert__0, fact_zdiv__zmult1__eq, fact_dvd_Oantisym__conv, fact_pos__imp__zdiv__neg__iff, fact_le__iff__add, fact_wf__measure, fact_diff__commute, fact_neq__if__length__neq, fact_map__add__empty, fact_diff__Suc__eq__diff__pred, fact_less__eq__number__of__int__code, fact_r__comp__rtrancl__eq, fact_less__add__eq__less, fact_wf__irrefl, fact_mod__1, fact_fold1Set_Oequations, fact_fun__upd__same, fact_add__lessD1, fact_add__le__mono1, fact_termination__basic__simps_I4_J, fact_wf__lex__prod, fact_fun__upds__append2__drop, fact_list_Osimps_I2_J, fact_in__measure, fact_rev__image__eqI, fact_zdvd__reduce, fact_folding__one_Oeq__fold, fact_dvd__mult__cancel2, fact_card__image, fact_nat_Oinject, fact_neg__mod__bound, fact_not__add__less2, fact_less__or__eq__imp__le, fact_rtrancl__listrel1__ConsI1, fact_option_Osimps_I3_J, fact_dvd_Oeq__refl, fact_int__div__less__self, fact_div__neg__neg__trivial, fact_Suc__less__SucD, fact_aset_I9_J, fact_zadd__strict__right__mono, fact_congruent2__implies__congruent, fact_zdiv__zadd1__eq, fact_q__neg__lemma, fact_zadd__zless__mono, fact_split__div, fact_dvd_Oord__eq__le__trans, fact_nat__eq__add__iff2, fact_dom__map__of__zip, fact_nth__length__takeWhile, fact_finite__acyclic__wf__converse, fact_domI, fact_mult__less__mono1, fact_com_Osimps_I5_J, fact_Field__converse, fact_ord_OatMost__iff, fact_le__div__geq, fact_Suc__leI, fact_folding__one_Oeq__fold_H, fact_div__nonneg__neg__le0, fact_folding__one__idem_Oeq__fold__idem_H, fact_inj__on__contraD, fact_Id__on__iff, fact_map__comp__empty_I1_J, fact_split__zdiv, fact_pos__imp__zdiv__pos__iff, fact_unique__quotient__lemma__neg, fact_set__map, fact_diff__less, fact_finite__imageD, fact_map__of_Osimps_I1_J, fact_refl__onD, fact_zle__diff1__eq, fact_fun__upd__idem, fact_zip__append2, fact_Suc__n__not__le__n, fact_distinct__takeWhile, fact_distinct__remove1, fact_not__less__less__Suc__eq, fact_vimage__eq, fact_converseE, fact_nat__mult__1, fact_append__listrel1I, fact_comp__cong, fact_diff__is__0__eq_H, fact_elem__set, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J, fact_option_Osize_I3_J, fact_trancl__converse, fact_converse__inv__image, fact_atLeastSucAtMost__greaterThanAtMost, fact_map__add__upd__left, fact_restrict__out, fact_div__mult2__eq, fact_pos__empty__def, fact_Rep__Integ__inject, help_c__fconj__2, fact_reflpE, fact_le__add2, fact_dvd_Oless__imp__neq, fact_minus__nat_Odiff__0, fact_Domain__insert, fact_ord_OgreaterThan__iff, fact_zadd__assoc, fact_pos__zmult__eq__1__iff, fact_distinct__take, fact_map__upd__upds__conv__if, fact_pair__box_Osize_I1_J, fact_fun__upd__comp, fact_lexord__append__left__rightI, fact_less__irrefl__nat, fact_in__set__zipE, fact_Powp__def, fact_length__takeWhile__le, fact_Suc__lessD, fact_sum__eq__0__conv, fact_takeWhile__tail, fact_acc__downwards, fact_not__less0, fact_zdiv__mono1__neg, fact_fst__conv, fact_split__beta, fact_map__Suc__upt, fact_lessThan__Suc, fact_trans__less__add2, fact_gr0__implies__Suc, fact_hoare__valids__def, fact_mod__less__divisor, fact_map__nth, fact_butlast__drop, fact_length__filter__le, fact_start__le__sum, fact_dvd_Oless__asym, fact_drop__1__Cons, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J, fact_finite__greaterThanAtMost__int, fact_add__diff__assoc, fact_mod__nat__def, fact_append__self__conv2, fact_snd__prod__fun, fact_Inr__inject, fact_divmod__nat__step, fact_ran__map__upd, fact_less__Suc__eq__le, fact_nat__diff__split, fact_map__pair__simp, fact_zadd__0, fact_nth__via__drop, fact_insert__code, fact_triples__valid__Suc, help_c__fNot__1, fact_card_Oinsert, fact_add__leD2, fact_butlast__snoc, fact_fun__left__comm_Ofold__insert2, fact_zmod__zdiv__trivial, fact_zmod__simps_I3_J, fact_zmod__zero, fact_one__le__mult__iff, fact_not__less__eq, fact_listrel1__converse, fact_o__eq__dest, fact_times__numeral__code_I5_J, fact_type__definition_ORep, fact_New__DSequence_Oneg__single__def, fact_filter_Osimps_I2_J, fact_fold__def, fact_fun__upd__other, fact_atLeastLessThanPlusOne__atLeastAtMost__int, fact_listrel__rtrancl__refl, fact_map__pair__imageI, fact_less__zeroE, fact_termination__basic__simps_I2_J, fact_RangeI, fact_evaln_OWhileFalse, fact_insert__image, fact_nat_Osimps_I2_J, fact_triple__valid__Suc, fact_nth__append__length, fact_mult__le__cancel1, fact_nat__neq__iff, fact_List_Oset_Osimps_I2_J, fact_nat__1__eq__mult__iff, fact_evaln_Oequations_I7_J, fact_nth__drop_H, fact_diff__mult__distrib2, fact_dvd_Ole__less, fact_drop__map, fact_upt__rec, fact_evaln__nonstrict, fact_fold1__def, fact_distinct_Osimps_I1_J, fact_append__self__conv, conj_2, fact_R__O__Id, fact_dvd_Oord__le__eq__trans, fact_butlast_Osimps_I2_J, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J, fact_nat__add__left__cancel__le, fact_wf__pred__nat, fact_all__set__conv__all__nth, fact_add__mult__distrib2, fact_take__Nil, fact_map__fun__upd, fact_set__ConsD, fact_foldl__Nil, fact_take__eq__Nil, fact_less__not__refl3, fact_DomainI, fact_mod__Suc, fact_div__nat__def, fact_one__less__mult, fact_map__upds__Cons, fact_nat__diff__split__asm, fact_zle__antisym, fact_nat__mult__dvd__cancel__disj, fact_dvd_Oorder__refl, fact_vimageI2, fact_eq__mem, fact_remove1__append, fact_finite__Field, fact_drop__all, fact_takeWhile__append1, fact_nat__size, fact_zmult__assoc, fact_zmult2__lemma__aux3, fact_sum_Osimps_I6_J, fact_some__eq__ex, fact_mult__div__cancel, fact_pair__in__Id__conv, fact_equivp__symp, fact_card__def, fact_insertI2, fact_folding__one__idem_Oidem, fact_le__Suc__eq, fact_bset_I7_J, fact_aset_I5_J, fact_rtrancl__converseI, fact_sum__case__KK, fact_card__greaterThanAtMost, fact_take__butlast, fact_Id__onE, fact_le__diff__conv, fact_finite__insert, fact_RangeE, fact_zmult__1, fact_div__less, fact_insert__absorb2, fact_diff__cancel, fact_finite__atLeastAtMost__int, fact_fun__upd__apply, fact_list_Oinject, fact_split__mod, fact_upt__0, fact_less__Suc__eq__0__disj, fact_drop__take, fact_insert__absorb, fact_eqset__imp__iff, fact_le__add__diff__inverse2, fact_Suc__mult__less__cancel1, fact_less__antisym, fact_Suc__le__eq, fact_take__0, fact_pair__imageI, fact_nat__mult__assoc, fact_upt__eq__Cons__conv, fact_pos__single__def, fact_bset_I4_J, fact_vimageI, fact_same__fstI, fact_nat__mult__le__cancel1, fact_trancl__trans, fact_mult__cancel2, fact_map__of__zip__inject, fact_converse__rtrancl__into__rtrancl, fact_nth__zip, fact_dvd_OatMost__iff, fact_wfP__accp__iff, fact_nth__drop, fact_zmod__zdiv__equality_H, fact_mod__neg__neg__trivial, help_c__fdisj__1, fact_less__imp__Suc__add, fact_atLeastPlusOneAtMost__greaterThanAtMost__int, fact_nat__diff__add__eq2, fact_inj__on__def, fact_inj__on__iff, help_c__fimplies__1, fact_nth__Cons__number__of, fact_lexord__Nil__right, fact_less__add__Suc2, fact_irrefl__def, fact_mod__le__divisor, fact_in__set__sublistD, fact_nat__mult__eq__cancel1, help_c__fequal__1, fact_Suc__pred_H, fact_dvd_Oless__not__sym, fact_zdiv__zmod__equality2, fact_finite__nat__set__iff__bounded, fact_divmod__int__rel__div__eq, fact_split__zmod, fact_rtrancl__trans, fact_less__eq__Suc__le, fact_evalc__WHILE__case, fact_append__eq__append__conv__if, fact_div__le__mono2, fact_accp__wfPD, fact_distinct__zipI1, fact_rp__inv__image__rp, fact_Pair__fst__snd__eq, fact_div__mult__self1__is__m, fact_insert__commute, fact_fun__upd__triv, fact_less__imp__diff__less, fact_trancl__converseD, fact_snd__comp__map__pair, fact_wf__converse__trancl, fact_map__pair_Ocompositionality, fact_folding__image__simple_Oinsert, fact_override__on__apply__in, fact_foldl__Cons, fact_map__of__Cons__code_I2_J, fact_pair__box_Orecs, fact_pred__comp_Ointros, fact_zmult__commute, fact_finite__imageI, fact_zdiv__mono2__neg, fact_map__upds__append1, fact_dvd__mult__cancel1, fact_not__Cons__self, fact_mlex__leq, fact_dvd__diffD1, fact_vimage__code, fact_listrel__Cons2, fact_not__Some__eq, fact_nth__append, fact_DomainP_Ointros, fact_finite__set, fact_total__on__def, fact_nat__mult__div__cancel__disj, fact_accp__downward, fact_diffs0__imp__equal, fact_SigmaE, fact_map__upd__triv, fact_distinct__card, fact_nat__mult__less__cancel1, fact_listrel__reflcl__if__listrel1, fact_equivp__def, fact_remove1_Osimps_I2_J, fact_pos__mod__sign, fact_neg__imp__zdiv__neg__iff, fact_linorder__neqE__nat, fact_mult__less__mono2, fact_card__ge__0__finite, fact_map__of__zip__map, fact_in__set__butlast__appendI, fact_Nil__is__map__conv, fact_diff__diff__left, fact_fun__upd__idem__iff, fact_listrel__Nil1, fact_less__number__of__int__code, fact_conjI__realizer, fact_ex__nat__less, fact_r__r__into__trancl, fact_dvd_OatLeast__iff, fact_in__set__butlastD, fact_append__same__eq, fact_add__is__1, fact_Range__Id__on, fact_eq__Nil__appendI, fact_diff__Suc__diff__eq2, fact_upt__add__eq__append, fact_listrel1__eq__len, fact_ord_OlessThan__iff, fact_map__of__zip__is__None, fact_diff__add__assoc2, fact_image__Suc__atLeastAtMost, fact_rtrancl__into__trancl2, fact_divmod__nat__def, fact_divmod__nat__rel__mult2__eq, fact_Pair__inject, fact_mod__geq, fact_div__pos__pos__trivial, fact_zadd__left__commute, fact_card__insert__if, fact_in__set__takeD, help_c__fdisj__2, fact_domIff, fact_card__length, fact_zmod__eq__dvd__iff, fact_fun__left__comm_Ofold__fun__comm, fact_unique__quotient__lemma, fact_not__None__eq, fact_divmod__nat__div__mod, fact_diff__diff__right, fact_wf__acc__iff, fact_Range__iff, help_c__fconj__1, fact_dvd_Oneq__le__trans, fact_pos__mod__bound, fact_distinct__butlast, fact_atMost__Suc, fact_Suc__mult__cancel1, fact_CollectE, fact_mem__Collect__eq, fact_Suc__le__lessD, fact_acyclic__insert, fact_not__add__less1, fact_div__add1__eq, fact_Nitpick_Orefl_H__def, fact_zdiv__zmult2__eq, fact_append__Nil, fact_neg__mod__conj, fact_zip__eq__conv, fact_fold__graph_OinsertI, fact_zless__le, fact_nat__le__add__iff2, fact_Suc__inject, fact_less__diff__conv, fact_ext, fact_nth__map__upt, fact_drop__Cons_H, help_c__fNot__2, fact_zmult2__lemma__aux2, fact_zless__imp__add1__zle, fact_semilattice__big_OF__eq, fact_RangeP_Ointros, fact_length__remove1, fact_lexord__cons__cons, fact_single__valued__confluent, fact_map__upds__Nil1, fact_length__append, fact_nth__mem, fact_zle__trans, fact_acc__wfD, fact_eq__diff__iff, fact_filter__remove1, fact_finite__atLeastAtMost, fact_Suc__neq__Zero, fact_zdiv__mono1, fact_snoc__listrel1__snoc__iff, fact_diff__less__Suc, fact_add__eq__self__zero, fact_evaln__WHILE__case, fact_map__upd__eqD1, fact_mult__le__cancel2, fact_map__of__is__SomeI, fact_dvd_Oless__imp__le, fact_prod__fun__imageE, fact_rtrancl__trancl__absorb, fact_nat__less__add__iff1, fact_converse__iff, fact_finite__atMost, fact_trancl__range, fact_map__of__Cons__code_I1_J, fact_nat__add__left__cancel, fact_Suc__diff__1, fact_mult__is__0, fact_map__comp__empty_I2_J, fact_append__Cons, fact_wf__in__rel, fact_zmod__eq__0__iff, fact_equivp__reflp, fact_takeWhile__eq__take, fact_someI, fact_take__append, fact_map__pair_Ocomp, fact_filter__append, fact_zmod__le__nonneg__dividend, fact_div__less__dividend, fact_in__set__remove1, fact_fun__upd__upd, fact_mult__le__mono, fact_Collect__def, fact_dvd__imp__le, fact_nat__mult__dvd__cancel1, fact_triple_Osimps_I2_J, fact_in__set__dropD, fact_map__comp__None__iff, fact_n__not__Suc__n, fact_nat__le__linear, fact_take__Suc__Cons, fact_Id__on__eqI, fact_listrel1I2, fact_acyclic__def, fact_drop__drop, fact_filter__id__conv, fact_trancl__into__rtrancl, fact_rtrancl__eq__or__trancl, fact_listrel__eq__len, fact_Inl__inject, fact_lexord__append__leftD, fact_wf__eq__minimal, fact_wf__iff__no__infinite__down__chain, fact_lexord__Nil__left, fact_mlex__less, fact_aset_I8_J, fact_card__distinct, fact_trancl_Or__into__trancl, fact_all__nat__less, fact_zdiv__zmod__equality, fact_dvd__1__left, fact_add__mult__distrib, fact_restrict__in, 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fact_int__0__neq__1, fact_ord_OgreaterThanLessThan__iff, fact_zdiff__zmult__distrib, fact_option_Osize_I4_J, fact_inj__on__iff__eq__card, fact_ord_OatLeastLessThan__iff, fact_Suc__eq__plus1__left, fact_Zero__not__Suc, fact_SigmaI, fact_zdiff__zmod__left, fact_mem__Sigma__iff, fact_acc__downwards__aux, fact_weak__map__of__SomeI, fact_wf__insert, fact_bset_I6_J, fact_converseD, fact_Range__def, fact_pigeonhole, fact_split__def, fact_diff__less__mono, fact_finite__acyclic__wf, fact_Suc__leD, fact_evalc_OWhileTrue, fact_div__geq, fact_sum_Osimps_I4_J, fact_finite__Range, fact_the__inv__into__comp, fact_mult__Suc, fact_less__eq__Suc__le__raw, fact_append__eq__appendI, fact_DomainE, fact_left__add__mult__distrib, fact_mod__mult__self3, fact_zadd__zmult__distrib2, fact_sum_Osimps_I1_J, fact_zmod__self, fact_map__snd__zip, fact_map__add__dom__app__simps_I1_J, fact_trancl__rtrancl__absorb, fact_takeWhile_Osimps_I1_J, fact_New__DSequence_Opos__empty__def, fact_card__atMost, fact_less__trans__Suc, fact_trancl__into__trancl2, fact_Nat_Odiff__diff__eq, fact_le__refl, fact_nat__add__assoc, fact_divmod__nat__rel__add1__eq, fact_split__pos__lemma, fact_sublist__nil, fact_less__not__refl2, fact_le__add1, fact_mult__cancel1, fact_list_Osize_I3_J, fact_single__valued__def, fact_trans__le__add2, fact_zdvd__mono, fact_accp_Osimps, fact_set__zip__leftD, fact_zmod__zmult1__eq, fact_atLeastSucLessThan__greaterThanLessThan, fact_not0__implies__Suc, fact_the__sym__eq__trivial, fact_atLeast0LessThan, conj_1, fact_One__nat__def, fact_length__butlast, fact_fst__def, fact_mod__induct__0, fact_mod__eq__0__iff, fact_map__is__Nil__conv, fact_wf__trancl, fact_drop__zip, fact_le__imp__less__Suc, fact_mod__less__eq__dividend, fact_o__eq__dest__lhs, fact_rtrancl__listrel1__eq__len, fact_upt__rec__number__of, fact_in__set__conv__nth, fact_comp__equivI, fact_pred__comp_Oequations, fact_comm__monoid__big_OF__eq, fact_K__record__comp, fact_insert__fold1SetE, fact_Suc__mult__le__cancel1, fact_listrel__Nil2, fact_less__add__Suc1, fact_all__nat__less__eq, fact_listrelp_Oequations_I1_J, fact_tfl__some, fact_o__def, fact_append__eq__Cons__conv, fact_div__mult__self__is__m, fact_append__assoc, fact_take__all, fact_listrel__rtrancl__eq__rtrancl__listrel1, fact_finite__Domain, fact_in__lex__prod, fact_zip__same, fact_add__is__0, fact_neg__imp__zdiv__nonneg__iff, fact_nat__diff__add__eq1, fact_termination__basic__simps_I3_J, fact_remove1__commute, fact_SigmaD2, fact_trancl__unfold__right, fact_pos__mod__conj, fact_Domain__Id__on, fact_distinct__map, fact_wf__no__infinite__down__chainE, fact_drop__0, fact_length__drop, fact_elem__le__sum, fact_nth__append__length__plus, fact_nat__eq__add__iff1, fact_dvd__mult__cancel, fact_in__rel__def, fact_mult__le__mono1, fact_diff__self__eq__0, fact_atLeastAtMostSuc__conv, fact_length__upt, fact_div__neg__pos__less0, fact_diff__add__0, fact_the__inv__into__onto, fact_Zero__neq__Suc, fact_drop__Nil, fact_evaln_OWhileTrue, fact_congruentD, fact_diff__cancel2, fact_map__comp__Some__iff, fact_surjective__pairing, fact_CollectD, fact_nat__less__add__iff2, fact_less__imp__add__positive, fact_Pair__eq, fact_Projr_Osimps, fact_Suc__eq__plus1, fact_map__add__assoc, fact_image__iff, fact_rtrancl_Ortrancl__into__rtrancl, fact_map__map, fact_map__of__eq__None__iff, fact_sublist__upt__eq__take, fact_Divides_Otransfer__nat__int__function__closures_I1_J, fact_self__quotient__aux2, fact_refl__on__converse, fact_distinct__filter, fact_split__conv, fact_listrelp_OCons, fact_congruent2D, fact_nat__mult__div__cancel1, fact_Suc__diff__le, fact_IdE, fact_atLeastAtMost__upt, fact_split__weak__cong, fact_listrel1I1, fact_zmult2__lemma__aux1, fact_distinct__conv__nth, fact_ord_OgreaterThanAtMost__iff, fact_le0, fact_le__diff__conv2, fact_zmult__zless__mono2, fact_plus__numeral__code_I9_J, fact_sum__case__inject, fact_fun__upd__twist, fact_finite_OinsertI, fact_nat__mult__eq__1__iff, fact_not__less__eq__eq, fact_n__less__n__mult__m, fact_less__not__refl, fact_zmod__zmult2__eq, fact_drop__append, fact_fun__upd__def, fact_finite__lessThan, fact_prod__case__beta, fact_ex__least__nat__less, fact_Domain__converse, fact_the__inv__into__f__eq, fact_card_Oeq__fold__g, fact_dvd_Oantisym, fact_f__the__inv__into__f, fact_le__trans, fact_diff__Suc__diff__eq1, fact_wf__mlex, fact_snd__conv, fact_Suc__pred, fact_equalityCE, fact_r__into__rtrancl, fact_nat__dvd__1__iff__1, fact_card__lessThan, fact_option_Oinject, fact_gr__implies__not0, fact_dvd_Ole__neq__trans, fact_fun__left__comm_Ofold__graph__determ, help_c__COMBK__1, fact_le__mod__geq, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J, fact_rtrancl__into__trancl1, fact_dvd__antisym, fact_insert__dom, fact_append__take__drop__id, fact_less__Suc__eq, fact_wf__same__fst, fact_add__leE, fact_fst__eqD, fact_fun__left__comm_Ofold__insert, fact_diff__Suc__1, fact_bset_I8_J, fact_Not__Domain__rtrancl, 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fact_nat__mult__commute, fact_divmod__int__rel__mod__eq, fact_card_Oneutral, fact_add1__zle__eq, fact_takeWhile_Osimps_I2_J, fact_eq__imp__le, fact_lexord__linear, help_c__fTrue__1, fact_card__atLeastLessThan, fact_map__add__find__right, fact_trancl__unfold__left, fact_impossible__Cons, fact_Range__insert, fact_diff__add__inverse2, fact_in__inv__image, fact_plus__nat_Oadd__0, fact_set__upt, fact_map__upds__Nil2, fact_Nil__is__append__conv, fact_append__eq__append__conv2, fact_listrel__rtrancl__trans, fact_nat_Osize_I3_J, fact_insertE, fact_dvd_Oless__le, conj_4, fact_finite__greaterThanLessThan, fact_some__sym__eq__trivial, fact_type__definition_ORep__inject, fact_exE__some, fact_le__SucE, fact_acyclicI, fact_aset_I7_J, fact_le__less__Suc__eq, fact_inj__onD, fact_div__le__mono, fact_take__1__Cons, fact_zdvd__period, fact_map__eq__imp__length__eq, fact_le__antisym, fact_zless__linear, fact_trans__le__add1, fact_map__of__SomeD, fact_upt__conv__Nil, fact_map__comp__map, 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fact_wf__asym, conj_5, fact_mod__lemma, fact_nth__eq__iff__index__eq, fact_SigmaD1, fact_wf__iff__acyclic__if__finite, fact_triple_Orecs, fact_le__add__diff__inverse, fact_butlast__conv__take, fact_evaln_Oequations_I8_J, fact_less__Suc0, fact_div__mult1__eq, fact_add__diff__inverse, fact_finite__atLeastLessThan__int, fact_mem__def, fact_diff__Suc__Suc, fact_rtrancl__converseD, fact_distinct__drop, fact_vimageD, fact_atLeastLessThanSuc__atLeastAtMost, fact_Cons__listrel1__Cons, fact_take__zip, fact_rtrancl__trancl__trancl, fact_filter_Osimps_I1_J, fact_refl__on__Id__on, fact_bset_I10_J, fact_map__of__zip__is__Some, fact_equiv__comp__eq, fact_dvd_Ole__imp__less__or__eq, fact_nat__less__le, fact_map__add__None, fact_type__definition_ORep__inverse, fact_zip__map__fst__snd, fact_le__square, fact_Id__O__R, fact_wf__pair__less, fact_mult__eq__if, fact_take__map, fact_length__greater__0__conv, fact_card__insert__le, fact_zadd__zmult__distrib, fact_rel__compE, fact_less__SucE, fact_le__cube, fact_zless__add1__eq, fact_map__pair__compose, fact_drop__Suc__Cons, fact_add__less__mono1, fact_finite__converse, fact_identity__equivp, fact_o__assoc, fact_sublist__singleton, fact_map__of__zip__upd, fact_less__diff__iff, fact_restrict__map__empty, fact_odd__less__0, fact_dvd_Oless__imp__not__eq2, fact_not__acc__down, fact_map__eq__conv, fact_zdvd__iff__zmod__eq__0__number__of, fact_folding__image__simple__idem_Oidem, fact_evalc_Oequations_I7_J, fact_atLeast0AtMost, fact_converse__Id, fact_map_Osimps_I2_J, fact_eval__eq, fact_Image__Id, fact_zdiv__mono2__neg__lemma, fact_map__of__map__restrict, fact_vimage__compose, fact_Inl__not__Inr, fact_lexord__append__rightI, fact_distinct__sublistI, fact_ord_OatLeast__iff, fact_imageI, fact_distinct__upt, fact_self__append__conv2, fact_converse__rel__comp, fact_add__Suc__shift, fact_map__of__eq__dom, fact_less__SucI, fact_Suc__not__Zero, fact_butlast_Osimps_I1_J, fact_same__append__eq, fact_Suc__lessI, fact_add__Suc__right, fact_less__bin__lemma, help_c__fdisj__3, fact_mod__mult__distrib, fact_trancl__domain, fact_lexord__irreflexive, fact_listrelp_ONil, fact_evaln__evalc, fact_single__valuedD
% 56.97/14.35 % No. of inferences in proof: 2597
% 56.97/14.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 13827 ms resp. 12978 ms w/o parsing
% 58.36/14.93 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 58.36/14.94 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------